Cluster analysis for JM article
Kenneth Benoit
Load the data
library("dplyr", warn.conflicts = FALSE)
unzip("job descriptors.csv.zip", exdir = "~/tmp/")
df_raw <- data.table::fread("~/tmp/job descriptors.csv", data.table = FALSE)Group by worker ID (mem_id):
df_grouped <- df_raw %>%
group_by(mem_id) %>%
summarize(n_bids = n(), n_unique_job_title = length(unique(job_title)),
job_title = head(job_title, 1))`summarise()` ungrouping output (override with `.groups` argument)# sort by descending number of bids
df_grouped <- arrange(df_grouped, desc(n_bids))
# verify that job_title is the same for each mem_id
stopifnot(all(select(df_grouped, n_unique_job_title) == 1))
# remove some intermediate variables
df_grouped <- select(df_grouped, -n_unique_job_title)So we can see here that every unique mem_id (worker) had only one job title. (Good for us!)
Characterize the data
Most workers had only a single bid. The median number was 3.
summary(df_grouped$n_bids) Min. 1st Qu. Median Mean 3rd Qu. Max.
1.00 1.00 3.00 22.37 11.00 14273.00 We can see the skew:
library("ggplot2")Want to understand how all the pieces fit together? Read R for Data Science: https://r4ds.had.co.nz/ggplot(df_grouped, aes(x = n_bids)) +
scale_x_continuous(breaks=c(1, 2, 5, 10, 25, 50, 100, 500, 1000, 10000),
trans = "log") +
geom_histogram(aes(y = ..density..),
binwidth = .5, colour = "black", fill = "white") +
geom_density(alpha = .2, fill = "#FF6655", colour = "blue")
So, four lunatics have apparently submitted more than 10,000 bids each:
# top 10 list
head(df_grouped, 10)Also, six bidders had no description:
filter(df_grouped, is.na(job_title))Characterize the descriptions
library("quanteda", warn.conflicts = FALSE)
job_corpus <- filter(df_grouped, !is.na(job_title)) %>%
corpus(text_field = "job_title", docid_field = "mem_id")
job_tokens <- tokens(job_corpus, remove_punct = TRUE, remove_symbols = TRUE,
padding = TRUE) %>%
tokens_tolower()
# top terms
job_tokens %>%
tokens_remove(c("", stopwords("en"))) %>%
dfm() %>%
textstat_frequency(n = 30)We can refine this by finding some multi-word expressions:
job_mwe <- job_tokens %>%
tokens_remove(stopwords("en"), padding = TRUE) %>%
tokens_wordstem(language = "en") %>%
textstat_collocations()
head(job_mwe, 30)Now let’s turn the top 100 multi-word bigrams into single tokens:
job_tokens_mwe <- job_tokens %>%
tokens_remove(stopwords("en"), padding = TRUE) %>%
tokens_wordstem(language = "en") %>%
tokens_compound(head(job_mwe, 100), concatenator = " ") %>%
tokens_compound(phrase("word press"), concatenator = " ") %>%
tokens_remove("")
job_dfmat <- dfm(job_tokens_mwe)
textstat_frequency(job_dfmat, n = 30)Some of these occur very infrequently:
textstat_frequency(job_dfmat) %>%
ggplot(aes(x = frequency)) +
scale_x_continuous(breaks = 10^(0:6),
trans = "log") +
geom_histogram(aes(y = ..density..),
binwidth = .5, colour = "black", fill = "white") +
geom_density(alpha = .2, fill = "#FF6655", colour = "blue")
Identify some clusters
job_dfmat_trimmed <- dfm_trim(job_dfmat, min_termfreq = 10,
min_docfreq = .01, docfreq_type = "prop",
verbose = TRUE)Removing features occurring:
- fewer than 10 times: 18,870
- in fewer than 2159.74 documents: 21,612
Total features removed: 21,612 (99.7%).print(job_dfmat_trimmed, 0, 0)Document-feature matrix of: 215,974 documents, 55 features (97.2% sparse) and 1 docvar.library("ClusterR")Loading required package: gtoolsOptimal_Clusters_KMeans(as.matrix(job_dfmat_trimmed), 10, criterion = "AIC") [1] 342019.5 322244.6 313601.9 300477.2 293531.6 275992.6 281111.3 270818.3 270928.3 268875.4
attr(,"class")
[1] "k-means clustering"
From this plot, it looks like k = 8 might be the optimal number of clusters, but since there are 7 job description fields, we will fit 7.
job_kmeans <- KMeans_arma(as.matrix(job_dfmat_trimmed), clusters = 7)
Warning messages:
1: In readChar(file, size, TRUE) : truncating string with embedded nuls
2: In readChar(file, size, TRUE) : truncating string with embedded nuls
3: In readChar(file, size, TRUE) : truncating string with embedded nulsjob_corpus$cluster <- job_dfmat$cluster <-
predict_KMeans(as.matrix(job_dfmat_trimmed), job_kmeans)Now we can look at the top terms in each cluster:
textstat_frequency(job_dfmat, n = 10, groups = "cluster") %>%
as.data.frame() %>%
select(-rank)We could say this:
LDA on job_title, k = 7
I used the stm package for this, which implements a faster and more modern version of LDA than the older packages. If you want to cite what it is, just call it “LDA”. (See https://www.structuraltopicmodel.com/ for details, citations, etc.)
Here I trimmed the (very) sparse dfm a bit less agressively. The min_docfreq = .001 means that a term had to occur in 1/1000 of the documents to be retained, or in this case, at least 216 documents (since there are 215,974 documents).
job_dfmat_trimmed2 <- dfm_trim(job_dfmat, min_termfreq = 10, Warning messages:
1: In readChar(file, size, TRUE) : truncating string with embedded nuls
2: In readChar(file, size, TRUE) : truncating string with embedded nuls
3: In readChar(file, size, TRUE) : truncating string with embedded nuls min_docfreq = .001, docfreq_type = "prop",
verbose = TRUE)Removing features occurring:
- fewer than 10 times: 18,870
- in fewer than 215.974 documents: 21,201
Total features removed: 21,201 (97.8%).# remove the empty documents
job_dfmat_trimmed2 <- dfm_subset(job_dfmat_trimmed2, ntoken(job_dfmat_trimmed2) > 0)
print(job_dfmat_trimmed2, 0, 0)Document-feature matrix of: 209,294 documents, 466 features (99.4% sparse) and 2 docvars.Now we can fit a topic model. Since there are seven service categories, we will start by seeing how \(k = 7\) works. Note: the categories are: 1. Design 2. Writing & Translation
3. Video, Photo, & Audio
4. Business Support
5. Social Media, Sales, & Marketing
6. Software Development 7. Web Development
library("stm")stm v1.3.5 successfully loaded. See ?stm for help.
Papers, resources, and other materials at structuraltopicmodel.comtmod <- stm(job_dfmat_trimmed2, K = 7, emtol = 1e-05)Beginning Spectral Initialization
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Topic 1: develop, consult, wordpress, expert, websit
Topic 2: freelanc, seo, editor, profession, virtual assist
Topic 3: writer, data entri, account, engin, director
Topic 4: web design, translat, market, sale, joomla
Topic 5: graphic design, web, illustr, administr, graphic
Topic 6: design, web develop, photograph, research, busi
Topic 7: manag, php, copywrit, artist, proofread
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Topic 4: web design, translat, market, sale, product
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Topic 4: web design, translat, market, sale, product
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Topic 1: develop, expert, consult, wordpress, websit
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Topic 1: develop, expert, consult, wordpress, websit
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Topic 3: writer, data entri, account, engin, director
Topic 4: web design, translat, market, sale, product
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Topic 3: writer, data entri, account, engin, director
Topic 4: web design, translat, market, sale, product
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Topic 1: develop, expert, consult, wordpress, websit
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Topic 3: writer, data entri, account, engin, director
Topic 4: web design, translat, market, sale, product
Topic 5: graphic design, web, illustr, administr, graphic
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Model Converged labelTopics(tmod)Topic 1 Top Words:
Highest Prob: develop, expert, consult, wordpress, websit, social media, softwar develop
FREX: consult, websit, develop, softwar develop, softwar engin, android, freelanc writer
Lift: consult, android, drupal, game, market consult, softwar develop, softwar engin
Score: develop, consult, wordpress, expert, quantiti, websit, magento
Topic 2 Top Words:
Highest Prob: freelanc, seo, editor, profession, virtual assist, specialist, english
FREX: english, teacher, freelanc, interpret, virtual assist, editor, articl writer
Lift: en, french, interpret, italian, link build, teacher, english
Score: interpret, freelanc, english, editor, seo, profession, virtual assist
Topic 3 Top Words:
Highest Prob: writer, data entri, account, engin, director, senior, write
FREX: engin, director, write, system, comput, financi, project
Lift: advis, articl write, busi analyst, can, ceo, charter, civil
Score: writer, civil, data entri, account, engin, write, director
Topic 4 Top Words:
Highest Prob: web design, translat, market, sale, product, journalist, architect
FREX: sale, market, busi develop, experi, architect, translat, owner
Lift: sale, market, busi develop, lawyer, onlin market, promot, surveyor
Score: translat, web design, surveyor, market, sale, admin, architect
Topic 5 Top Words:
Highest Prob: graphic design, web, illustr, administr, graphic, programm, logo design
FREX: graphic design, illustr, student, logo design, programm, book, art
Lift: art, art director, book, illustr, graphic design, 3d model, cartoonist
Score: graphic design, illustr, web, concept artist, administr, graphic, logo design
Topic 6 Top Words:
Highest Prob: design, web develop, photograph, research, busi, content writer, 3d
FREX: design, photograph, web develop, logo, sound, brand, content writer
Lift: web develop, photograph, brand, brochur, camera oper, card, cutter
Score: design, web develop, cutter, photograph, research, busi, 3d
Topic 7 Top Words:
Highest Prob: manag, php, copywrit, artist, proofread, creativ, project manag
FREX: creativ, copywrit, respons, css, ecommerc, bookkeep, html5
Lift: javascript, technologist, ajax, amazon, respons, ebay, ecommerc
Score: php, manag, copywrit, artist, technologist, proofread, creativ plot(tmod, n = 5)
# put the topics back into the dfm
theta <- as.data.frame(tmod$theta)
names(theta) <- paste0("theta_", seq_len(ncol(theta)))
# add topic prevalence estimates, add mem_id
docvars(job_dfmat_trimmed2) <-
data.frame(cluster = job_dfmat_trimmed2$cluster,
theta, max_topic = max.col(theta),
mem_id = as.integer(docnames(job_dfmat_trimmed2)))
# join them back to the original df
df_grouped2 <- left_join(df_grouped, docvars(job_dfmat_trimmed2), by = "mem_id")
# join the grouped info back to the original long df
df_raw2 <- left_join(df_raw, select(df_grouped2, -n_bids, -job_title), by = "mem_id")
# write the output
data.table::fwrite(df_raw2, "~/tmp/job descriptors LDA.csv")
Written 29.6% of 4832204 rows in 2 secs using 1 thread. maxBuffUsed=27%. ETA 4 secs.
Written 50.0% of 4832204 rows in 3 secs using 1 thread. maxBuffUsed=27%. ETA 3 secs.
Written 70.7% of 4832204 rows in 4 secs using 1 thread. maxBuffUsed=30%. ETA 1 secs.
Written 90.8% of 4832204 rows in 5 secs using 1 thread. maxBuffUsed=30%. ETA 0 secs.
Verifying the number of topics
job_stm_trimmed2 <- convert(job_dfmat_trimmed2, to = "stm")
k_search <- searchK(documents = job_stm_trimmed2$documents,
vocab = job_stm_trimmed2$vocab,
K = c(6, 7, 8, 9, 10, 12, 15, 20), emtol = 1e-04)Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
......
Recovering initialization...
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Initialization complete.
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Completed E-Step (37 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -5.767)
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Completing Iteration 5 (approx. per word bound = -5.471, relative change = 6.504e-03)
Topic 1: translat, freelanc, seo, research, administr
Topic 2: web design, web, editor, copywrit, artist
Topic 3: web develop, expert, market, php, profession
Topic 4: graphic design, consult, writer, photograph, senior
Topic 5: design, develop, illustr, data entri, virtual assist
Topic 6: manag, wordpress, busi, graphic, programm
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Completing Iteration 10 (approx. per word bound = -5.397, relative change = 1.449e-03)
Topic 1: translat, freelanc, seo, research, administr
Topic 2: web design, web, editor, copywrit, artist
Topic 3: web develop, expert, market, php, profession
Topic 4: graphic design, writer, consult, photograph, senior
Topic 5: design, develop, data entri, illustr, virtual assist
Topic 6: manag, wordpress, busi, proofread, graphic
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Completing Iteration 15 (approx. per word bound = -5.375, relative change = 5.653e-04)
Topic 1: translat, freelanc, seo, research, administr
Topic 2: web design, web, editor, copywrit, artist
Topic 3: web develop, expert, market, php, profession
Topic 4: graphic design, writer, consult, photograph, senior
Topic 5: design, develop, data entri, illustr, virtual assist
Topic 6: manag, wordpress, busi, proofread, graphic
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Completing Iteration 20 (approx. per word bound = -5.364, relative change = 3.197e-04)
Topic 1: translat, freelanc, seo, research, administr
Topic 2: web design, web, editor, copywrit, artist
Topic 3: web develop, expert, market, php, profession
Topic 4: graphic design, writer, consult, photograph, senior
Topic 5: design, develop, data entri, illustr, virtual assist
Topic 6: manag, wordpress, busi, proofread, graphic
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Completing Iteration 25 (approx. per word bound = -5.358, relative change = 1.511e-04)
Topic 1: translat, freelanc, seo, research, administr
Topic 2: web design, web, editor, copywrit, artist
Topic 3: web develop, expert, market, php, profession
Topic 4: graphic design, writer, consult, photograph, senior
Topic 5: design, develop, data entri, illustr, virtual assist
Topic 6: manag, wordpress, busi, proofread, graphic
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Completing Iteration 26 (approx. per word bound = -5.357, relative change = 1.329e-04)
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Completing Iteration 30 (approx. per word bound = -5.355, relative change = 1.158e-04)
Topic 1: translat, freelanc, seo, research, administr
Topic 2: web design, web, editor, copywrit, artist
Topic 3: web develop, expert, market, php, profession
Topic 4: graphic design, writer, consult, photograph, senior
Topic 5: design, develop, data entri, illustr, virtual assist
Topic 6: manag, wordpress, busi, proofread, graphic
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Completed E-Step (27 seconds).
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Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
.......
Recovering initialization...
....
Initialization complete.
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Completed E-Step (39 seconds).
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Completing Iteration 5 (approx. per word bound = -5.465, relative change = 7.311e-03)
Topic 1: consult, editor, copywrit, web, busi
Topic 2: data entri, graphic, programm, servic, sale
Topic 3: web develop, translat, virtual assist, account, administr
Topic 4: web design, expert, wordpress, seo, engin
Topic 5: design, graphic design, photograph, php, english
Topic 6: develop, freelanc, manag, illustr, creativ
Topic 7: writer, market, profession, artist, web
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Completing Iteration 10 (approx. per word bound = -5.379, relative change = 1.785e-03)
Topic 1: consult, editor, copywrit, busi, proofread
Topic 2: data entri, graphic, programm, servic, sale
Topic 3: web develop, translat, virtual assist, account, administr
Topic 4: web design, expert, seo, wordpress, php
Topic 5: design, graphic design, photograph, english, logo design
Topic 6: develop, freelanc, manag, illustr, creativ
Topic 7: writer, web, market, profession, research
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Completed E-Step (24 seconds).
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Completing Iteration 15 (approx. per word bound = -5.351, relative change = 7.690e-04)
Topic 1: consult, editor, copywrit, busi, proofread
Topic 2: data entri, graphic, programm, servic, sale
Topic 3: web develop, translat, virtual assist, account, administr
Topic 4: web design, expert, seo, php, wordpress
Topic 5: design, graphic design, photograph, english, logo design
Topic 6: develop, freelanc, manag, illustr, creativ
Topic 7: writer, web, market, profession, research
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Completing Iteration 16 (approx. per word bound = -5.347, relative change = 7.073e-04)
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Completing Iteration 20 (approx. per word bound = -5.335, relative change = 4.110e-04)
Topic 1: consult, editor, copywrit, busi, proofread
Topic 2: data entri, graphic, programm, servic, sale
Topic 3: web develop, translat, virtual assist, account, administr
Topic 4: web design, expert, seo, php, wordpress
Topic 5: design, graphic design, photograph, english, logo design
Topic 6: develop, freelanc, manag, illustr, creativ
Topic 7: writer, web, market, profession, research
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Completing Iteration 25 (approx. per word bound = -5.328, relative change = 2.030e-04)
Topic 1: consult, editor, copywrit, busi, proofread
Topic 2: data entri, graphic, programm, servic, sale
Topic 3: web develop, translat, virtual assist, account, administr
Topic 4: web design, expert, seo, php, wordpress
Topic 5: design, graphic design, photograph, english, logo design
Topic 6: develop, freelanc, manag, illustr, creativ
Topic 7: writer, web, market, profession, research
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Completed E-Step (28 seconds).
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Completing Iteration 26 (approx. per word bound = -5.327, relative change = 1.694e-04)
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Completing Iteration 30 (approx. per word bound = -5.324, relative change = 1.065e-04)
Topic 1: consult, editor, copywrit, busi, proofread
Topic 2: data entri, graphic, programm, servic, sale
Topic 3: web develop, translat, virtual assist, account, administr
Topic 4: web design, expert, seo, php, wordpress
Topic 5: design, graphic design, photograph, logo design, english
Topic 6: develop, freelanc, manag, illustr, creativ
Topic 7: writer, web, market, profession, research
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Completed E-Step (29 seconds).
Completed M-Step.
Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
........
Recovering initialization...
....
Initialization complete.
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Completed E-Step (42 seconds).
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Completing Iteration 1 (approx. per word bound = -5.819)
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Completing Iteration 5 (approx. per word bound = -5.467, relative change = 7.706e-03)
Topic 1: develop, consult, web design, seo, graphic
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: virtual assist, research, seo, proofread, director
Topic 4: design, illustr, artist, profession, softwar develop
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, web design, data entri, copywrit
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, web develop, websit, social media
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Completed E-Step (27 seconds).
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Completed E-Step (26 seconds).
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Completing Iteration 10 (approx. per word bound = -5.379, relative change = 1.818e-03)
Topic 1: develop, web design, consult, jqueri, graphic
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: seo, virtual assist, research, proofread, director
Topic 4: design, illustr, artist, profession, softwar develop
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, data entri, copywrit, assist
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, websit, social media, senior
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Completed E-Step (25 seconds).
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Completing Iteration 11 (approx. per word bound = -5.371, relative change = 1.458e-03)
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Completing Iteration 15 (approx. per word bound = -5.352, relative change = 6.520e-04)
Topic 1: develop, web design, consult, jqueri, transcrib
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: seo, virtual assist, research, proofread, director
Topic 4: design, illustr, profession, artist, graphic
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, data entri, copywrit, assist
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, websit, social media, senior
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Completed E-Step (26 seconds).
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Completing Iteration 16 (approx. per word bound = -5.349, relative change = 5.559e-04)
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Completing Iteration 20 (approx. per word bound = -5.340, relative change = 3.194e-04)
Topic 1: develop, web design, consult, jqueri, transcrib
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: seo, virtual assist, research, proofread, director
Topic 4: design, illustr, profession, artist, graphic
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, data entri, copywrit, assist
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, websit, social media, senior
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Completed E-Step (28 seconds).
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Topic 1: develop, web design, consult, jqueri, transcrib
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: seo, virtual assist, research, proofread, director
Topic 4: design, illustr, profession, artist, graphic
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, data entri, copywrit, assist
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, websit, social media, senior
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Completed E-Step (29 seconds).
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Completing Iteration 30 (approx. per word bound = -5.330, relative change = 1.419e-04)
Topic 1: develop, web design, consult, jqueri, transcrib
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: seo, virtual assist, research, proofread, director
Topic 4: design, illustr, profession, artist, graphic
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, data entri, copywrit, assist
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, websit, social media, senior
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Completed E-Step (29 seconds).
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Completing Iteration 35 (approx. per word bound = -5.327, relative change = 1.030e-04)
Topic 1: develop, web design, consult, jqueri, transcrib
Topic 2: web develop, freelanc, market, photograph, account
Topic 3: seo, virtual assist, research, proofread, director
Topic 4: design, illustr, profession, artist, graphic
Topic 5: web, wordpress, engin, creativ, programm
Topic 6: graphic design, translat, data entri, copywrit, assist
Topic 7: writer, expert, editor, busi, sale
Topic 8: manag, php, websit, social media, senior
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Completed E-Step (30 seconds).
Completed M-Step.
Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
.........
Recovering initialization...
....
Initialization complete.
....................................................................................................
Completed E-Step (43 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -5.790)
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Completed E-Step (36 seconds).
Completed M-Step.
Completing Iteration 2 (approx. per word bound = -5.668, relative change = 2.103e-02)
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Completed E-Step (35 seconds).
Completed M-Step.
Completing Iteration 3 (approx. per word bound = -5.576, relative change = 1.622e-02)
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Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 4 (approx. per word bound = -5.514, relative change = 1.112e-02)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 5 (approx. per word bound = -5.471, relative change = 7.793e-03)
Topic 1: seo, profession, editor, engin, proofread
Topic 2: writer, consult, illustr, research, translat
Topic 3: manag, data entri, busi, softwar develop, wordpress
Topic 4: develop, artist, wordpress, programm, digit
Topic 5: design, graphic design, web, director, websit
Topic 6: web design, expert, market, copywrit, sale
Topic 7: web develop, freelanc, creativ, develop, servic
Topic 8: translat, virtual assist, photograph, account, graphic
Topic 9: php, web, html, content, magento
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 6 (approx. per word bound = -5.438, relative change = 6.032e-03)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 7 (approx. per word bound = -5.411, relative change = 4.879e-03)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 8 (approx. per word bound = -5.390, relative change = 3.994e-03)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 9 (approx. per word bound = -5.373, relative change = 3.062e-03)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 10 (approx. per word bound = -5.362, relative change = 2.100e-03)
Topic 1: seo, editor, profession, engin, proofread
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, css
Topic 4: develop, wordpress, artist, programm, digit
Topic 5: design, graphic design, web, websit, director
Topic 6: web design, expert, market, copywrit, sale
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: php, web, html, content, magento
....................................................................................................
Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 11 (approx. per word bound = -5.353, relative change = 1.654e-03)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 12 (approx. per word bound = -5.346, relative change = 1.362e-03)
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Completed E-Step (25 seconds).
Completed M-Step.
Completing Iteration 13 (approx. per word bound = -5.340, relative change = 1.107e-03)
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Completed E-Step (25 seconds).
Completed M-Step.
Completing Iteration 14 (approx. per word bound = -5.335, relative change = 9.226e-04)
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Completed E-Step (25 seconds).
Completed M-Step.
Completing Iteration 15 (approx. per word bound = -5.331, relative change = 7.815e-04)
Topic 1: seo, editor, profession, engin, proofread
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, css
Topic 4: develop, wordpress, artist, programm, digit
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, copywrit, sale
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, html, content, magento
....................................................................................................
Completed E-Step (25 seconds).
Completed M-Step.
Completing Iteration 16 (approx. per word bound = -5.327, relative change = 6.611e-04)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 17 (approx. per word bound = -5.324, relative change = 5.641e-04)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 18 (approx. per word bound = -5.322, relative change = 4.910e-04)
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Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 19 (approx. per word bound = -5.319, relative change = 4.397e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 20 (approx. per word bound = -5.317, relative change = 4.033e-04)
Topic 1: seo, editor, profession, engin, proofread
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, pr
Topic 4: develop, wordpress, artist, programm, digit
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, sale, logo design
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, html, content, magento
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 21 (approx. per word bound = -5.315, relative change = 3.790e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 22 (approx. per word bound = -5.313, relative change = 3.679e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 23 (approx. per word bound = -5.311, relative change = 3.748e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 24 (approx. per word bound = -5.309, relative change = 3.878e-04)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 25 (approx. per word bound = -5.307, relative change = 3.809e-04)
Topic 1: seo, editor, profession, copywrit, engin
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, pr
Topic 4: develop, wordpress, artist, programm, digit
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, sale, logo design
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, html, content, magento
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 26 (approx. per word bound = -5.305, relative change = 3.468e-04)
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Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 27 (approx. per word bound = -5.304, relative change = 2.970e-04)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 28 (approx. per word bound = -5.303, relative change = 2.498e-04)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 29 (approx. per word bound = -5.301, relative change = 2.195e-04)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 30 (approx. per word bound = -5.300, relative change = 2.050e-04)
Topic 1: seo, editor, profession, copywrit, engin
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, pr
Topic 4: develop, wordpress, artist, programm, digit
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, sale, logo design
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, html, content, magento
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 31 (approx. per word bound = -5.299, relative change = 2.109e-04)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 32 (approx. per word bound = -5.298, relative change = 2.510e-04)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 33 (approx. per word bound = -5.296, relative change = 3.032e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 34 (approx. per word bound = -5.294, relative change = 3.261e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 35 (approx. per word bound = -5.293, relative change = 3.033e-04)
Topic 1: seo, editor, profession, copywrit, engin
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, pr
Topic 4: develop, wordpress, artist, programm, digit
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, sale, logo design
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, html, content, magento
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 36 (approx. per word bound = -5.292, relative change = 2.480e-04)
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Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 37 (approx. per word bound = -5.291, relative change = 1.911e-04)
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Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 38 (approx. per word bound = -5.290, relative change = 1.588e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 39 (approx. per word bound = -5.289, relative change = 1.511e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 40 (approx. per word bound = -5.288, relative change = 1.546e-04)
Topic 1: seo, editor, profession, copywrit, engin
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, pr
Topic 4: develop, artist, wordpress, programm, digit
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, sale, logo design
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, wordpress, html, content
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 41 (approx. per word bound = -5.287, relative change = 1.641e-04)
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Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 42 (approx. per word bound = -5.286, relative change = 1.774e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 43 (approx. per word bound = -5.285, relative change = 1.925e-04)
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Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 44 (approx. per word bound = -5.284, relative change = 2.033e-04)
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Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 45 (approx. per word bound = -5.283, relative change = 2.036e-04)
Topic 1: seo, editor, profession, copywrit, engin
Topic 2: writer, translat, consult, illustr, research
Topic 3: manag, data entri, busi, softwar develop, pr
Topic 4: develop, artist, programm, digit, analyst
Topic 5: design, graphic design, websit, director, anim
Topic 6: web design, expert, market, sale, logo design
Topic 7: web develop, freelanc, creativ, servic, android
Topic 8: photograph, virtual assist, account, administr, graphic
Topic 9: web, php, wordpress, html, content
....................................................................................................
Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 46 (approx. per word bound = -5.282, relative change = 1.913e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 47 (approx. per word bound = -5.281, relative change = 1.681e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 48 (approx. per word bound = -5.280, relative change = 1.397e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 49 (approx. per word bound = -5.280, relative change = 1.121e-04)
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Completed E-Step (32 seconds).
Completed M-Step.
Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
..........
Recovering initialization...
....
Initialization complete.
....................................................................................................
Completed E-Step (48 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -5.770)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 2 (approx. per word bound = -5.704, relative change = 1.154e-02)
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Completed E-Step (37 seconds).
Completed M-Step.
Completing Iteration 3 (approx. per word bound = -5.605, relative change = 1.737e-02)
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Completed E-Step (36 seconds).
Completed M-Step.
Completing Iteration 4 (approx. per word bound = -5.525, relative change = 1.411e-02)
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Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 5 (approx. per word bound = -5.471, relative change = 9.819e-03)
Topic 1: develop, php, seo, websit, sale
Topic 2: manag, editor, copywrit, account, administr
Topic 3: writer, html, journalist, write, css
Topic 4: writer, softwar develop, senior, softwar, engin
Topic 5: translat, data entri, web, graphic, busi
Topic 6: web develop, virtual assist, research, profession, data entri
Topic 7: design, expert, illustr, wordpress, artist
Topic 8: web design, market, specialist, director, project manag
Topic 9: graphic design, freelanc, photograph, consult, creativ
Topic 10: anim, web, profession, servic, video
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 6 (approx. per word bound = -5.432, relative change = 7.185e-03)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 7 (approx. per word bound = -5.402, relative change = 5.522e-03)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 8 (approx. per word bound = -5.378, relative change = 4.435e-03)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 9 (approx. per word bound = -5.360, relative change = 3.424e-03)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 10 (approx. per word bound = -5.346, relative change = 2.530e-03)
Topic 1: develop, seo, php, wordpress, websit
Topic 2: manag, editor, copywrit, account, administr
Topic 3: html, write, journalist, css, technic
Topic 4: writer, engin, softwar develop, senior, softwar
Topic 5: translat, busi, graphic, english, support
Topic 6: web develop, virtual assist, research, data entri, profession
Topic 7: design, expert, illustr, artist, wordpress
Topic 8: web design, market, specialist, programm, director
Topic 9: graphic design, freelanc, consult, photograph, creativ
Topic 10: web, servic, social media, anim, profession
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 11 (approx. per word bound = -5.335, relative change = 2.095e-03)
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 12 (approx. per word bound = -5.326, relative change = 1.717e-03)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 13 (approx. per word bound = -5.318, relative change = 1.487e-03)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 14 (approx. per word bound = -5.310, relative change = 1.390e-03)
....................................................................................................
Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 15 (approx. per word bound = -5.304, relative change = 1.255e-03)
Topic 1: develop, seo, php, wordpress, websit
Topic 2: manag, editor, copywrit, account, administr
Topic 3: html, write, journalist, css, technic
Topic 4: writer, engin, softwar develop, senior, softwar
Topic 5: translat, busi, graphic, english, support
Topic 6: web develop, data entri, virtual assist, research, profession
Topic 7: design, expert, illustr, artist, product
Topic 8: web design, market, specialist, programm, director
Topic 9: graphic design, freelanc, consult, photograph, creativ
Topic 10: web, servic, social media, anim, video
....................................................................................................
Completed E-Step (26 seconds).
Completed M-Step.
Completing Iteration 16 (approx. per word bound = -5.298, relative change = 9.915e-04)
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 17 (approx. per word bound = -5.294, relative change = 7.330e-04)
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 18 (approx. per word bound = -5.291, relative change = 5.726e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 19 (approx. per word bound = -5.289, relative change = 4.822e-04)
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 20 (approx. per word bound = -5.287, relative change = 4.069e-04)
Topic 1: develop, seo, php, wordpress, websit
Topic 2: manag, editor, copywrit, account, administr
Topic 3: html, write, journalist, css, technic
Topic 4: writer, engin, softwar develop, senior, softwar
Topic 5: translat, busi, graphic, english, support
Topic 6: web develop, data entri, profession, virtual assist, research
Topic 7: design, expert, illustr, artist, product
Topic 8: web design, market, specialist, programm, director
Topic 9: graphic design, freelanc, consult, photograph, creativ
Topic 10: web, servic, social media, anim, video
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 21 (approx. per word bound = -5.285, relative change = 3.409e-04)
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 22 (approx. per word bound = -5.283, relative change = 2.823e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 23 (approx. per word bound = -5.282, relative change = 2.389e-04)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 24 (approx. per word bound = -5.281, relative change = 2.108e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 25 (approx. per word bound = -5.280, relative change = 1.912e-04)
Topic 1: develop, seo, php, wordpress, websit
Topic 2: manag, editor, copywrit, account, administr
Topic 3: html, write, journalist, css, technic
Topic 4: writer, engin, softwar develop, senior, softwar
Topic 5: translat, busi, graphic, english, support
Topic 6: web develop, data entri, profession, virtual assist, research
Topic 7: design, expert, illustr, artist, product
Topic 8: web design, market, specialist, programm, director
Topic 9: graphic design, freelanc, consult, photograph, creativ
Topic 10: web, servic, social media, anim, video
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 26 (approx. per word bound = -5.279, relative change = 1.701e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 27 (approx. per word bound = -5.278, relative change = 1.523e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 28 (approx. per word bound = -5.278, relative change = 1.342e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 29 (approx. per word bound = -5.277, relative change = 1.251e-04)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 30 (approx. per word bound = -5.276, relative change = 1.314e-04)
Topic 1: develop, seo, php, wordpress, websit
Topic 2: manag, editor, copywrit, account, administr
Topic 3: html, write, journalist, css, technic
Topic 4: writer, engin, softwar develop, senior, softwar
Topic 5: translat, busi, graphic, english, support
Topic 6: web develop, data entri, profession, virtual assist, research
Topic 7: design, expert, illustr, artist, product
Topic 8: web design, market, specialist, programm, director
Topic 9: graphic design, freelanc, consult, photograph, creativ
Topic 10: web, servic, social media, anim, video
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 31 (approx. per word bound = -5.276, relative change = 1.440e-04)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 32 (approx. per word bound = -5.275, relative change = 1.488e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 33 (approx. per word bound = -5.274, relative change = 1.394e-04)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 34 (approx. per word bound = -5.273, relative change = 1.213e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 35 (approx. per word bound = -5.273, relative change = 1.014e-04)
Topic 1: develop, seo, php, wordpress, websit
Topic 2: manag, editor, copywrit, account, administr
Topic 3: html, write, journalist, css, technic
Topic 4: writer, engin, softwar develop, senior, softwar
Topic 5: translat, busi, graphic, english, support
Topic 6: web develop, data entri, profession, virtual assist, research
Topic 7: design, expert, illustr, artist, product
Topic 8: web design, market, specialist, programm, director
Topic 9: graphic design, freelanc, consult, photograph, creativ
Topic 10: web, servic, social media, anim, video
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
............
Recovering initialization...
....
Initialization complete.
....................................................................................................
Completed E-Step (47 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -5.782)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 2 (approx. per word bound = -5.689, relative change = 1.604e-02)
....................................................................................................
Completed E-Step (38 seconds).
Completed M-Step.
Completing Iteration 3 (approx. per word bound = -5.546, relative change = 2.518e-02)
....................................................................................................
Completed E-Step (37 seconds).
Completed M-Step.
Completing Iteration 4 (approx. per word bound = -5.458, relative change = 1.581e-02)
....................................................................................................
Completed E-Step (34 seconds).
Completed M-Step.
Completing Iteration 5 (approx. per word bound = -5.411, relative change = 8.635e-03)
Topic 1: develop, wordpress, web design, html, php
Topic 2: freelanc, profession, expert, project manag, journalist
Topic 3: market, account, sale, manag, research
Topic 4: web, programm, support, student, excel
Topic 5: graphic design, writer, web design, editor, proofread
Topic 6: web develop, english, director, translat, teacher
Topic 7: design, manag, specialist, market, social media
Topic 8: consult, busi, seo, copywrit, servic
Topic 9: virtual assist, php, logo design, content writer, android
Topic 10: illustr, artist, design, graphic, anim
Topic 11: photograph, engin, creativ, design, 3d
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 6 (approx. per word bound = -5.375, relative change = 6.633e-03)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 7 (approx. per word bound = -5.348, relative change = 5.037e-03)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 8 (approx. per word bound = -5.329, relative change = 3.626e-03)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 9 (approx. per word bound = -5.314, relative change = 2.725e-03)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 10 (approx. per word bound = -5.302, relative change = 2.381e-03)
Topic 1: develop, wordpress, php, web design, websit
Topic 2: freelanc, expert, profession, project manag, journalist
Topic 3: market, research, account, manag, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, proofread
Topic 6: web develop, english, director, translat, teacher
Topic 7: design, specialist, manag, social media, pr
Topic 8: consult, seo, busi, copywrit, servic
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 11 (approx. per word bound = -5.291, relative change = 2.023e-03)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 12 (approx. per word bound = -5.282, relative change = 1.712e-03)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 13 (approx. per word bound = -5.276, relative change = 1.187e-03)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 14 (approx. per word bound = -5.270, relative change = 1.006e-03)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 15 (approx. per word bound = -5.266, relative change = 8.881e-04)
Topic 1: develop, php, wordpress, websit, html
Topic 2: freelanc, expert, profession, project manag, journalist
Topic 3: market, manag, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, proofread
Topic 6: web develop, english, director, translat, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 16 (approx. per word bound = -5.262, relative change = 6.909e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 17 (approx. per word bound = -5.259, relative change = 5.511e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 18 (approx. per word bound = -5.257, relative change = 4.804e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 19 (approx. per word bound = -5.254, relative change = 4.378e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 20 (approx. per word bound = -5.252, relative change = 4.034e-04)
Topic 1: develop, php, wordpress, websit, html
Topic 2: freelanc, expert, profession, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, teacher, softwar
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 21 (approx. per word bound = -5.250, relative change = 3.773e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 22 (approx. per word bound = -5.248, relative change = 3.646e-04)
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Completed E-Step (27 seconds).
Completed M-Step.
Completing Iteration 23 (approx. per word bound = -5.246, relative change = 3.609e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 24 (approx. per word bound = -5.245, relative change = 3.466e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 25 (approx. per word bound = -5.243, relative change = 3.187e-04)
Topic 1: develop, php, wordpress, websit, html
Topic 2: freelanc, expert, profession, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, softwar, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 26 (approx. per word bound = -5.241, relative change = 2.935e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 27 (approx. per word bound = -5.240, relative change = 2.778e-04)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 28 (approx. per word bound = -5.238, relative change = 2.748e-04)
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Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 29 (approx. per word bound = -5.237, relative change = 2.753e-04)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 30 (approx. per word bound = -5.236, relative change = 2.521e-04)
Topic 1: develop, php, wordpress, websit, expert
Topic 2: freelanc, profession, expert, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, softwar, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 31 (approx. per word bound = -5.234, relative change = 2.278e-04)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 32 (approx. per word bound = -5.233, relative change = 2.188e-04)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 33 (approx. per word bound = -5.232, relative change = 2.200e-04)
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Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 34 (approx. per word bound = -5.231, relative change = 2.280e-04)
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Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 35 (approx. per word bound = -5.230, relative change = 2.255e-04)
Topic 1: develop, php, wordpress, websit, expert
Topic 2: freelanc, profession, expert, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, softwar, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 36 (approx. per word bound = -5.229, relative change = 2.217e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 37 (approx. per word bound = -5.227, relative change = 2.150e-04)
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Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 38 (approx. per word bound = -5.226, relative change = 2.358e-04)
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Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 39 (approx. per word bound = -5.225, relative change = 2.201e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 40 (approx. per word bound = -5.224, relative change = 2.153e-04)
Topic 1: develop, php, wordpress, expert, websit
Topic 2: freelanc, profession, expert, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, softwar, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 41 (approx. per word bound = -5.223, relative change = 2.092e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 42 (approx. per word bound = -5.222, relative change = 1.526e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 43 (approx. per word bound = -5.221, relative change = 1.213e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 44 (approx. per word bound = -5.221, relative change = 1.131e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 45 (approx. per word bound = -5.220, relative change = 1.115e-04)
Topic 1: develop, php, wordpress, expert, websit
Topic 2: freelanc, profession, expert, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, softwar, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 46 (approx. per word bound = -5.220, relative change = 1.129e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 47 (approx. per word bound = -5.219, relative change = 1.164e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 48 (approx. per word bound = -5.218, relative change = 1.199e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 49 (approx. per word bound = -5.218, relative change = 1.221e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 50 (approx. per word bound = -5.217, relative change = 1.229e-04)
Topic 1: develop, php, wordpress, expert, websit
Topic 2: freelanc, profession, expert, project manag, journalist
Topic 3: manag, market, research, account, sale
Topic 4: web, programm, support, excel, student
Topic 5: graphic design, web design, writer, editor, copywrit
Topic 6: web develop, english, director, softwar, teacher
Topic 7: design, specialist, social media, pr, brand
Topic 8: consult, seo, busi, servic, softwar develop
Topic 9: virtual assist, logo design, content writer, android, softwar engin
Topic 10: illustr, artist, graphic, anim, product
Topic 11: photograph, engin, creativ, 3d, digit
Topic 12: translat, data entri, administr, write, admin
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 51 (approx. per word bound = -5.217, relative change = 1.199e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 52 (approx. per word bound = -5.216, relative change = 1.145e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 53 (approx. per word bound = -5.215, relative change = 1.077e-04)
....................................................................................................
Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 54 (approx. per word bound = -5.215, relative change = 1.007e-04)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
...............
Recovering initialization...
....
Initialization complete.
....................................................................................................
Completed E-Step (54 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -5.787)
....................................................................................................
Completed E-Step (44 seconds).
Completed M-Step.
Completing Iteration 2 (approx. per word bound = -5.702, relative change = 1.455e-02)
....................................................................................................
Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 3 (approx. per word bound = -5.559, relative change = 2.516e-02)
....................................................................................................
Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 4 (approx. per word bound = -5.472, relative change = 1.566e-02)
....................................................................................................
Completed E-Step (37 seconds).
Completed M-Step.
Completing Iteration 5 (approx. per word bound = -5.414, relative change = 1.059e-02)
Topic 1: web develop, softwar engin, c, net, asp.net
Topic 2: writer, freelanc, translat, profession, copywrit
Topic 3: consult, wordpress, joomla, magento, technic
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, anim, fashion, video editor
Topic 6: photograph, english, translat, teacher, admin
Topic 7: busi, servic, student, owner, architectur
Topic 8: manag, seo, websit, sale, account
Topic 9: develop, web, php, softwar develop, senior
Topic 10: illustr, artist, graphic, video, graphic design
Topic 11: engin, 3d, architect, brand, photoshop
Topic 12: web design, virtual assist, data entri, research, expert
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, expert
Topic 15: account, bookkeep, financi, market, book
....................................................................................................
Completed E-Step (35 seconds).
Completed M-Step.
Completing Iteration 6 (approx. per word bound = -5.372, relative change = 7.737e-03)
....................................................................................................
Completed E-Step (34 seconds).
Completed M-Step.
Completing Iteration 7 (approx. per word bound = -5.344, relative change = 5.209e-03)
....................................................................................................
Completed E-Step (34 seconds).
Completed M-Step.
Completing Iteration 8 (approx. per word bound = -5.323, relative change = 4.017e-03)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 9 (approx. per word bound = -5.304, relative change = 3.443e-03)
....................................................................................................
Completed E-Step (33 seconds).
Completed M-Step.
Completing Iteration 10 (approx. per word bound = -5.290, relative change = 2.727e-03)
Topic 1: web develop, php, softwar engin, c, net
Topic 2: writer, freelanc, translat, profession, copywrit
Topic 3: consult, wordpress, expert, php, joomla
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, anim, fashion, video editor
Topic 6: photograph, english, translat, admin, teacher
Topic 7: busi, servic, student, architectur, owner
Topic 8: manag, seo, market, websit, sale
Topic 9: develop, web, php, softwar develop, senior
Topic 10: illustr, artist, graphic, video, photo editor
Topic 11: engin, 3d, architect, photoshop, brand
Topic 12: web design, data entri, virtual assist, research, support
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, offic
Topic 15: account, market, analyst, bookkeep, experienc
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 11 (approx. per word bound = -5.279, relative change = 2.132e-03)
....................................................................................................
Completed E-Step (32 seconds).
Completed M-Step.
Completing Iteration 12 (approx. per word bound = -5.269, relative change = 1.736e-03)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 13 (approx. per word bound = -5.262, relative change = 1.413e-03)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 14 (approx. per word bound = -5.256, relative change = 1.149e-03)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 15 (approx. per word bound = -5.251, relative change = 9.907e-04)
Topic 1: web develop, php, softwar engin, c, net
Topic 2: writer, freelanc, translat, profession, copywrit
Topic 3: consult, wordpress, expert, php, html
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, logo design, anim, fashion
Topic 6: photograph, english, translat, admin, teacher
Topic 7: busi, servic, student, architectur, owner
Topic 8: manag, seo, websit, sale, market
Topic 9: develop, web, softwar develop, senior, android
Topic 10: illustr, artist, graphic, video, photo editor
Topic 11: engin, 3d, architect, photoshop, brand
Topic 12: web design, data entri, virtual assist, research, support
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, offic
Topic 15: account, market, analyst, bookkeep, experienc
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 16 (approx. per word bound = -5.246, relative change = 8.138e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 17 (approx. per word bound = -5.243, relative change = 6.452e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 18 (approx. per word bound = -5.240, relative change = 4.784e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 19 (approx. per word bound = -5.238, relative change = 4.481e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 20 (approx. per word bound = -5.236, relative change = 3.897e-04)
Topic 1: web develop, php, softwar engin, net, c
Topic 2: writer, freelanc, translat, profession, copywrit
Topic 3: consult, expert, wordpress, php, html
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, logo design, anim, fashion
Topic 6: photograph, english, translat, admin, teacher
Topic 7: busi, servic, student, architectur, owner
Topic 8: manag, seo, websit, sale, project manag
Topic 9: develop, web, softwar develop, senior, android
Topic 10: illustr, artist, graphic, video, photo editor
Topic 11: engin, 3d, architect, photoshop, brand
Topic 12: web design, data entri, virtual assist, research, support
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, offic
Topic 15: market, account, analyst, bookkeep, experienc
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 21 (approx. per word bound = -5.234, relative change = 3.546e-04)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 22 (approx. per word bound = -5.233, relative change = 3.305e-04)
....................................................................................................
Completed E-Step (28 seconds).
Completed M-Step.
Completing Iteration 23 (approx. per word bound = -5.231, relative change = 2.898e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 24 (approx. per word bound = -5.230, relative change = 2.652e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 25 (approx. per word bound = -5.228, relative change = 2.523e-04)
Topic 1: web develop, softwar engin, net, c, digit market
Topic 2: writer, freelanc, translat, profession, copywrit
Topic 3: expert, consult, wordpress, php, html
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, logo design, anim, fashion
Topic 6: photograph, english, translat, admin, teacher
Topic 7: busi, servic, student, architectur, owner
Topic 8: manag, seo, websit, sale, project manag
Topic 9: develop, web, softwar develop, senior, android
Topic 10: illustr, artist, graphic, video, photo editor
Topic 11: engin, 3d, architect, photoshop, brand
Topic 12: web design, data entri, virtual assist, research, support
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, offic
Topic 15: market, account, analyst, bookkeep, experienc
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 26 (approx. per word bound = -5.227, relative change = 2.433e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 27 (approx. per word bound = -5.226, relative change = 2.408e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 28 (approx. per word bound = -5.224, relative change = 2.436e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 29 (approx. per word bound = -5.223, relative change = 2.488e-04)
....................................................................................................
Completed E-Step (29 seconds).
Completed M-Step.
Completing Iteration 30 (approx. per word bound = -5.222, relative change = 2.461e-04)
Topic 1: web develop, softwar engin, net, c, digit market
Topic 2: writer, translat, freelanc, profession, copywrit
Topic 3: expert, consult, php, wordpress, html
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, logo design, anim, fashion
Topic 6: photograph, english, translat, admin, teacher
Topic 7: busi, servic, student, architectur, owner
Topic 8: manag, seo, websit, sale, project manag
Topic 9: develop, web, softwar develop, senior, android
Topic 10: illustr, artist, graphic, video, photo editor
Topic 11: engin, 3d, architect, photoshop, brand
Topic 12: web design, data entri, virtual assist, research, support
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, offic
Topic 15: market, account, analyst, bookkeep, experienc
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 31 (approx. per word bound = -5.221, relative change = 2.377e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 32 (approx. per word bound = -5.220, relative change = 2.204e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 33 (approx. per word bound = -5.218, relative change = 1.982e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 34 (approx. per word bound = -5.218, relative change = 1.668e-04)
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 35 (approx. per word bound = -5.217, relative change = 1.476e-04)
Topic 1: web develop, softwar engin, net, c, digit market
Topic 2: writer, translat, freelanc, profession, copywrit
Topic 3: expert, consult, php, wordpress, html
Topic 4: programm, product, softwar, produc, oper
Topic 5: design, graphic design, logo design, fashion, video editor
Topic 6: photograph, english, translat, admin, teacher
Topic 7: busi, servic, student, architectur, owner
Topic 8: manag, seo, websit, sale, project manag
Topic 9: develop, web, softwar develop, senior, android
Topic 10: illustr, artist, graphic, anim, video
Topic 11: engin, 3d, architect, photoshop, brand
Topic 12: web design, data entri, virtual assist, research, support
Topic 13: editor, proofread, creativ, director, freelanc writer
Topic 14: administr, specialist, social media, data, offic
Topic 15: market, account, analyst, bookkeep, experienc
....................................................................................................
Completed E-Step (30 seconds).
Completed M-Step.
Completing Iteration 36 (approx. per word bound = -5.216, relative change = 1.362e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 37 (approx. per word bound = -5.216, relative change = 1.189e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Completing Iteration 38 (approx. per word bound = -5.215, relative change = 1.017e-04)
....................................................................................................
Completed E-Step (31 seconds).
Completed M-Step.
Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
....................
Recovering initialization...
....
Initialization complete.
....................................................................................................
Completed E-Step (69 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -5.834)
....................................................................................................
Completed E-Step (59 seconds).
Completed M-Step.
Completing Iteration 2 (approx. per word bound = -5.729, relative change = 1.813e-02)
....................................................................................................
Completed E-Step (56 seconds).
Completed M-Step.
Completing Iteration 3 (approx. per word bound = -5.574, relative change = 2.700e-02)
....................................................................................................
Completed E-Step (52 seconds).
Completed M-Step.
Completing Iteration 4 (approx. per word bound = -5.482, relative change = 1.644e-02)
....................................................................................................
Completed E-Step (52 seconds).
Completed M-Step.
Completing Iteration 5 (approx. per word bound = -5.421, relative change = 1.109e-02)
Topic 1: php, wordpress, develop, html, css
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, onlin market, consult, experi, social
Topic 4: design, engin, softwar develop, support, network
Topic 5: anim, video editor, video, art, 2d
Topic 6: copywrit, pr, market, work, communic
Topic 7: specialist, student, brand, comput, architectur
Topic 8: busi, creativ, servic, social media, account
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, digit, architect, 3d, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, data entri, assist, write
Topic 13: freelanc writer, content, journalist, blogger, editor
Topic 14: administr, consult, product, android, c
Topic 15: manag, market, director, sale, account
Topic 16: web design, websit design, develop, facebook, rubi
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, research, data entri, data, wordpress
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: consult, pattern, experienc, market, develop
....................................................................................................
Completed E-Step (49 seconds).
Completed M-Step.
Completing Iteration 6 (approx. per word bound = -5.375, relative change = 8.541e-03)
....................................................................................................
Completed E-Step (46 seconds).
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Completing Iteration 7 (approx. per word bound = -5.342, relative change = 6.119e-03)
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Completed E-Step (46 seconds).
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Completing Iteration 8 (approx. per word bound = -5.319, relative change = 4.244e-03)
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Completed E-Step (46 seconds).
Completed M-Step.
Completing Iteration 9 (approx. per word bound = -5.303, relative change = 3.164e-03)
....................................................................................................
Completed E-Step (44 seconds).
Completed M-Step.
Completing Iteration 10 (approx. per word bound = -5.288, relative change = 2.773e-03)
Topic 1: php, wordpress, develop, html, joomla
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, network
Topic 5: anim, video editor, video, edit, 2d
Topic 6: copywrit, pr, communic, work, virtual
Topic 7: specialist, student, brand, comput, architectur
Topic 8: busi, creativ, servic, social media, account
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, assist, write
Topic 13: freelanc writer, blogger, content, journalist, editor
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, sale, director, account
Topic 16: web design, websit design, develop, facebook, rubi
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, research, data entri, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, etc, skill, pattern, consult
....................................................................................................
Completed E-Step (45 seconds).
Completed M-Step.
Completing Iteration 11 (approx. per word bound = -5.276, relative change = 2.338e-03)
....................................................................................................
Completed E-Step (43 seconds).
Completed M-Step.
Completing Iteration 12 (approx. per word bound = -5.266, relative change = 1.832e-03)
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Completed E-Step (42 seconds).
Completed M-Step.
Completing Iteration 13 (approx. per word bound = -5.257, relative change = 1.723e-03)
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Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 14 (approx. per word bound = -5.249, relative change = 1.443e-03)
....................................................................................................
Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 15 (approx. per word bound = -5.243, relative change = 1.275e-03)
Topic 1: php, wordpress, html, develop, joomla
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, 2d
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, architectur
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, assist, write
Topic 13: freelanc writer, blogger, content, journalist, editor
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, research, data entri, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, etc, skill, custom, pattern
....................................................................................................
Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 16 (approx. per word bound = -5.237, relative change = 1.070e-03)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 17 (approx. per word bound = -5.232, relative change = 9.119e-04)
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Completed E-Step (42 seconds).
Completed M-Step.
Completing Iteration 18 (approx. per word bound = -5.228, relative change = 8.062e-04)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 19 (approx. per word bound = -5.224, relative change = 7.338e-04)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 20 (approx. per word bound = -5.221, relative change = 6.707e-04)
Topic 1: php, wordpress, html, joomla, magento
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, 2d
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, architectur
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, assist, write
Topic 13: freelanc writer, blogger, content, journalist, technic
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, data entri, research, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, photoshop, custom, etc, skill
....................................................................................................
Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 21 (approx. per word bound = -5.218, relative change = 5.480e-04)
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Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 22 (approx. per word bound = -5.215, relative change = 5.613e-04)
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Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 23 (approx. per word bound = -5.213, relative change = 4.007e-04)
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Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 24 (approx. per word bound = -5.211, relative change = 3.661e-04)
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Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 25 (approx. per word bound = -5.209, relative change = 3.452e-04)
Topic 1: php, wordpress, html, joomla, magento
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, flash
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, technician
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, write, assist
Topic 13: freelanc writer, blogger, content, journalist, technic
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, data entri, research, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, photoshop, custom, etc, skill
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 26 (approx. per word bound = -5.207, relative change = 3.414e-04)
....................................................................................................
Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 27 (approx. per word bound = -5.206, relative change = 3.165e-04)
....................................................................................................
Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 28 (approx. per word bound = -5.204, relative change = 2.714e-04)
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Completed E-Step (38 seconds).
Completed M-Step.
Completing Iteration 29 (approx. per word bound = -5.203, relative change = 2.819e-04)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 30 (approx. per word bound = -5.201, relative change = 2.714e-04)
Topic 1: php, wordpress, html, joomla, magento
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, flash
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, technician
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, write, assist
Topic 13: freelanc writer, blogger, content, journalist, technic
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, data entri, research, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, photoshop, etc, custom, skill
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 31 (approx. per word bound = -5.200, relative change = 2.577e-04)
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Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 32 (approx. per word bound = -5.199, relative change = 2.238e-04)
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Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 33 (approx. per word bound = -5.198, relative change = 2.074e-04)
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Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 34 (approx. per word bound = -5.197, relative change = 2.038e-04)
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Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 35 (approx. per word bound = -5.196, relative change = 1.989e-04)
Topic 1: php, wordpress, html, joomla, magento
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, flash
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, technician
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, write, assist
Topic 13: freelanc writer, blogger, content, journalist, technic
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, data entri, research, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, photoshop, etc, custom, skill
....................................................................................................
Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 36 (approx. per word bound = -5.195, relative change = 1.928e-04)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 37 (approx. per word bound = -5.194, relative change = 1.801e-04)
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Completed E-Step (39 seconds).
Completed M-Step.
Completing Iteration 38 (approx. per word bound = -5.193, relative change = 1.705e-04)
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Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 39 (approx. per word bound = -5.192, relative change = 1.765e-04)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Completing Iteration 40 (approx. per word bound = -5.191, relative change = 1.816e-04)
Topic 1: php, wordpress, html, joomla, magento
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, flash
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, technician
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: expert, seo, logo design, write, assist
Topic 13: freelanc writer, blogger, content, journalist, technic
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, data entri, research, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, photoshop, etc, custom, skill
....................................................................................................
Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 41 (approx. per word bound = -5.190, relative change = 1.712e-04)
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Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 42 (approx. per word bound = -5.189, relative change = 1.747e-04)
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Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 43 (approx. per word bound = -5.188, relative change = 1.641e-04)
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Completed E-Step (42 seconds).
Completed M-Step.
Completing Iteration 44 (approx. per word bound = -5.187, relative change = 1.623e-04)
....................................................................................................
Completed E-Step (42 seconds).
Completed M-Step.
Completing Iteration 45 (approx. per word bound = -5.187, relative change = 1.279e-04)
Topic 1: php, wordpress, html, joomla, magento
Topic 2: writer, virtual assist, project manag, content writer, interpret
Topic 3: analyst, experi, year, onlin market, social
Topic 4: design, engin, softwar develop, support, ui
Topic 5: anim, video editor, video, edit, flash
Topic 6: copywrit, pr, custom servic, communic, work
Topic 7: specialist, student, brand, comput, technician
Topic 8: busi, creativ, servic, social media, onlin
Topic 9: graphic design, graphic, programm, senior, softwar
Topic 10: artist, 3d, digit, architect, visual
Topic 11: develop, web, photograph, websit, fashion
Topic 12: seo, expert, logo design, write, assist
Topic 13: freelanc writer, blogger, content, journalist, technic
Topic 14: consult, administr, product, android, net
Topic 15: manag, market, account, sale, director
Topic 16: web design, websit design, facebook, rubi, convers
Topic 17: translat, editor, proofread, english, teacher
Topic 18: web develop, data entri, research, data, mobil
Topic 19: freelanc, illustr, profession, print, retouch
Topic 20: experienc, photoshop, etc, skill, custom
....................................................................................................
Completed E-Step (42 seconds).
Completed M-Step.
Completing Iteration 46 (approx. per word bound = -5.186, relative change = 1.319e-04)
....................................................................................................
Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 47 (approx. per word bound = -5.186, relative change = 1.200e-04)
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Completed E-Step (41 seconds).
Completed M-Step.
Completing Iteration 48 (approx. per word bound = -5.185, relative change = 1.038e-04)
....................................................................................................
Completed E-Step (40 seconds).
Completed M-Step.
Model Converged plot(k_search)Warning messages:
1: In readChar(file, size, TRUE) : truncating string with embedded nuls
2: In readChar(file, size, TRUE) : truncating string with embedded nuls
3: In readChar(file, size, TRUE) : truncating string with embedded nuls
4: In readChar(file, size, TRUE) : truncating string with embedded nuls
5: In readChar(file, size, TRUE) : truncating string with embedded nuls
6: In readChar(file, size, TRUE) : truncating string with embedded nuls
Fitting 12 topics
Based on the above fit, it looks like 12 is a better meaure of topics, all things considered.
summary(tmod12)
A topic model with 12 topics, 209294 documents and a 466 word dictionary.
Topic 1 Top Words:
Highest Prob: expert, seo, sale, social media, admin, excel, work
FREX: seo, social media, work, retouch, digit market, compani, internet market
Lift: ad, advertis, adword, analyt, email market, googl adword, link build
Score: expert, seo, sale, social media, quantiti, admin, ppc
Topic 2 Top Words:
Highest Prob: writer, editor, copywrit, freelanc writer, content, journalist, experienc
FREX: writer, editor, copywrit, freelanc writer, content, journalist, experienc
Lift: cameraman, en, film, filmmak, law, writer, editor
Score: writer, editor, interpret, copywrit, freelanc writer, journalist, content
Topic 3 Top Words:
Highest Prob: consult, manag, engin, analyst, softwar, experi, databas
FREX: consult, manag, engin, analyst, softwar, databas, system
Lift: consult, internet, scienc, secur, system, analysi, analyst
Score: consult, manag, engin, analyst, civil, softwar, system
Topic 4 Top Words:
Highest Prob: translat, research, proofread, english, content writer, blogger, teacher
FREX: translat, research, proofread, english, content writer, teacher, articl writer
Lift: research, french, onlin, academ, arab, articl, articl writer
Score: translat, english, proofread, research, blogger, french, content writer
Topic 5 Top Words:
Highest Prob: design, artist, graphic, anim, 3d, video editor, print
FREX: design, artist, graphic, video editor, print, voic, game
Lift: actor, voic, 2d, 2d anim, 3d artist, 3d model, artist
Score: design, artist, graphic, 3d, anim, concept artist, video editor
Topic 6 Top Words:
Highest Prob: graphic design, develop, web design, websit, websit design, mobil, seo specialist
FREX: graphic design, web design, websit, seo specialist, founder, websit design, head
Lift: cutter, founder, graphic design, head, seo specialist, web design, websit
Score: develop, graphic design, web design, cutter, websit, websit design, mobil
Topic 7 Top Words:
Highest Prob: illustr, programm, assist, architect, execut, student, brand
FREX: illustr, programm, assist, architect, execut, student, brand
Lift: creativ director, illustr, master, technologist, architect, art, brand
Score: illustr, programm, architect, assist, architectur, visual, student
Topic 8 Top Words:
Highest Prob: php, wordpress, creativ, logo design, softwar develop, html, joomla
FREX: php, wordpress, softwar develop, html, joomla, magento, android
Lift: php, 5, access, android, app develop, applic develop, brochur
Score: php, wordpress, html, joomla, front end, css, mysql
Topic 9 Top Words:
Highest Prob: web develop, freelanc, senior, fashion, communic, ui, owner
FREX: freelanc, senior, owner, ux, sound, photographi, photo editor
Lift: art director, freelanc, industri, music compos, music produc, owner, photographi
Score: web develop, freelanc, textil, senior, fashion, ui, ux
Topic 10 Top Words:
Highest Prob: profession, account, busi, servic, director, support, project manag
FREX: profession, account, busi, servic, director, project manag, bookkeep
Lift: advisor, busi analyst, coach, coordin, corpor, event, event manag
Score: account, profession, busi, director, support, sap, servic
Topic 11 Top Words:
Highest Prob: web, market, photograph, specialist, video, audio, maker
FREX: web, market, photograph, specialist, video, video edit, audio
Lift: photograph, web, creation, generalist, make, market, mechan engin
Score: web, market, photograph, specialist, generalist, video, audio
Topic 12 Top Words:
Highest Prob: data entri, virtual assist, administr, write, data, offic, custom servic
FREX: virtual assist, administr, write, data, offic, custom servic, pa
Lift: offic, admin assist, admin support, administr assist, appoint, articl write, call
Score: virtual assist, data entri, administr, write, custom servic, clerk, offic plot(tmod12)
---
title: "Cluster analysis for JM article"
author: "Kenneth Benoit"
output:
  html_notebook: default
  pdf_document: default
---

## Load the data

```{r}
library("dplyr", warn.conflicts = FALSE)

unzip("job descriptors.csv.zip", exdir = "~/tmp/")
df_raw <- data.table::fread("~/tmp/job descriptors.csv", data.table = FALSE)
```

Group by worker ID (`mem_id`):
```{r}
df_grouped <- df_raw %>%
    group_by(mem_id) %>%
    summarize(n_bids = n(), n_unique_job_title = length(unique(job_title)),
              job_title = head(job_title, 1))

# sort by descending number of bids
df_grouped <- arrange(df_grouped, desc(n_bids))

# verify that job_title is the same for each mem_id
stopifnot(all(select(df_grouped, n_unique_job_title) == 1))
# remove some intermediate variables
df_grouped <- select(df_grouped, -n_unique_job_title)
```
So we can see here that every unique `mem_id` (worker) had only one job title.  (Good for us!)

## Characterize the data

Most workers had only a single bid.  The median number was 3.
```{r}
summary(df_grouped$n_bids)
```

We can see the skew:
```{r, fig.width = 6}
library("ggplot2")
ggplot(df_grouped, aes(x = n_bids)) +
  scale_x_continuous(breaks=c(1, 2, 5, 10, 25, 50, 100, 500, 1000, 10000), 
                     trans = "log") +
  geom_histogram(aes(y = ..density..),
                 binwidth = .5, colour = "black", fill = "white") +
  geom_density(alpha = .2, fill = "#FF6655", colour = "blue")
```

So, four lunatics have apparently submitted more than 10,000 bids each:
```{r}
# top 10 list
head(df_grouped, 10)
```
Also, six bidders had no description:
```{r}
filter(df_grouped, is.na(job_title))
```



## Characterize the descriptions

```{r}
library("quanteda", warn.conflicts = FALSE)

job_corpus <- filter(df_grouped, !is.na(job_title)) %>%
    corpus(text_field = "job_title", docid_field = "mem_id")

job_tokens <- tokens(job_corpus, remove_punct = TRUE, remove_symbols = TRUE,
                     padding = TRUE) %>%
    tokens_tolower()

# top terms
job_tokens %>%
    tokens_remove(c("", stopwords("en"))) %>%
    dfm() %>%
    textstat_frequency(n = 30)
```
We can refine this by finding some multi-word expressions:
```{r}
job_mwe <- job_tokens %>%
    tokens_remove(stopwords("en"), padding = TRUE) %>%
    tokens_wordstem(language = "en") %>%
    textstat_collocations()
head(job_mwe, 30)
```

Now let's turn the top 100 multi-word bigrams into single tokens:
```{r}
job_tokens_mwe <- job_tokens %>%
    tokens_remove(stopwords("en"), padding = TRUE) %>%
    tokens_wordstem(language = "en") %>%
    tokens_compound(head(job_mwe, 100), concatenator = " ") %>%
    tokens_compound(phrase("word press"), concatenator = " ") %>%
    tokens_remove("")

job_dfmat <- dfm(job_tokens_mwe)
textstat_frequency(job_dfmat, n = 30)
```

Some of these occur _very_ infrequently:
```{r}
textstat_frequency(job_dfmat) %>%
  ggplot(aes(x = frequency)) +
    scale_x_continuous(breaks = 10^(0:6), 
                       trans = "log") +
    geom_histogram(aes(y = ..density..),
                   binwidth = .5, colour = "black", fill = "white") +
    geom_density(alpha = .2, fill = "#FF6655", colour = "blue")
```


# Identify some clusters

```{r}
job_dfmat_trimmed <- dfm_trim(job_dfmat, min_termfreq = 10, 
                              min_docfreq = .01, docfreq_type = "prop", 
                              verbose = TRUE)
print(job_dfmat_trimmed, 0, 0)

library("ClusterR")
Optimal_Clusters_KMeans(as.matrix(job_dfmat_trimmed), 10, criterion = "AIC")
```

From this plot, it looks like _k_ = 8 might be the optimal number of clusters, but since there are 7 job description fields, we will fit 7.
```{r}
job_kmeans <- KMeans_arma(as.matrix(job_dfmat_trimmed), clusters = 7)
job_corpus$cluster <- job_dfmat$cluster <- 
  predict_KMeans(as.matrix(job_dfmat_trimmed), job_kmeans)
```

Now we can look at the top terms in each cluster:
```{r}
textstat_frequency(job_dfmat, n = 10, groups = "cluster") %>%
  as.data.frame() %>%
  select(-rank)
```

We could say this:
```{r}
cluster_label <- c("financial", "web development", "web developer", "graphic designer", 
                   "website design", "business support", "admin")
tsf <- textstat_frequency(job_dfmat, n = 10, groups = "cluster")
tab <- data.frame(cluster = 1:7, cluster_label, 
                  "Top terms" = sapply(split(tsf$feature, f = tsf$group), paste, collapse = ", "))
# knitr::kable(tab, format = "markdown")
tab
```


## LDA on `job_title`, k = 7

I used the **stm** package for this, which implements a faster and more modern version of LDA than the older packages.  If you want to cite what it is, just call it "LDA".  (See https://www.structuraltopicmodel.com/ for details, citations, etc.)

Here I trimmed the (very) sparse dfm a bit less agressively.  The `min_docfreq = .001` means that a term had to occur in 1/1000 of the documents to be retained, or in this case, at least 216 documents (since there are 215,974 documents).
```{r}
job_dfmat_trimmed2 <- dfm_trim(job_dfmat, min_termfreq = 10, 
                              min_docfreq = .001, docfreq_type = "prop", 
                              verbose = TRUE)
# remove the empty documents
job_dfmat_trimmed2 <- dfm_subset(job_dfmat_trimmed2, ntoken(job_dfmat_trimmed2) > 0)
print(job_dfmat_trimmed2, 0, 0)
```

Now we can fit a topic model.  Since there are seven service categories, we will start by seeing how $k = 7$ works.  Note: the categories are:
1. Design 
2. Writing & Translation   
3. Video, Photo, & Audio  
4. Business Support           
5. Social Media, Sales, & Marketing            
6. Software Development
7. Web Development

```{r}
library("stm")
tmod <- stm(job_dfmat_trimmed2, K = 7, emtol = 1e-05)
```

```{r}
labelTopics(tmod)
```
```{r}
plot(tmod, n = 5)
```
```{r}
# put the topics back into the dfm
theta <- as.data.frame(tmod$theta)
names(theta) <- paste0("theta_", seq_len(ncol(theta)))

# add topic prevalence estimates, add mem_id
docvars(job_dfmat_trimmed2) <- 
  data.frame(cluster = job_dfmat_trimmed2$cluster,
             theta, max_topic = max.col(theta),
             mem_id = as.integer(docnames(job_dfmat_trimmed2)))

# join them back to the original df
df_grouped2 <- left_join(df_grouped, docvars(job_dfmat_trimmed2), by = "mem_id")

# join the grouped info back to the original long df
df_raw2 <- left_join(df_raw, select(df_grouped2, -n_bids, -job_title), by = "mem_id")

# write the output
data.table::fwrite(df_raw2, "~/tmp/job descriptors LDA.csv")
```

## Verifying the number of topics

```{r}
job_stm_trimmed2 <- convert(job_dfmat_trimmed2, to = "stm")

k_search <- searchK(documents = job_stm_trimmed2$documents, 
                    vocab = job_stm_trimmed2$vocab,
                    K = c(6, 7, 8, 9, 10, 12, 15, 20), emtol = 1e-04)
```
```{r}
plot(k_search)
```

## Fitting 12 topics

Based on the above fit, it looks like 12 is a better meaure of topics, all things considered.
```{r}
tmod12 <- stm(job_dfmat_trimmed2, K = 12, emtol = 1e-05)
summary(tmod12)
plot(tmod12)
```

