DataHoppers - Group Homework Session 4 - Topic analysis

Group: Data Hoppers

1. 71610049 - Praison Selvaraj
2. 71610006 - Anupam Piareji
3. 71610035 - Kulpreeth Singh

Topic analyze Item 1A- Risk Factors of Form 10-K

In the section Item 1A of Form 10-K firms reveal exposure to anticipated risks in the coming year. Here, the company lays anything that could go wrong, likely external effects, possible future failures to meet obligations, and other risks disclosed to adequately warn investors and potential investors.

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When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

Clear the workspace and invoke required libraries

rm(list=ls()) # Clear the workspace

library("tm")

## Loading required package: NLP

library("wordcloud")

## Loading required package: RColorBrewer

library("maptpx")

## Loading required package: slam

library("igraph")

## 
## Attaching package: 'igraph'

## The following object is masked from 'package:maptpx':
## 
##     normalize

## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum

## The following object is masked from 'package:base':
## 
##     union

library("ggplot2")

## 
## Attaching package: 'ggplot2'

## The following object is masked from 'package:NLP':
## 
##     annotate

library("reshape")

## Warning: package 'reshape' was built under R version 3.2.4

Read ITEM 1A. Risk Factor related data that has been scraped and provided in ‘RF.Technology.Rds’

textdata = readRDS(file.choose()) # Select RF.Technology.Rds data set

textdata is a data frame with 2 columns. First column is Company name and second column is text of Item 1A- Risk Factors of Form 10-K.

Select the Document Term Matrix (DTM). The DTM has been created from the second column of textdata

dtm1 = readRDS(file.choose()) # Select dtm1.RF.Rds

The LDA Model requires us to specify how many latent topics (K) we think exist in the corpus. As we do not the number of latent topics we start with K=2, K=3, K=4, K=5 to see which K yields the ‘best’ or most interpret-able and clear story

K = 2 # Choose number of topics in the model
simfit = topics(dtm1, K = K, verb = 2) # Fit the K topic model

## 
## Estimating on a 85 document collection.
## Fitting the 2 topic model.
## log posterior increase: 111.9, done. (L = -2347579.3)

Display the summary of top 12 phrases

summary(simfit, nwrd = 12) # Summary of simfit model

## 
## Top 12 phrases by topic-over-null term lift (and usage %):
## 
## [1] 'abandon', 'atic', 'dominance', 'fastest', 'instruction', 'pack', 'sunnyvale', 'amk', 'applied-products', 'linewidths', 'varian', 'dense' (80.2) 
## [2] 'peo', 'adp', 'motivated', 'employer', 'multitude', 'transmitter', 'statutes', 'withheld', 'worsening', 'highest', 'security-systems', 'borrowers' (19.8) 
## 
## Dispersion = 2.12

Let us examine the outputs of the topic model. Suppose there are D documents and T term-tokens in the corpus. And we are fitting K topics.One, a theta matrix of term-probabilities - which tells us for each term, what is the probability that the term belongs to each topic. So its dimension is T x K.

simfit$theta[1:10,]

##              topic
## phrase                   1            2
##   abandon     8.417557e-06 8.040463e-10
##   abandoned   3.785483e-05 9.538075e-08
##   abandonment 4.835164e-07 3.196205e-05
##   abatement   1.297934e-06 4.563540e-05
##   abide       4.718840e-07 3.200891e-05
##   abilities   2.886747e-06 1.579139e-04
##   ability     7.447915e-03 5.827765e-06
##   abroad      1.851574e-04 1.003033e-07
##   abruptly    9.114345e-07 3.023824e-05
##   absence     2.351180e-06 1.431172e-04

theta <- simfit$theta[1:10,]

Let’s sort this matrix with decreasing order of total term probability and check the few top terms

a0 = apply(simfit$theta, 1, sum);
a01 = order(a0, decreasing = TRUE)
simfit$theta[a01[1:10],]

##             topic
## phrase                  1            2
##   products   0.0141411246 1.440973e-07
##   business   0.0128248911 1.273608e-05
##   operations 0.0101151951 9.944519e-06
##   customers  0.0092253760 1.925722e-07
##   result     0.0090019883 1.513073e-06
##   services   0.0074996323 3.484800e-05
##   ability    0.0074479148 5.827765e-06
##   change     0.0004822414 5.907110e-03
##   addition   0.0063839862 2.334829e-06
##   results    0.0060873876 1.035554e-05

Two, a omega document-composition matrix - which is probability mass distribution of topic proportions in document. So its dimension is D x K.

simfit$omega[1:10,]

##         topic
## document         1            2
##       1  0.9998552 0.0001448060
##       2  0.9995329 0.0004670551
##       3  0.9998276 0.0001724272
##       4  0.5186917 0.4813083067
##       5  0.9997058 0.0002941557
##       6  0.8072293 0.1927706932
##       7  0.7768235 0.2231765152
##       8  0.7928529 0.2071471166
##       9  0.8002837 0.1997162711
##       10 0.7840141 0.2159859383

We see that Documents 1 to 10 heavily on Topic 1 and Document 4 is a mix of Topic 1 and Topic 2. Some terms have high frequency, others have low frequency. We want to ensure that term frequency does not unduly influence topic weights. So we normalize term frequency in a metric called ‘lift’. The lift of a term is topic membership probability normalized by occurrence probability of the term. If lift of a term for a topic is high, then we can say that, that term is useful in constructing that topic.Since topics function doesn’t return lift matrix for terms we can write a simple function to calculate lift of each term. Based on the number of terms in DocumentTermMatrix lift calculation may take some time.

t = Sys.time()
theta = simfit$theta
lift = theta*0;  sum1 = sum(dtm1)
for (i in 1:nrow(theta)){  
  for (j in 1:ncol(theta)){
    ptermtopic = 0; pterm = 0;
    ptermtopic = theta[i, j]     # term i's probability of topic j membership
    pterm = sum(dtm1[,i])/sum1   # marginal probability of term i's occurrence in corpus
    lift[i, j] = ptermtopic/pterm   # so, lift is topic membership probability normalized by occurrence probability
      }
}
Sys.time() - t # Total time for calculating lift

## Time difference of 1.247762 mins

let’s print lift for first 10 terms.

lift[1:10,]

##              topic
## phrase                 1            2
##   abandon     1.24826471 0.0001192344
##   abandoned   1.24746803 0.0031431774
##   abandonment 0.07170210 4.7397489451
##   abatement   0.12831632 4.5116064902
##   abide       0.06997709 4.7466979203
##   abilities   0.08561688 4.6835044100
##   ability     1.24799280 0.0009765162
##   abroad      1.24807000 0.0006761038
##   abruptly    0.13515935 4.4841196489
##   absence     0.07748079 4.7162848842

Now we have lift and theta for each term and each topic. We can plot a wordcloud for each topic in which terms will be selected if lift is above 1 and size will be proportional to term-probability. This wordclod will give us an idea of the Latent Topic. Let’s plot top 100 terms in each topic

for (i in 1:K){       # For each topic 
a0 = which(lift[,i] > 1) # terms with lift greator than 1 for topic i
freq = theta[a0,i] # Theta for terms greator than 1
freq = sort(freq,decreasing = T) # Terms with higher probilities for topic i

# Auto Correction -  Sometime terms in topic with lift above 1 are less than 100. So auto correction
n = ifelse(length(freq) >= 100, 100, length(freq))
top_word = as.matrix(freq[1:n])

# Plot wordcloud
wordcloud(rownames(top_word), top_word,  scale=c(4,0.5), 1,
          random.order=FALSE, random.color=FALSE, 
          colors=brewer.pal(8, "Dark2"))
mtext(paste("Latent Topic",i), side = 3, line = 2, cex=2)
}

From these wordclouds we can label and interpret topics. Topic 1 highlights that the risk factors have to do with business, products, results, customers, operations etc. Topic 2 highlights TDS, change, business reputation etc.

To get clearer picture of topics, let’s plot top 20 terms co-occurrence graph. Once co-occurrence matrix is constructed, we can plot this matrix using graph.adjacency function from igraph package. Note that for better readability we are censoring this matrix for top 2 edges.

for (i in 1:K){       # For each topic 
a0 = which(lift[,i] > 1) # terms with lift greator than 1 for topic i
freq = theta[a0,i] # Theta for terms greator than 1
freq = sort(freq,decreasing = T) # Terms with higher probilities for topic i

# Auto Correction -  Sometime terms in topic with lift above 1 are less than 30. So auto correction
n = ifelse(length(freq) >= 20, 20, length(freq))
top_word = as.matrix(freq[1:n])

# now for top 30 words let's find Document Term Matrix
mat  = dtm1[,match(row.names(top_word),colnames(dtm1))]

mat = as.matrix(mat)
cmat  = t(mat) %*% (mat)
diag(cmat) = 0

# Let's limit number of connections to 2
for (p in 1:nrow(cmat)){
  vec = cmat[p,]
  cutoff = sort(vec, decreasing = T)[2]
  cmat[p,][cmat[p,] < cutoff] = 0
}

#cmat[cmat <  quantile(cmat,.80)] = 0

graph <- graph.adjacency(cmat, mode = "undirected",weighted=T)

plot(graph,         #the graph to be plotted
 layout=layout.fruchterman.reingold,    # the layout method. 
 vertex.frame.color='blue',         #the color of the border of the dots 
 vertex.label.color='black',        #the color of the name labels
 vertex.label.font=1,           #the font of the name labels
 vertex.size = .00001,   # Dots size
 vertex.label.cex=1.3)
 mtext(paste("Topic",i), side = 3, line = 2, cex=2)
}

Now we have lift matrix and also we have DocumentTermMatrix. So we can create a weighing scheme for each document and each topic, which will give proportion of a topic in a document. Here is a function to calculate topic proportion in documents.

eta = function(mat, dtm) {

mat1 = mat/mean(mat);  terms1 = rownames(mat1);
eta.mat = matrix(0, 1, ncol(mat1))

for (i in 1:nrow(dtm)){
    a11 = as.data.frame(matrix(dtm[i,])); 
    rownames(a11) = colnames(dtm)
    a12 = as.matrix(a11[(a11>0),]);  
    rownames(a12) = rownames(a11)[(a11>0)]; 
    rownames(a12)[1:4]
    a13 = intersect(terms1, rownames(a12)); 
    a13[1:15];  length(a13)
    a14a = match(a13, terms1);      # positions of matching terms in mat1 matrix
    a14b = match(a13, rownames(a12))        
    a15 = mat1[a14a,]*matrix(rep(a12[a14b,], 
                                 ncol(mat1)), 
                             ncol = ncol(mat1))
    eta.mat = rbind(eta.mat, apply(a15, 2, mean))   
    rm(a11, a12, a13, a14a, a14b, a15)
  }
  eta.mat = eta.mat[2:nrow(eta.mat), ]  # remove top zeroes row
  row.names(eta.mat)=row.names(dtm)
  return(eta.mat)
}

twc = eta(lift, dtm1)
head(twc)

##           1          2
## 1 1.8058129 0.07338217
## 2 1.3752730 0.12560819
## 3 1.7365399 0.05202135
## 4 0.6121672 1.86188229
## 5 1.6841064 0.13873854
## 6 1.2361259 1.18955013

Now we have topic proportion in a Document, we can find the top documents loading on a topic and read them for better interpretation of topics. Here is a function which first sorts twc matrix in decreasing order and then picks top n (n = 5) documents name. Then the function is called with required arguments and printing the company names for each topic.

eta.file.name = function(mat,calib,n) {
  s = list()                   # Blank List
  for (i in  1: ncol(mat))     # For each topic
  {
    read_doc = mat[order(mat[,i], decreasing= T),]  # Sort document prop matrix (twc)
    read_names = row.names(read_doc[1:n,])          # docuemnt index for first n document
    s[[i]] = calib[as.numeric(read_names),1]     # Store first n companies name in list  
      }
  return(s)
}

temp1 = eta.file.name(twc,textdata,5)

for (i in 1:length(temp1)){
  print(paste('Companies loading heavily on topic',i,'are'))
  print(temp1[[i]])
  print('--------------------------')
}

## [1] "Companies loading heavily on topic 1 are"
## [1] "SUNPOWER CORP"          "ADVANCED MICRO DEVICES"
## [3] "SANDISK CORP"           "APPLIED MATERIALS INC" 
## [5] "LEAP WIRELESS INTL INC"
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 2 are"
## [1] "SPRINT CORP"                  "TELEPHONE & DATA SYSTEMS INC"
## [3] "SUNPOWER CORP"                "FACEBOOK INC"                
## [5] "BROCADE COMMUNICATIONS SYS"  
## [1] "--------------------------"

Similarly we can find top text document. Since these documents are very large theya are not being printed here.

eta.file = function(mat,calib,n) {
  s = list()                   # Blank List
  for (i in  1: ncol(mat))     # For each topic
  {
    read_doc = mat[order(mat[,i], decreasing= T),]  # Sort document prop matrix (twc)
    read_names = row.names(read_doc[1:n,])          # docuemnt index for first n document
    s[[i]] = calib[as.numeric(read_names),2]     # Store first n documents in list  
      }
  return(s)
}

temp2 = eta.file(twc,textdata,5)

# for (i in 1:length(temp2)){
#   print(paste('Documents loading heavily on topic',i,'are'))
#   print(temp2[[i]])
#   print('--------------------------')
# }

Label for Topic 1 - Factors adversely affecting business

Interpretation - The performance of a business is determined by the operating results, sales, financial growth and stability, continuity in offering timely services, addition of more products and services to the portfolio. Not performing well on any of these parameters can adversely affect the business and turn out be risks that must be accounted for and adequate mitigation plans put into place. The following companies have expressed the above factors as risks affecting their business.SUNPOWER CORP, ADVANCED MICRO DEVICES, SANDISK CORP, APPLIED MATERIALS INC, LEAP WIRELESS INTL INC

Label for Topic 2 - Change agents affecting reputation

Interpretation - Changes such as taxation laws, damage to infrastructure necessitating capital expenditure, changes in client tastes, stockholders can affect liquidity and this can damage the company’s reputation among the stockholders. The following companies consider the above change agents as affecting the reputation and hence risks to their businesses: SPRINT CORP, TELEPHONE & DATA SYSTEMS INC, SUNPOWER CORP, FACEBOOK INC, BROCADE COMMUNICATIONS SYS.

A potential application of such analysis - The “U.S. Securities and Exchange Commission”, for instance, can use this data to undestand what elements pose risk to the sucessful functioning of the business enterprises. A thorough undestanding such risks and taking proactive measures taken to check them can help the nation sustain its economic growth. Companies such as Sprint Corp and Telephone & Data Systems Inc. have expressed ‘tax’ as one of the risk factors. The commission could offer consultation to and collaborate with institutions and boards in formulating such legislations. With the wealth of information business risks that can make or break companies, the legislations can be made with confidence after taking informed decisions.

The commission could compile a comprehensive list of risks faced by businesses categorized by industry, state, size etc. This list can serve as a guide to new and existing enterprises to identify risks that they may have overlooked.

The commission could issue alerts to all enterprises operating in a given category when it observes any patterns in problems faced by such enterprises which were previously identified as risks. The commission can identify risks that are related and seem to have a domino effect and issue early warnings to enterprises when such risks are seen in the real world. This can provide a healthy and conducive playing field for the enterprises and prevent economic slowdowns from occuring.

The commission can identify most common risks, highly-prevalent risks with remote occurence.

The lists of risks categorized by industry can serve as a good input for management consultants for studying risk aversion techniques.

The risk catalog can serve as a valuable tool to investors and potential investors who can validate the picture painted by the “annual report to the share holders” by comapring it in the backdrop of the risks as listed by the commission. A measure, such as Risk Index can be used to compare the risks faced by players in different industries.

Here is a function to repeat the study with K topics in the model

studyLDAModel = function(K) {

simfit = topics(dtm1, K = K, verb = 2) # Fit the K topic model
summary(simfit, nwrd = 12) # Summary of simfit model
simfit$theta[1:10,]

theta <- simfit$theta[1:10,]
a0 = apply(simfit$theta, 1, sum);
a01 = order(a0, decreasing = TRUE)
simfit$theta[a01[1:10],]
simfit$omega[1:10,]

t = Sys.time()
theta = simfit$theta
lift = theta*0;  sum1 = sum(dtm1)
for (i in 1:nrow(theta)){  
  for (j in 1:ncol(theta)){
    ptermtopic = 0; pterm = 0;
    ptermtopic = theta[i, j]     # term i's probability of topic j membership
    pterm = sum(dtm1[,i])/sum1   # marginal probability of term i's occurrence in corpus
    lift[i, j] = ptermtopic/pterm   # so, lift is topic membership probability normalized by occurrence probability
      }
}
Sys.time() - t # Total time for calculating lift
lift[1:10,]
for (i in 1:K){       # For each topic 
a0 = which(lift[,i] > 1) # terms with lift greator than 1 for topic i
freq = theta[a0,i] # Theta for terms greator than 1
freq = sort(freq,decreasing = T) # Terms with higher probilities for topic i

# Auto Correction -  Sometime terms in topic with lift above 1 are less than 100. So auto correction
n = ifelse(length(freq) >= 100, 100, length(freq))
top_word = as.matrix(freq[1:n])

# Plot wordcloud
wordcloud(rownames(top_word), top_word,  scale=c(4,0.5), 1,
          random.order=FALSE, random.color=FALSE, 
          colors=brewer.pal(8, "Dark2"))
mtext(paste("Latent Topic",i), side = 3, line = 2, cex=2)
}

for (i in 1:K){       # For each topic 
a0 = which(lift[,i] > 1) # terms with lift greator than 1 for topic i
freq = theta[a0,i] # Theta for terms greator than 1
freq = sort(freq,decreasing = T) # Terms with higher probilities for topic i

# Auto Correction -  Sometime terms in topic with lift above 1 are less than 30. So auto correction
n = ifelse(length(freq) >= 20, 20, length(freq))
top_word = as.matrix(freq[1:n])

# now for top 30 words let's find Document Term Matrix
mat  = dtm1[,match(row.names(top_word),colnames(dtm1))]

mat = as.matrix(mat)
cmat  = t(mat) %*% (mat)
diag(cmat) = 0

# Let's limit number of connections to 2
for (p in 1:nrow(cmat)){
  vec = cmat[p,]
  cutoff = sort(vec, decreasing = T)[2]
  cmat[p,][cmat[p,] < cutoff] = 0
}

#cmat[cmat <  quantile(cmat,.80)] = 0

graph <- graph.adjacency(cmat, mode = "undirected",weighted=T)

plot(graph,         #the graph to be plotted
 layout=layout.fruchterman.reingold,    # the layout method. 
 vertex.frame.color='blue',         #the color of the border of the dots 
 vertex.label.color='black',        #the color of the name labels
 vertex.label.font=1,           #the font of the name labels
 vertex.size = .00001,   # Dots size
 vertex.label.cex=1.3)
 mtext(paste("Topic",i), side = 3, line = 2, cex=2)
}
twc = eta(lift, dtm1)
head(twc)
temp1 = eta.file.name(twc,textdata,5)

for (i in 1:length(temp1)){
  print(paste('Companies loading heavily on topic',i,'are'))
  print(temp1[[i]])
  print('--------------------------')
}
}

For K=3

K=3
studyLDAModel(K)

## 
## Estimating on a 85 document collection.
## Fitting the 3 topic model.
## log posterior increase: 890.2, 1133.3, done. (L = -2335640.4)
## 
## Top 12 phrases by topic-over-null term lift (and usage %):
## 
## [1] 'abandon', 'atic', 'dominance', 'fastest', 'instruction', 'pack', 'sunnyvale', 'amk', 'applied-products', 'linewidths', 'varian', 'manufacture-product' (75.3) 
## [2] 'access-facilities', 'blurred', 'control-management', 'dated', 'deploys', 'mvno', 'revenues-future', 'subsidized', 'waiting', 'dividing', 'holdco', 'sprint-clearwire' (13.1) 
## [3] 'multitude', 'withheld', 'broadridge', 'censures', 'solutions-business', 'intentionally', 'clients-customers', 'clearpath', 'adequate-security', 'acquirors', 'admissions', 'cerner' (11.6) 
## 
## Dispersion = 2

## [1] "Companies loading heavily on topic 1 are"
## [1] "SUNPOWER CORP"          "ADVANCED MICRO DEVICES"
## [3] "APPLIED MATERIALS INC"  "SANDISK CORP"          
## [5] "LEAP WIRELESS INTL INC"
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 2 are"
## [1] "SPRINT CORP"                  "TELEPHONE & DATA SYSTEMS INC"
## [3] "SUNPOWER CORP"                "BROCADE COMMUNICATIONS SYS"  
## [5] "ECHOSTAR CORP"               
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 3 are"
## [1] "IAC/INTERACTIVECORP"          "GROUPON INC"                 
## [3] "CERNER CORP"                  "AUTOMATIC DATA PROCESSING"   
## [5] "BROADRIDGE FINANCIAL SOLUTNS"
## [1] "--------------------------"

Label for Topic 3 - Implications of Regulations and Contracts

Interpretation - Regulation changes at different levels of jurisdiction (local, state, federal), such as Health Care ACA, contacts with merchant-partners, violations in compliance resulting in penalties, breach of information privacy, retention of clients. Companies loading heavily on Topic 3 are include Automatic Data Processing (ADP) and Broadridge Financials Solutions. One of our team members works with ADP and reiterated how these are indeed the risk factors he has heard the senior leadership talk about.

For K=4

K=4
studyLDAModel(K)

## 
## Estimating on a 85 document collection.
## Fitting the 4 topic model.
## log posterior increase: 3545.4, 1671.9, 1348.9, 693.1, 463.3, done. (L = -2314418.5)
## 
## Top 12 phrases by topic-over-null term lift (and usage %):
## 
## [1] 'abandon', 'atic', 'dominance', 'fastest', 'instruction', 'pack', 'sunnyvale', 'amk', 'applied-products', 'linewidths', 'varian', 'dense' (59.6) 
## [2] 'consequent', 'mdash', 'repealed', 'affect-reported', 'company-customers', 'facilities-equipment', 'hai', 'hon', 'kill', 'lived', 'pricings', 'quick' (16.4) 
## [3] 'access-facilities', 'blurred', 'control-management', 'dated', 'deploys', 'mvno', 'revenues-future', 'subsidized', 'waiting', 'rollout', 'household', 'sign' (14) 
## [4] 'withheld', 'broadridge', 'censures', 'solutions-business', 'clearpath', 'intentionally', 'adequate-security', 'clients-customers', 'admissions', 'cerner', 'coding', 'diagnosis' (10) 
## 
## Dispersion = 1.88

## [1] "Companies loading heavily on topic 1 are"
## [1] "SUNPOWER CORP"          "ADVANCED MICRO DEVICES"
## [3] "APPLIED MATERIALS INC"  "SANDISK CORP"          
## [5] "CENTURYLINK INC"       
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 2 are"
## [1] "CISCO SYSTEMS INC"         "JABIL CIRCUIT INC"        
## [3] "SANDISK CORP"              "AMKOR TECHNOLOGY INC"     
## [5] "TELEDYNE TECHNOLOGIES INC"
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 3 are"
## [1] "SPRINT CORP"                  "TELEPHONE & DATA SYSTEMS INC"
## [3] "LEAP WIRELESS INTL INC"       "SUNPOWER CORP"               
## [5] "FACEBOOK INC"                
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 4 are"
## [1] "MANTECH INTL CORP"            "CERNER CORP"                 
## [3] "BROADRIDGE FINANCIAL SOLUTNS" "UNISYS CORP"                 
## [5] "COMPUTER SCIENCES CORP"      
## [1] "--------------------------"

For K=5

K=5
studyLDAModel(K)

## 
## Estimating on a 85 document collection.
## Fitting the 5 topic model.
## log posterior increase: 1271.3, 2374.8, 1480.8, 855.8, 702.2, 514.6, 470.4, done. (L = -2305161.6)
## 
## Top 12 phrases by topic-over-null term lift (and usage %):
## 
## [1] 'amk', 'applied-products', 'linewidths', 'varian', 'affect-applied', 'general-industry', 'inflections', 'tvs', 'abandon', 'atic', 'dominance', 'fastest' (46) 
## [2] 'access-facilities', 'blurred', 'control-management', 'dated', 'deploys', 'mvno', 'revenues-future', 'subsidized', 'waiting', 'rollout', 'acs', 'baseline' (21.8) 
## [3] 'manufacture-product', 'axis', 'guarantor', 'rejection', 'removable', 'spills', 'wdc', 'yokkaichi', 'unsold', 'expenses-including', 'controllers', 'lsi' (14.3) 
## [4] 'broadridge', 'censures', 'solutions-business', 'intentionally', 'clearpath', 'adequate-security', 'clients-customers', 'admissions', 'cerner', 'coding', 'diagnosis', 'displaying' (12.3) 
## [5] 'reputation-harm', 'depreciating', 'disadvantageous', 'equity-debt', 'federal-tax', 'foot', 'payouts', 'stockholders-including', 'tanks', 'trs', 'cabinet', 'prevailing-market' (5.6) 
## 
## Dispersion = 1.82

## [1] "Companies loading heavily on topic 1 are"
## [1] "APPLIED MATERIALS INC"  "ADVANCED MICRO DEVICES"
## [3] "SUNPOWER CORP"          "CISCO SYSTEMS INC"     
## [5] "CENTURYLINK INC"       
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 2 are"
## [1] "SPRINT CORP"                  "TELEPHONE & DATA SYSTEMS INC"
## [3] "LEAP WIRELESS INTL INC"       "FACEBOOK INC"                
## [5] "SUNPOWER CORP"               
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 3 are"
## [1] "SANDISK CORP"         "AMKOR TECHNOLOGY INC" "WESTERN DIGITAL CORP"
## [4] "JABIL CIRCUIT INC"    "SANMINA CORP"        
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 4 are"
## [1] "MANTECH INTL CORP"            "CERNER CORP"                 
## [3] "UNISYS CORP"                  "BROADRIDGE FINANCIAL SOLUTNS"
## [5] "COMPUTER SCIENCES CORP"      
## [1] "--------------------------"
## [1] "Companies loading heavily on topic 5 are"
## [1] "ECHOSTAR CORP"          "EQUINIX INC"           
## [3] "IRON MOUNTAIN INC"      "TRIMBLE NAVIGATION LTD"
## [5] "ITRON INC"             
## [1] "--------------------------"

TFIDF discounts or normalizes the TF by document frequency - this better reflects the term’s presumed importance

(a) Should you use TF or TFIDF? I suggest you try both and go with whatever yields cleaner results.

(b) Should you use K = 2 topics? 3? 4? I suggest you try between 2 and 5 topics and see which yields the ‘best’ or most interpret-able and clear story.

(c) Debate, discuss, tweak the code, try-and-err etc. Massive learning opportunity if you are willing to go the distance.

Interpret the topic. Label it in < 6 words and describe your interpretation in a few lines

Bonus question: Any potential applications of such analysis you can think of? For instance, ask yourself why might the results of your analysis be interesting to which firms? Remember, I’m not looking for just some results putup in a file. I’m looking for interconnections, deeper meaning, story

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.