Migrants
library(readr)
Migrants <- read_csv("C:/Users/lazarus/Downloads/Migrants.csv")
## Rows: 90 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (7): rownames, migrants, distance, pops66, pops71, popd66, popd71
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
View(Migrants)
Migrants
## # A tibble: 90 × 7
## rownames migrants distance pops66 pops71 popd66 popd71
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 255 924 108535 111641 493396 522104
## 2 2 2380 952 756039 788960 493396 522104
## 3 3 1140 1119 616788 534557 493396 522104
## 4 4 2145 1641 5780845 6027764 493396 522104
## 5 5 6295 1996 6960870 7703106 493396 522104
## 6 6 215 3159 963066 988247 493396 522104
## 7 7 185 3542 955344 926242 493396 522104
## 8 8 425 4059 1463203 1627874 493396 522104
## 9 9 425 4838 1873674 2184621 493396 522104
## 10 10 340 924 493396 522104 108535 111641
## # ℹ 80 more rows
mg<-Migrants
str(mg)
## spc_tbl_ [90 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ rownames: num [1:90] 1 2 3 4 5 6 7 8 9 10 ...
## $ migrants: num [1:90] 255 2380 1140 2145 6295 ...
## $ distance: num [1:90] 924 952 1119 1641 1996 ...
## $ pops66 : num [1:90] 108535 756039 616788 5780845 6960870 ...
## $ pops71 : num [1:90] 111641 788960 534557 6027764 7703106 ...
## $ popd66 : num [1:90] 493396 493396 493396 493396 493396 ...
## $ popd71 : num [1:90] 522104 522104 522104 522104 522104 ...
## - attr(*, "spec")=
## .. cols(
## .. rownames = col_double(),
## .. migrants = col_double(),
## .. distance = col_double(),
## .. pops66 = col_double(),
## .. pops71 = col_double(),
## .. popd66 = col_double(),
## .. popd71 = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
View(mg)
summary(mg)
## rownames migrants distance pops66
## Min. : 1.00 Min. : 95.0 Min. : 164 Min. : 108535
## 1st Qu.:23.25 1st Qu.: 912.5 1st Qu.: 924 1st Qu.: 616788
## Median :45.50 Median : 3087.5 Median :1763 Median : 959205
## Mean :45.50 Mean : 9227.3 Mean :1945 Mean :1997176
## 3rd Qu.:67.75 3rd Qu.:10291.2 3rd Qu.:2940 3rd Qu.:1873674
## Max. :90.00 Max. :99430.0 Max. :4838 Max. :6960870
## pops71 popd66 popd71
## Min. : 111641 Min. : 108535 Min. : 111641
## 1st Qu.: 534557 1st Qu.: 616788 1st Qu.: 534557
## Median : 957244 Median : 959205 Median : 957244
## Mean :2141512 Mean :1997176 Mean :2141512
## 3rd Qu.:2184621 3rd Qu.:1873674 3rd Qu.:2184621
## Max. :7703106 Max. :6960870 Max. :7703106
#check for na
any(is.na(mg))
## [1] FALSE
#drop the rownames column
mg1<-mg[-1]
View(mg1)
dim(mg1)
## [1] 90 6
sapply(mg1, class)
## migrants distance pops66 pops71 popd66 popd71
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
sapply(mg1[,1:6], sd)
## migrants distance pops66 pops71 popd66 popd71
## 15180.645 1218.896 2263918.696 2468572.880 2263918.696 2468572.880
library(mlbench)
## Warning: package 'mlbench' was built under R version 4.3.3
library(e1071)
## Warning: package 'e1071' was built under R version 4.3.3
skew<-apply(mg1[,1:6], 2, skewness)
print(skew)
## migrants distance pops66 pops71 popd66 popd71
## 3.2352733 0.4086444 1.3736931 1.3828426 1.3736931 1.3828426
plot(skew, type="l", col='black')
mg1correlation<- cor(mg1[,1:6])
print(mg1correlation)
## migrants distance pops66 pops71 popd66 popd71
## migrants 1.0000000 -0.3065114 0.3369534 0.3362471 0.3769860 0.3926451
## distance -0.3065114 1.0000000 -0.1251918 -0.1146829 -0.1251918 -0.1146829
## pops66 0.3369534 -0.1251918 1.0000000 0.9988841 -0.1111111 -0.1109871
## pops71 0.3362471 -0.1146829 0.9988841 1.0000000 -0.1109871 -0.1111111
## popd66 0.3769860 -0.1251918 -0.1111111 -0.1109871 1.0000000 0.9988841
## popd71 0.3926451 -0.1146829 -0.1109871 -0.1111111 0.9988841 1.0000000
plot(mg1correlation, type="b", col="black")
suppressPackageStartupMessages(library(caret))
## Warning: package 'caret' was built under R version 4.3.3
summary(mg1[,1:6])
## migrants distance pops66 pops71
## Min. : 95.0 Min. : 164 Min. : 108535 Min. : 111641
## 1st Qu.: 912.5 1st Qu.: 924 1st Qu.: 616788 1st Qu.: 534557
## Median : 3087.5 Median :1763 Median : 959205 Median : 957244
## Mean : 9227.3 Mean :1945 Mean :1997176 Mean :2141512
## 3rd Qu.:10291.2 3rd Qu.:2940 3rd Qu.:1873674 3rd Qu.:2184621
## Max. :99430.0 Max. :4838 Max. :6960870 Max. :7703106
## popd66 popd71
## Min. : 108535 Min. : 111641
## 1st Qu.: 616788 1st Qu.: 534557
## Median : 959205 Median : 957244
## Mean :1997176 Mean :2141512
## 3rd Qu.:1873674 3rd Qu.:2184621
## Max. :6960870 Max. :7703106
preprocessParams<-preProcess(mg1[,1:6], method=c("scale"))
print(preprocessParams)
## Created from 90 samples and 6 variables
##
## Pre-processing:
## - ignored (0)
## - scaled (6)
transformed_mg1<-predict(preprocessParams, mg1[,1:6])
summary(transformed_mg1)
## migrants distance pops66 pops71
## Min. :0.006258 Min. :0.1345 Min. :0.04794 Min. :0.04522
## 1st Qu.:0.060109 1st Qu.:0.7581 1st Qu.:0.27244 1st Qu.:0.21654
## Median :0.203384 Median :1.4464 Median :0.42369 Median :0.38777
## Mean :0.607835 Mean :1.5958 Mean :0.88218 Mean :0.86751
## 3rd Qu.:0.677919 3rd Qu.:2.4120 3rd Qu.:0.82762 3rd Qu.:0.88497
## Max. :6.549788 Max. :3.9692 Max. :3.07470 Max. :3.12047
## popd66 popd71
## Min. :0.04794 Min. :0.04522
## 1st Qu.:0.27244 1st Qu.:0.21654
## Median :0.42369 Median :0.38777
## Mean :0.88218 Mean :0.86751
## 3rd Qu.:0.82762 3rd Qu.:0.88497
## Max. :3.07470 Max. :3.12047
summary(mg1)
## migrants distance pops66 pops71
## Min. : 95.0 Min. : 164 Min. : 108535 Min. : 111641
## 1st Qu.: 912.5 1st Qu.: 924 1st Qu.: 616788 1st Qu.: 534557
## Median : 3087.5 Median :1763 Median : 959205 Median : 957244
## Mean : 9227.3 Mean :1945 Mean :1997176 Mean :2141512
## 3rd Qu.:10291.2 3rd Qu.:2940 3rd Qu.:1873674 3rd Qu.:2184621
## Max. :99430.0 Max. :4838 Max. :6960870 Max. :7703106
## popd66 popd71
## Min. : 108535 Min. : 111641
## 1st Qu.: 616788 1st Qu.: 534557
## Median : 959205 Median : 957244
## Mean :1997176 Mean :2141512
## 3rd Qu.:1873674 3rd Qu.:2184621
## Max. :6960870 Max. :7703106
preprocessParams<-preProcess(transformed_mg1[,1:6], method=c("range"))
print(preprocessParams)
## Created from 90 samples and 6 variables
##
## Pre-processing:
## - ignored (0)
## - re-scaling to [0, 1] (6)
transformed_mg2<-predict(preprocessParams, transformed_mg1[,1:6])
summary(transformed_mg2)
## migrants distance pops66 pops71
## Min. :0.00000 Min. :0.0000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00823 1st Qu.:0.1626 1st Qu.:0.07417 1st Qu.:0.05571
## Median :0.03013 Median :0.3421 Median :0.12414 Median :0.11139
## Mean :0.09193 Mean :0.3811 Mean :0.27562 Mean :0.26739
## 3rd Qu.:0.10265 3rd Qu.:0.5939 3rd Qu.:0.25760 3rd Qu.:0.27307
## Max. :1.00000 Max. :1.0000 Max. :1.00000 Max. :1.00000
## popd66 popd71
## Min. :0.00000 Min. :0.00000
## 1st Qu.:0.07417 1st Qu.:0.05571
## Median :0.12414 Median :0.11139
## Mean :0.27562 Mean :0.26739
## 3rd Qu.:0.25760 3rd Qu.:0.27307
## Max. :1.00000 Max. :1.00000
library(cluster)
set.seed(1234)
dist_mat<-dist(transformed_mg2, method = 'euclidean')
methds<-c('complete','single','average')
avgS<-matrix(NA, ncol=3, nrow=5, dimnames=list(2:6, methds))
for(k in 2:6){
for (m in seq_along(methds)){
h<-hclust(dist_mat, meth=methds[m])
c<-cutree(h,k)
s<-silhouette(c,dist_mat)
avgS[k-1, m]=mean(s[,3])
}
}
avgS
## complete single average
## 2 0.4974456 0.4490366 0.4490366
## 3 0.6117387 0.4811353 0.4826988
## 4 0.6315946 0.6315946 0.6315946
## 5 0.5546771 0.6161266 0.6161266
## 6 0.5025381 0.5670597 0.5670597
plot(s)
dist_mat2<-dist(transformed_mg2, method='euclidean')
h_clust<-hclust(dist_mat2, method = 'average')
#visualize the dendogram
plot(h_clust)
h_cut<-cutree(h_clust, k =3)
#visualize the clusters
plot(h_clust)
rect.hclust(h_clust, k=3 ,border = 2:6)
abline(h=4, col='blue')
suppressPackageStartupMessages(library(dendextend))
## Warning: package 'dendextend' was built under R version 4.3.3
avg_dend_obj <- as.dendrogram(h_clust)
avg_col_dend <- color_branches(avg_dend_obj, h = 3)
plot(avg_col_dend)
suppressPackageStartupMessages(library(dplyr))
#library(dplyr)
migrants_cl<-mutate(transformed_mg2, cluster = h_cut)
migrants_cl
## # A tibble: 90 × 7
## migrants distance pops66 pops71 popd66 popd71 cluster
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 0.00161 0.163 0 0 0.0562 0.0541 1
## 2 0.0230 0.169 0.0945 0.0892 0.0562 0.0541 1
## 3 0.0105 0.204 0.0742 0.0557 0.0562 0.0541 1
## 4 0.0206 0.316 0.828 0.779 0.0562 0.0541 2
## 5 0.0624 0.392 1 1 0.0562 0.0541 2
## 6 0.00121 0.641 0.125 0.115 0.0562 0.0541 1
## 7 0.000906 0.723 0.124 0.107 0.0562 0.0541 1
## 8 0.00332 0.833 0.198 0.200 0.0562 0.0541 1
## 9 0.00332 1 0.258 0.273 0.0562 0.0541 1
## 10 0.00247 0.163 0.0562 0.0541 0 0 1
## # ℹ 80 more rows
count(migrants_cl, cluster)
## # A tibble: 3 × 2
## cluster n
## <int> <int>
## 1 1 72
## 2 2 16
## 3 3 2
library(clValid)
## Warning: package 'clValid' was built under R version 4.3.3
dunn(dist_mat2, h_cut)
## [1] 0.4718926
library(fpc)
## Warning: package 'fpc' was built under R version 4.3.3
sol<-pamk(transformed_mg2, krange=2:6, criterion="asw", usepam=TRUE)
sol
## $pamobject
## Medoids:
## ID migrants distance pops66 pops71 popd66 popd71
## [1,] 24 0.01741582 0.4679076 0.1247065 0.1154726 0.09449392 0.08922112
## [2,] 69 0.06795188 0.3421053 1.0000000 1.0000000 0.12357963 0.10730485
## [3,] 52 0.11788393 0.3421053 0.1235796 0.1073048 1.00000000 1.00000000
## Clustering vector:
## [1] 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 3 3
## [39] 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1
## [77] 2 2 1 1 1 1 1 1 1 2 2 1 1 1
## Objective function:
## build swap
## 0.3221549 0.3221549
##
## Available components:
## [1] "medoids" "id.med" "clustering" "objective" "isolation"
## [6] "clusinfo" "silinfo" "diss" "call" "data"
##
## $nc
## [1] 3
##
## $crit
## [1] 0.0000000 0.4974456 0.6171584 0.5270395 0.4226829 0.4468736
set.seed(1234)
mg3<-kmeans(transformed_mg2, center=3, iter.max=200)
mg3
## K-means clustering with 3 clusters of sizes 56, 17, 17
##
## Cluster means:
## migrants distance pops66 pops71 popd66 popd71
## 1 0.05797841 0.4287090 0.1160510 0.1118216 0.1160510 0.1118216
## 2 0.15828199 0.3025875 0.1579182 0.1510858 0.9189611 0.8961470
## 3 0.13744341 0.3025875 0.9189611 0.8961470 0.1579182 0.1510858
##
## Clustering vector:
## [1] 1 1 1 3 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 1 1 1 1 2 2
## [39] 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1
## [77] 3 3 1 1 1 1 1 1 1 3 3 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 6.791390 2.801417 2.271840
## (between_SS / total_SS = 74.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
library(cluster)
migrants_s<-silhouette(mg3$cluster, dist(transformed_mg2))
plot(migrants_s)
