How to statistically identify emissions using Kmeans clustering

Question

I have the following data:

head(df.num1)
##   num_critic_for_reviews duration director_facebook_likes
## 1                    723      178                       0
## 2                    302      169                     563
## 3                    602      148                       0
## 4                    813      164                   22000
## 5                    388      100                     131
## 6                    462      132                     475
##   actor_3_facebook_likes actor_1_facebook_likes     gross num_voted_users
## 1                    855                   1000 760505847          886204
## 2                   1000                  40000 309404152          471220
## 3                    161                  11000 200074175          275868
## 4                  23000                  27000 448130642         1144337
## 5                    365                    131  46975183               8
## 6                    530                    640  73058679          212204
##   cast_total_facebook_likes facenumber_in_poster num_user_for_reviews
## 1                      4834                    0                 3054
## 2                     48350                    0                 1238
## 3                     11700                    1                  994
## 4                    106759                    0                 2701
## 5                       143                    0                  450
## 6                      1873                    1                  738
##    budget title_year actor_2_facebook_likes imdb_score aspect_ratio
## 1 2.4e+08       2009                    936        7.9          1.8
## 2 3.0e+08       2007                   5000        7.1          2.4
## 3 2.4e+08       2015                    393        6.8          2.4
## 4 2.5e+08       2012                  23000        8.5          2.4
## 5 1.0e+07       2015                     12        7.1          2.4
## 6 2.6e+08       2012                    632        6.6          2.4
##   movie_facebook_likes
## 1                33000
## 2                    0
## 3                85000
## 4               164000
## 5                    0
 ## 6                24000

Then I run kmeans as shown below:

set.seed(111)
km_out <- kmeans(df.num1,centers=3) #perform kmeans cluster with k=3

Now we calculate the distance between objects and cluster centers to determine the outliers and identify, for example, the 5 largest distances that are outliers (arbitrary identification).

centers <- km_out$centers[km_out$cluster, ] # "centers" is a data frame of 3    centers but the length of dataset so we can calculate distance difference easily.
distances <- sqrt(rowSums((df.num1 - centers)^2))
(outliers <- order(distances, decreasing=T)[1:5])# these rows are 5 top outliers
## [1] 3860 3006 2324 2335 3424

allows you to get a data block with added distance:

df.num1$distance<-distances
df.num1$cluster<-km_out$cluster

print out emissions information (the largest five distance values)

(df.num1[outliers,])

##      num_critic_for_reviews duration director_facebook_likes
## 3860                    202      112                       0
## 3006                     73      134                      45
## 2324                    174      134                    6000
## 2335                    105      103                      78
## 3424                    150      124                      78
##      actor_3_facebook_likes actor_1_facebook_likes   gross num_voted_users
## 3860                     38                    717  211667           53508
## 3006                      0                      9  195888            5603
## 2324                    745                    893 2298191          221552
## 2335                    101                    488  410388           13727
## 3424                      4                      6  439162          106160
##      cast_total_facebook_likes facenumber_in_poster num_user_for_reviews
## 3860                       907                    0                  131
## 3006                        11                    0                   45
## 2324                      2710                    0                  570
## 2335                       991                    1                   79
## 3424                        28                    0                  430
##       budget title_year actor_2_facebook_likes imdb_score aspect_ratio
## 3860 4.2e+09       2005                    126        7.7          2.4
## 3006 2.5e+09       2005                      2        7.1          2.4
## 2324 2.4e+09       1997                    851        8.4          1.8
## 2335 2.1e+09       2004                    336        6.9          1.8
## 3424 1.1e+09       1988                      5        8.1          1.8
##      movie_facebook_likes distance cluster
## 3860                 4000  4.1e+09       2
## 3006                  607  2.4e+09       2
## 2324                11000  2.3e+09       2
## 2335                  973  2.0e+09       2
## 3424                    0  9.8e+08       2

But these are just data points selected based on the greatest distance from the centers of the clusters .....

, , - -, , , z ( > 2sd, outlier) , ()........

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Answer 1

, , , z-score, .

iris. QUITE , , outlier .

df.num1 = iris[,-5]

set.seed(111)

km_out = kmeans(df.num1, 3)
km_out_global = kmeans(df.num1, 1)

cluster_centers = km_out$centers[km_out$cluster,]

cluster_distances = sqrt(rowSums(df.num1 - cluster_centers)^2)
global_distances  = sqrt(rowSums(df.num1 - km_out_global$centers)^2)

df.num1_v1 = data.frame(df.num1, cluster = km_out$cluster, c_dist = cluster_distances)

CM = ave(df.num1_v1$c_dist, df.num1_v1$cluster, FUN = function(x) mean(x, na.rm=TRUE))
CSd = ave(df.num1_v1$c_dist, df.num1_v1$cluster, FUN = function(x) sd(x, na.rm=TRUE))
GM = mean(df.num1_v1$c_dist)
GSd = sd(df.num1_v1$c_dist)

cluster_z_score = (cluster_distances - CM)/CSd
global_z_score  = (global_distances  - GM)/GSd 

df.num1_v2 = data.frame(df.num1_v1, CM, CSd, cluster_z_score, 
                        cluster_outlier = ifelse(cluster_z_score > 2 | cluster_z_score < -2, T , F))

df.num1_v3 = data.frame(df.num1, 
                        cluster_outlier = ifelse(cluster_z_score > 2 | cluster_z_score < -2, T , F),
                        global_outlier  = ifelse(global_z_score > 2 | global_z_score < -2, T , F)
                        )
#You can modify your threshold at ifelse

table(df.num1_v2$cluster_outlier)
FALSE  TRUE 
141     9 

df.num1_v2[11:16,]
   Sepal.Length Sepal.Width Petal.Length Petal.Width cluster distances      CM       CSd     z_score Outlier
11          5.4         3.7          1.5         0.2       3     0.658 0.63232 0.4551378  0.05642247   FALSE
12          4.8         3.4          1.6         0.2       3     0.142 0.63232 0.4551378 -1.07730008   FALSE
13          4.8         3.0          1.4         0.1       3     0.842 0.63232 0.4551378  0.46069563   FALSE
14          4.3         3.0          1.1         0.1       3     1.642 0.63232 0.4551378  2.21840501    TRUE
15          5.8         4.0          1.2         0.2       3     1.058 0.63232 0.4551378  0.93527716   FALSE
16          5.7         4.4          1.5         0.4       3     1.858 0.63232 0.4551378  2.69298655    TRUE

, , , . , , , .

table(df.num1_v3$global_outlier)

FALSE  TRUE 
   31   119 

, .

df.num1_v3[11:16,]
   Sepal.Length Sepal.Width Petal.Length Petal.Width cluster_outlier global_outlier
11          5.4         3.7          1.5         0.2           FALSE           TRUE
12          4.8         3.4          1.6         0.2           FALSE          FALSE
13          4.8         3.0          1.4         0.1           FALSE           TRUE
14          4.3         3.0          1.1         0.1            TRUE          FALSE
15          5.8         4.0          1.2         0.2           FALSE           TRUE
16          5.7         4.4          1.5         0.4            TRUE           TRUE