Silhouette analysis: observation level performance

Cluster Analysis in R

Dmitriy (Dima) Gorenshteyn

Lead Data Scientist, Memorial Sloan Kettering Cancer Center

Soccer lineup with K = 3

Silhouette width

Within Cluster Distance: C(i)

Closest Neighbor Distance: N(i)

Silhouette width

Within Cluster Distance: C(i)

Closest Neighbor Distance: N(i)

Silhouette width

Within Cluster Distance: C(i)

Closest Neighbor Distance: N(i)

Silhouette width

Within Cluster Distance: C(i)

Closest Neighbor Distance: N(i)

Silhouette width

Within Cluster Distance: C(i)

Closest Neighbor Distance: N(i)

Silhouette width: S(i)

1: Well matched to cluster
0: On border between two clusters
-1: Better fit in neighboring cluster

Calculating S(i)

library(cluster)
pam_k3 <- pam(lineup, k = 3)

pam_k3$silinfo$widths

   cluster neighbor    sil_width
4        1        2  0.465320054
2        1        3  0.321729341
10       1        2  0.311385893
1        1        3  0.271890169
9        2        1  0.443606497
...     ...      ...         ...

Silhouette plot

sil_plot <- silhouette(pam_k3)
plot(sil_plot)

Silhouette plot

sil_plot <- silhouette(pam_k3)
plot(sil_plot)

Average silhouette width

pam_k3$silinfo$avg.width

[1] 0.353414

1: Well matched to each cluster
0: On border between clusters
-1: Poorly matched to each cluster

Highest average silhouette width

library(purrr)

sil_width <- map_dbl(2:10,  function(k){
  model <- pam(x = lineup, k = k)
  model$silinfo$avg.width
})
sil_df <- data.frame(
  k = 2:10,
  sil_width = sil_width
)
print(sil_df)

     k    sil_width
1    2    0.4164141
2    3    0.3534140
3    4    0.3535534
4    5    0.3724115
...  ...        ...

Choosing K using average silhouette width

ggplot(sil_df, aes(x = k, y = sil_width)) +
  geom_line() +
  scale_x_continuous(breaks = 2:10)

Choosing K using average silhouette width

ggplot(sil_df, aes(x = k, y = sil_width)) +
  geom_line() +
  scale_x_continuous(breaks = 2:10)

Let's practice!

Cluster Analysis in R