UNIT07A：Clusting Analysis & Dimemnsion Reduction

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pacman::p_load(dplyr, ggplot2, readr, FactoMineR, factoextra, dendextend)

【A】The wholesales dataset

W = read.csv('data/wholesales.csv')
W$Channel = factor( paste0("Ch",W$Channel) )
W$Region = factor( paste0("Reg",W$Region) )
W[3:8] = lapply(W[3:8], log, base=10) 
summary(W)

 Channel    Region        Fresh            Milk         Grocery     
 Ch1:298   Reg1: 77   Min.   :0.477   Min.   :1.74   Min.   :0.477  
 Ch2:142   Reg2: 47   1st Qu.:3.495   1st Qu.:3.19   1st Qu.:3.333  
           Reg3:316   Median :3.930   Median :3.56   Median :3.677  
                      Mean   :3.792   Mean   :3.53   Mean   :3.666  
                      3rd Qu.:4.229   3rd Qu.:3.86   3rd Qu.:4.028  
                      Max.   :5.050   Max.   :4.87   Max.   :4.968  
     Frozen     Detergents_Paper   Delicassen   
 Min.   :1.40   Min.   :0.477    Min.   :0.477  
 1st Qu.:2.87   1st Qu.:2.409    1st Qu.:2.611  
 Median :3.18   Median :2.912    Median :2.985  
 Mean   :3.17   Mean   :2.947    Mean   :2.895  
 3rd Qu.:3.55   3rd Qu.:3.594    3rd Qu.:3.260  
 Max.   :4.78   Max.   :4.611    Max.   :4.681  

【B】Clustering Analysis

Clustering: Group similar subjects for easier observation and operation

• subjects： a retail store in each row
• variables： each column is the sales amount (normalized) of a product category

The most common used Methods of Clustering :

• Hierarchical Clustering
• Kmean Clustering
• …

💡 Steps of Hierarchical Cluster Analysis：
  ■ scale() : Standardize the Variable
  ■ dist() : Calculate Distance Matrix
  ■ hclust() : Call hclust Function
  ■ plot() : Make Deprogram
  ■ rect.hclust() : Cut the Dendrogram
  ■ cutree() : Obtain the Clustering Vector

For simplicity, let’s start with two clutering variables

hc = W[,3:4] %>% scale %>% dist %>% hclust

The result of the cultering analysis is returned and kept in the data object hc.

Make and Interpreting the Dendrogram Determining the number of groups and Cut Dendrogram

plot(hc)
k=6; rect.hclust(hc, k=k, border="red")

Obtain and Save the Clustering Vector

W$group = cutree(hc, k=8) %>% factor

Save it as an categorical variable, so it won’t be interpreted as numerics.

Plot the subjects in the Variable Space

ggplot(W, aes(x=Fresh, y=Milk, col=group)) +
  geom_point(size=3, alpha=0.5)

【C】Clustering with 5 Variables

hc = W[,3:7] %>% scale %>% dist %>% hclust
plot(hc)
k = 6; rect.hclust(hc, k, border="red")

W$group = cutree(hc, k) %>% factor

For better looks …

hc %>% as.dendrogram %>% color_branches(k) %>% color_labels(k,col='white') %>% plot

【D】Dimension Reduction

Dimension Reduction: Compress the space of many variables into a low dimension space for easier observation

• Why doing Dimension Reduction？
• The underlying logic of Dimension Reduction
• The pro and con of Dimension Reduction

The most used Methods of Dimension Reduction：

• Principle Component Analysis - PCA()
• Multi-Dimensional Scaling - cmdscale()
• …

W[,3:8] %>% PCA(graph=F) %>% fviz_pca_biplot()

W[,3:8] %>% PCA(graph=FALSE) %>% fviz_pca_biplot(
  col.ind=W$group,  # 
  label="var", pointshape=19, mean.point=F,
  addEllipses=T, ellipse.level=0.7,
  ellipse.type = "convex", palette="ucscgb",
  repel=T
  )

💡 Key Learnings：
  ■ The Concept and Purpose of Clustering Analysis
  ■ Clustering Analysis in a pipeline
    ■ df %>% scale %>% dist %>% hclust
  ■ Making, Interpreting and Cutting Dendrogram

  ■ The Concept and Purpose of Dimension Reduction
  ■ Combining Dimension Reduction and Clustering Analysis
  ■ Visualize the subject/groups in an Reduced Variable Space.

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