UNSUPERVISED LEARNING IN R. Introduction to hierarchical clustering
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1 UNSUPERVISED LEARNING IN R Introduction to hierarchical clustering
2 Hierarchical clustering Number of clusters is not known ahead of time Two kinds: bottom-up and top-down, this course bottom-up
3 Hierarchical clustering Simple Example
4 Hierarchical clustering 5 Clusters Each point a cluster
5 Hierarchical clustering 4 Clusters
6 Hierarchical clustering 3 Clusters
7 Hierarchical clustering 2 Clusters
8 Hierarchical clustering 1 Cluster
9 Hierarchical clustering in R > # Calculates similarity as Euclidean distance between observations > dist_matrix <- dist(x) > # Returns hierarchical clustering model > hclust(d = dist_matrix) Call: hclust(d = s) Cluster method : complete Distance : euclidean Number of objects: 50 x is a data matrix
10 UNSUPERVISED LEARNING IN R Let s practice!
11 UNSUPERVISED LEARNING IN R Selecting number of clusters
12 Interpreting results > # Create hierarchical cluster model: hclust.out > hclust.out <- hclust(dist(x)) > # Inspect the result > summary(hclust.out) Length Class Mode merge 98 -none- numeric height 49 -none- numeric order 50 -none- numeric labels 0 -none- NULL method 1 -none- character call 2 -none- call dist.method 1 -none- character Information isn t particularly useful
13 Dendrogram Tree shaped structure used to interpret hierarchical clustering models height
14 Dendrogram Tree shaped structure used to interpret hierarchical clustering models height
15 Dendrogram Tree shaped structure used to interpret hierarchical clustering models height
16 Dendrogram Tree shaped structure used to interpret hierarchical clustering models height
17 Dendrogram Tree shaped structure used to interpret hierarchical clustering models height
18 Dendrogram plo!ing in R height 6 > # Draws a dendrogram > plot(hclust.out) > abline(h = 6, col = "red")
19 Tree 'cutting' in R Need to cut the tree to get cluster assignments > # Cut by height h > cutree(hclust.out, h = 6) [1] [32] > # Cut by number of clusters k > cutree(hclust.out, k = 2) [1] [32]
20 UNSUPERVISED LEARNING IN R Let s practice!
21 UNSUPERVISED LEARNING IN R Clustering linkage and practical matters
22 Linking clusters in hierarchical clustering How is distance between clusters determined? Rules? Four methods to determine which cluster should be linked Complete: pairwise similarity between all observations in cluster 1 and cluster 2, and uses largest of similarities Single: same as above but uses smallest of similarities Average: same as above but uses average of similarities Centroid: finds centroid of cluster 1 and centroid of cluster 2, and uses similarity between two centroids
23 Linking methods: complete and average
24 Linking method: single
25 Linking method: centroid
26 Linkage in R > # Fitting hierarchical clustering models using different methods > hclust.complete <- hclust(d, method = "complete") > hclust.average <- hclust(d, method = "average") > hclust.single <- hclust(d, method = "single")
27 Practical matters Data on different scales can cause undesirable results in clustering methods Solution is to scale data so that features have same mean and standard deviation Subtract mean of a feature from all observations Divide each feature by the standard deviation of the feature Normalized features have a mean of zero and a standard deviation of one
28 Practical matters > # Check if scaling is necessary > colmeans(x) x is a data matrix [1] > apply(x, 2, sd) [1] > # Produce new matrix with columns of mean of 0 and sd of 1 > scaled_x <- scale(x) > colmeans(scaled_x) [1] e e-17 > apply(scaled_x, 2, sd) [1] 1 1 Normalized features have mean of 0 and standard deviation of 1
29 UNSUPERVISED LEARNING IN R Let s practice!
30 UNSUPERVISED LEARNING IN R Review of hierarchical clustering
31 Hierarchical clustering review > # Fitting various hierarchical clustering models > hclust.complete <- hclust(d, method = "complete") > hclust.average <- hclust(d, method = "average") > hclust.single <- hclust(d, method = "single")
32 Linking methods: complete and average
33 height Hierarchical clustering review
34 height Hierarchical clustering review
35 height Hierarchical clustering review
36 height Hierarchical clustering review
37 Hierarchical clustering review > # Scale the data > pokemon.scaled <- scale(pokemon) > # Create hierarchical and k-means clustering models > hclust.pokemon <- hclust(dist(pokemon.scaled), method = "complete") > km.pokemon <- kmeans(pokemon.scaled, centers = 3, nstart = 20, iter.max = 50) > # Compare results of the models > cut.pokemon <- cutree(hclust.pokemon, k = 3) > table(km.pokemon$cluster, cut.pokemon) cut.pokemon
38 UNSUPERVISED LEARNING IN R Let s practice!
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