Summary - Hierarchical clustering

In this group you learned hierarchical clustering and dendrograms.

Summary: hierarchical clustering

In this group:

Agglomerative clustering starts from every example and merges the closest clusters; the result is a tree.
The linkage matrix and the dendrogram; a large distance jump is a good cut point.
fcluster (maxclust/distance) and AgglomerativeClustering (n_clusters/distance_threshold).
Linkage types: single (chains), complete, average, ward (default).
It is deterministic; slow on large data; for new examples a classifier is trained on the labels.

Exercise Dendrogram and cut

Compute the Ward linkage on the small data, draw the dendrogram and save it. Cut at the middle of the largest jump between consecutive merge distances ((Z[i, 2] + Z[i + 1, 2]) / 2, i = np.diff(Z[:, 2]).argmax()) and print the labels with fcluster(..., criterion="distance").

Show example solution

import numpy as np
from scipy.cluster.hierarchy import linkage, fcluster

X = np.array([[0, 0], [0, 1], [1, 0], [5, 5], [5, 6], [6, 5], [12, 0], [12, 1]])
from scipy.cluster.hierarchy import dendrogram
import matplotlib.pyplot as plt

Z = linkage(X, method="ward")
fig, ax = plt.subplots()
dendrogram(Z, ax=ax)
fig.savefig("agac.png")
i = np.diff(Z[:, 2]).argmax()
esik = (Z[i, 2] + Z[i + 1, 2]) / 2
print(fcluster(Z, t=esik, criterion="distance"))

Test yourself

Which linkage produces clusters most similar to KMeans?
- single
- average
- complete
- ward
Show answer

ward — Like KMeans, Ward picks the merge that least increases the within-cluster squared distance.
Draw the dendrogram.
```
____(Z, ax=ax)
```
Show answer
```
dendrogram(Z, ax=ax)
```
Match the tools.

linkage

Merge matrix
dendrogram

Tree drawing
fcluster

Cutting the tree
AgglomerativeClustering

scikit-learn version

Next lesson: Preparing data

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