Ward
This notebook illustrates the hierarchical clustering of graphs by the Ward method, after embedding in a space of low dimension.
[1]:
from IPython.display import SVG
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import numpy as np
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from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import Spectral
from sknetwork.hierarchy import Ward, cut_straight, dasgupta_score, tree_sampling_divergence
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph, svg_dendrogram
Graphs
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graph = karate_club(metadata=True)
adjacency = graph.adjacency
position = graph.position
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# hierarchical clustering
ward = Ward()
dendrogram = ward.fit_transform(adjacency)
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image = svg_dendrogram(dendrogram)
SVG(image)
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[7]:
# cuts
labels = cut_straight(dendrogram)
print(labels)
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1]
[8]:
n_clusters = 4
labels, dendrogram_aggregate = cut_straight(dendrogram, n_clusters, return_dendrogram=True)
print(labels)
[0 2 0 3 0 0 0 3 0 0 0 0 3 3 1 1 0 2 1 2 1 2 1 0 0 0 0 0 0 0 0 0 1 1]
[9]:
_, counts = np.unique(labels, return_counts=True)
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# aggregate dendrogram
image = svg_dendrogram(dendrogram_aggregate, names=counts, rotate_names=False)
SVG(image)
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# clustering
image = svg_graph(adjacency, position, labels=labels)
SVG(image)
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# metrics
dasgupta_score(adjacency, dendrogram)
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0.5082956259426847
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# other embedding
ward = Ward(embedding_method=Spectral(4))
Directed graphs
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graph = painters(metadata=True)
adjacency = graph.adjacency
position = graph.position
names = graph.names
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# hierarchical clustering
ward = Ward()
dendrogram = ward.fit_transform(adjacency)
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image = svg_dendrogram(dendrogram, names, n_clusters=3, rotate=True)
SVG(image)
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# cut with 3 clusters
labels = cut_straight(dendrogram, n_clusters = 3)
print(labels)
[0 0 1 1 0 2 0 0 0 2 0 1 0 0]
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image = svg_digraph(adjacency, position, names=names, labels=labels)
SVG(image)
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[19]:
# metrics
dasgupta_score(adjacency, dendrogram)
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0.31285714285714294
Bipartite graphs
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graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col
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# hierarchical clustering
ward = Ward(co_cluster = True)
ward.fit(biadjacency)
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Ward(embedding_method=Spectral(n_components=10, decomposition='rw', regularization=-1, normalized=True), co_cluster=True)
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dendrogram_row = ward.dendrogram_row_
dendrogram_col = ward.dendrogram_col_
dendrogram_full = ward.dendrogram_full_
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image = svg_dendrogram(dendrogram_row, names_row, n_clusters=4, rotate=True)
SVG(image)
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image = svg_dendrogram(dendrogram_col, names_col, n_clusters=4, rotate=True)
SVG(image)
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[25]:
# cuts
labels = cut_straight(dendrogram_full, n_clusters = 4)
n_row = biadjacency.shape[0]
labels_row = labels[:n_row]
labels_col = labels[n_row:]
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image = svg_bigraph(biadjacency, names_row, names_col, labels_row, labels_col)
SVG(image)
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