Louvain
This notebook illustrates the clustering of a graph by the Louvain algorithm.
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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.clustering import Louvain, modularity, bimodularity
from sknetwork.linalg import normalize
from sknetwork.utils import bipartite2undirected, membership_matrix
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph
Graphs
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graph = karate_club(metadata=True)
adjacency = graph.adjacency
position = graph.position
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louvain = Louvain()
labels = louvain.fit_transform(adjacency)
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labels_unique, counts = np.unique(labels, return_counts=True)
print(labels_unique, counts)
[0 1 2 3] [12 11 6 5]
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image = svg_graph(adjacency, position, labels=labels)
SVG(image)
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# metric
modularity(adjacency, labels)
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0.4188034188034188
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# aggregate graph
adjacency_aggregate = louvain.aggregate_
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average = normalize(membership_matrix(labels).T)
position_aggregate = average.dot(position)
labels_unique, counts = np.unique(labels, return_counts=True)
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image = svg_graph(adjacency_aggregate, position_aggregate, counts, labels=labels_unique,
display_node_weight=True, node_weights=counts)
SVG(image)
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# soft clustering (here probability of label 1)
scores = louvain.membership_[:,1].toarray().ravel()
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image = svg_graph(adjacency, position, scores=scores)
SVG(image)
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Directed graphs
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graph = painters(metadata=True)
adjacency = graph.adjacency
names = graph.names
position = graph.position
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# clustering
louvain = Louvain()
labels = louvain.fit_transform(adjacency)
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labels_unique, counts = np.unique(labels, return_counts=True)
print(labels_unique, counts)
[0 1 2] [5 5 4]
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image = svg_digraph(adjacency, position, names=names, labels=labels)
SVG(image)
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modularity(adjacency, labels)
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0.32480000000000003
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# aggregate graph
adjacency_aggregate = louvain.aggregate_
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average = normalize(membership_matrix(labels).T)
position_aggregate = average.dot(position)
labels_unique, counts = np.unique(labels, return_counts=True)
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image = svg_digraph(adjacency_aggregate, position_aggregate, counts, labels=labels_unique,
display_node_weight=True, node_weights=counts)
SVG(image)
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# soft clustering
scores = louvain.membership_[:,1].toarray().ravel()
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image = svg_graph(adjacency, position, scores=scores)
SVG(image)
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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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# clustering
louvain = Louvain()
louvain.fit(biadjacency)
labels_row = louvain.labels_row_
labels_col = louvain.labels_col_
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image = svg_bigraph(biadjacency, names_row, names_col, labels_row, labels_col)
SVG(image)
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# metric
bimodularity(biadjacency, labels_row, labels_col)
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0.5742630385487529
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# aggregate graph
biadjacency_aggregate = louvain.aggregate_
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labels_unique_row, counts_row = np.unique(labels_row, return_counts=True)
labels_unique_col, counts_col = np.unique(labels_col, return_counts=True)
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image = svg_bigraph(biadjacency_aggregate, counts_row, counts_col, labels_unique_row, labels_unique_col,
display_node_weight=True, node_weights_row=counts_row, node_weights_col=counts_col)
SVG(image)
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# soft clustering
scores_row = louvain.membership_row_[:,1].toarray().ravel()
scores_col = louvain.membership_col_[:,1].toarray().ravel()
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image = svg_bigraph(biadjacency, names_row, names_col, scores_row=scores_row, scores_col=scores_col)
SVG(image)
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