PageRank
This notebook illustrates the classification of the nodes of a graph by PageRank, based on the labels of a few nodes.
[1]:
from IPython.display import SVG
[2]:
import numpy as np
[3]:
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.classification import PageRankClassifier
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph
Graphs
[4]:
graph = karate_club(metadata=True)
adjacency = graph.adjacency
position = graph.position
labels_true = graph.labels
[5]:
seeds = {i: labels_true[i] for i in [0, 33]}
[6]:
pagerank = PageRankClassifier()
labels_pred = pagerank.fit_transform(adjacency, seeds)
[7]:
precision = np.round(np.mean(labels_pred == labels_true), 2)
precision
[7]:
0.97
[8]:
image = svg_graph(adjacency, position, labels=labels_pred, seeds=seeds)
SVG(image)
[8]:
[9]:
# soft classification (here probability of label 1)
label = 1
membership = pagerank.membership_
scores = membership[:,label].toarray().ravel()
[10]:
image = svg_graph(adjacency, position, scores=scores, seeds=seeds)
SVG(image)
[10]:
Directed graphs
[11]:
graph = painters(metadata=True)
adjacency = graph.adjacency
position = graph.position
names = graph.names
[12]:
rembrandt = 5
klimt = 6
cezanne = 11
seeds = {cezanne: 0, rembrandt: 1, klimt: 2}
[13]:
pagerank = PageRankClassifier()
labels = pagerank.fit_transform(adjacency, seeds)
[14]:
image = svg_digraph(adjacency, position, names, labels=labels, seeds=seeds)
SVG(image)
[14]:
[15]:
# soft classification
membership = pagerank.membership_
scores = membership[:,0].toarray().ravel()
[16]:
image = svg_digraph(adjacency, position, names, scores=scores, seeds=[cezanne])
SVG(image)
[16]:
Bipartite graphs
[17]:
graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col
[18]:
inception = 0
drive = 3
budapest = 8
[19]:
seeds_row = {inception: 0, drive: 1, budapest: 2}
[20]:
pagerank = PageRankClassifier()
pagerank.fit(biadjacency, seeds_row)
labels_row = pagerank.labels_row_
labels_col = pagerank.labels_col_
[21]:
image = svg_bigraph(biadjacency, names_row, names_col, labels_row, labels_col, seeds_row=seeds_row)
SVG(image)
[21]:
[22]:
# soft classification
membership_row = pagerank.membership_row_
membership_col = pagerank.membership_col_
[23]:
label = 1
scores_row = membership_row[:,label].toarray().ravel()
scores_col = membership_col[:,label].toarray().ravel()
[24]:
image = svg_bigraph(biadjacency, names_row, names_col, scores_row=scores_row, scores_col=scores_col,
seeds_row=seeds_row)
SVG(image)
[24]:
