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Scikit-network-10：Embedding

Embedding

Spectral

介绍图的谱嵌入

from IPython.display import SVG
import numpy as np
from scipy import sparse
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import Spectral
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

# embedding in dimension 2
spectral = Spectral(2)
embedding = spectral.fit_transform(adjacency)
embedding

array([[-0.89876639,  0.43842784],
       [-0.30788795,  0.95142262],
       [ 0.04238223,  0.99910147],
       [-0.3441381 ,  0.93891904],
       [-0.82105705, -0.57084615],
       [-0.73816864, -0.67461624],
       [-0.73816864, -0.67461624],
       [-0.34568408,  0.93835096],
       [ 0.73618645,  0.67677878],
       [ 0.78358705,  0.62128201],
       [-0.82105705, -0.57084615],
       [-0.85986949,  0.51051392],
       [-0.51782927,  0.85548398],
       [-0.22290148,  0.97484098],
       [ 0.90007317, -0.43573879],
       [ 0.90007317, -0.43573879],
       [-0.66856684, -0.74365206],
       [-0.51516599,  0.85709043],
       [ 0.90007317, -0.43573879],
       [-0.28066995,  0.95980434],
       [ 0.90007317, -0.43573879],
       [-0.51516599,  0.85709043],
       [ 0.90007317, -0.43573879],
       [ 0.77997798, -0.62580696],
       [ 0.68984248, -0.7239595 ],
       [ 0.6717557 , -0.74077276],
       [ 0.8252923 , -0.56470578],
       [ 0.87212272, -0.4892872 ],
       [ 0.99996837, -0.00795388],
       [ 0.81142925, -0.58445066],
       [ 0.77271246,  0.63475622],
       [ 0.75614343, -0.65440593],
       [ 0.91271077, -0.40860622],
       [ 0.94609416, -0.32389172]])

# visualization
image = svg_graph(adjacency, position=embedding, labels=labels)
SVG(image)

在这里插入图片描述

# find the embedding of a new node
adjacency_vector = np.zeros(adjacency.shape[0], dtype = int)
adjacency_vector, adjacency_vector.shape

(array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
 (34,))

adjacency_vector[:6] = np.ones(6, dtype = int)
adjacency_vector

array([1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

embedding_vector = spectral.predict(adjacency_vector)
embedding_vector

array([-0.97908533,  0.20345003])

# visualization
adjacency_extend = sparse.vstack([adjacency, adjacency_vector])
adjacency_extend = sparse.hstack([adjacency_extend, sparse.csr_matrix((35, 1))], format='csr')
embedding_extend = np.vstack([embedding, embedding_vector])
labels_extend = list(labels) + [-1]

image = svg_graph(adjacency_extend, position=embedding_extend, labels=labels_extend, seeds={34:1})
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
position = graph.position
names = graph.names

# embedding
spectral = Spectral()  # 默认是2维
embedding = spectral.fit_transform(adjacency)

image = svg_digraph(adjacency, position=embedding, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

# embedding
spectral = Spectral(2)
spectral.fit(biadjacency)

Spectral(n_components=2, decomposition='rw', regularization=-1, normalized=True)

embedding_row = spectral.embedding_row_
embedding_col = spectral.embedding_col_

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=embedding_row, position_col=embedding_col,
                    color_row='blue', color_col='red')
SVG(image)

在这里插入图片描述

SVD

通过邻接矩阵的奇异值分解表示图的嵌入

 
from IPython.display import SVG
import numpy as np
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import SVD, cosine_modularity
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

svd = SVD(2)
embedding = svd.fit_transform(adjacency)
embedding

array([[-2.390928  ,  1.92543628],
       [-1.78876603,  1.33853197],
       [-2.13334091,  0.65279087],
       [-1.42033097,  1.25893017],
       [-0.51094331,  0.6664152 ],
       [-0.53457894,  0.72494643],
       [-0.53457894,  0.72494643],
       [-1.14982359,  1.03990599],
       [-1.52944994, -0.27381159],
       [-0.69055597, -0.23942952],
       [-0.51094331,  0.6664152 ],
       [-0.35549144,  0.38686107],
       [-0.56667116,  0.6398069 ],
       [-1.52318706,  0.66931691],
       [-0.68200769, -0.6951449 ],
       [-0.68200769, -0.6951449 ],
       [-0.15896609,  0.29131429],
       [-0.62145136,  0.6558006 ],
       [-0.68200769, -0.6951449 ],
       [-0.99481483,  0.28521152],
       [-0.68200769, -0.6951449 ],
       [-0.62145136,  0.6558006 ],
       [-0.68200769, -0.6951449 ],
       [-1.00965214, -1.08025878],
       [-0.38371747, -0.28076981],
       [-0.39820485, -0.37569412],
       [-0.50832429, -0.57716769],
       [-0.89772699, -0.51288909],
       [-0.88158982, -0.34166407],
       [-0.90770568, -1.02815711],
       [-1.17537152, -0.48121995],
       [-1.28483587, -0.50882896],
       [-2.07584773, -1.61533845],
       [-2.51112984, -1.84444934]])

image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
names = graph.names

svd = SVD(2)
embedding = svd.fit_transform(adjacency)

image = svg_digraph(adjacency, embedding, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

svd = SVD(2, normalized=False)
svd.fit(biadjacency)

embedding_row = svd.embedding_row_
embedding_col = svd.embedding_col_

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=embedding_row, position_col=embedding_col,
                    color_row='blue', color_col='red', scale=1.5)
SVG(image)

在这里插入图片描述

GSVD

通过邻接矩阵的广义奇异值分解表示图的嵌入

 
from IPython.display import SVG

import numpy as np
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import GSVD
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

gsvd = GSVD(2, normalized=False)
embedding = gsvd.fit_transform(adjacency)

image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
position = graph.position
names = graph.names

gsvd = GSVD(2, normalized=False)
embedding = gsvd.fit_transform(adjacency)

image = svg_digraph(adjacency, embedding, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

gsvd = GSVD(2, normalized=False)
gsvd.fit(biadjacency)

GSVD(n_components=2, regularization=None, factor_row=0.5, factor_col=0.5, factor_singular=0.0, normalized=False, solver=LanczosSVD(n_iter=None, tol=0.0))

embedding_row = gsvd.embedding_row_
embedding_col = gsvd.embedding_col_

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=embedding_row, position_col=embedding_col,
                    color_row='blue', color_col='red')
SVG(image)

在这里插入图片描述

PCA

通过邻接矩阵的主成分分析表示图的嵌入

 
import numpy as np
from IPython.display import SVG
from sknetwork.embedding import PCA
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

pca = PCA(2)
embedding = pca.fit_transform(adjacency)

image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
names = graph.names

pca = PCA(2)
embedding = pca.fit_transform(adjacency)

image = svg_digraph(adjacency, embedding, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

pca = PCA(2)
pca.fit(biadjacency)

PCA(n_components=2, normalized=False, solver=LanczosSVD(n_iter=None, tol=0.0))

embedding_row = pca.embedding_row_
embedding_col = pca.embedding_col_

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=embedding_row, position_col=embedding_col,
                    color_row='blue', color_col='red')
SVG(image)

在这里插入图片描述

Random Projection

通过随机投影表示图的嵌入

from IPython.display import SVG
import numpy as np
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import RandomProjection
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

projection = RandomProjection(2)
embedding = projection.fit_transform(adjacency)

image = svg_graph(adjacency, position=embedding, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
position = graph.position
names = graph.names

projection = RandomProjection(2)
embedding = projection.fit_transform(adjacency)

image = svg_digraph(adjacency, position=embedding, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

projection = RandomProjection(2, normalized=False)
projection.fit(biadjacency)

embedding_row = projection.embedding_row_
embedding_col = projection.embedding_col_

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=embedding_row, position_col=embedding_col,
                    color_row='blue', color_col='red')
SVG(image)

在这里插入图片描述

Louvain

通过Louvain聚类表示图的嵌入

from IPython.display import SVG
import numpy as np
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import LouvainEmbedding
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

louvain = LouvainEmbedding()
embedding = louvain.fit_transform(adjacency)
embedding.shape

(34, 4)

position = embedding[:, :2]
image = svg_graph(adjacency, position=position, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
names = graph.names

louvain = LouvainEmbedding()
embedding = louvain.fit_transform(adjacency)
embedding.shape

(14, 3)

position = embedding[:, :2]
image = svg_digraph(adjacency, position=position, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

louvain = LouvainEmbedding()
louvain.fit(biadjacency)

LouvainEmbedding(resolution=1, modularity='dugue', tol_optimization=0.001, tol_aggregation=0.001, n_aggregations=-1, shuffle_nodes=False, isolated_nodes='remove')

embedding_row = louvain.embedding_row_
embedding_col = louvain.embedding_col_
embedding_row.shape

(15, 4)

position_row = embedding_row[:, :2]
position_col = embedding_col[:, :2]

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=position_row, position_col=position_col,
                    color_row='blue', color_col='red')
SVG(image)

在这里插入图片描述

Hierarchical Louvain

使用分层Louvain算法表示图的嵌入

from IPython.display import SVG
import numpy as np
from sknetwork.data import karate_club, painters, movie_actor
from sknetwork.embedding import LouvainNE
from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

louvain = LouvainNE(2)
embedding = louvain.fit_transform(adjacency)

image = svg_graph(adjacency, position=embedding, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
position = graph.position
names = graph.names

louvain = LouvainNE(2)
embedding = louvain.fit_transform(adjacency)

image = svg_digraph(adjacency, position=embedding, names=names)
SVG(image)

在这里插入图片描述

二部图

graph = movie_actor(metadata=True)
biadjacency = graph.biadjacency
names_row = graph.names_row
names_col = graph.names_col

louvain = LouvainNE()
louvain.fit(biadjacency)

embedding_row = louvain.embedding_row_
embedding_col = louvain.embedding_col_

image = svg_bigraph(biadjacency, names_row, names_col,
                    position_row=embedding_row, position_col=embedding_col,
                    color_row='blue', color_col='red')
SVG(image)

在这里插入图片描述

Spring

通过力定向算法表示图的二维嵌入

 
from IPython.display import SVG
import numpy as np
from sknetwork.data import karate_club, painters
from sknetwork.embedding import Spring
from sknetwork.visualization import svg_graph, svg_digraph

图

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

spring = Spring(2)
embedding = spring.fit_transform(adjacency)

image = svg_graph(adjacency, position=embedding, labels=labels)
SVG(image)

在这里插入图片描述

有向图

graph = painters(metadata=True)
adjacency = graph.adjacency
names = graph.names

spring = Spring(2)
embedding = spring.fit_transform(adjacency)
embedding.shape

image = svg_digraph(adjacency, position=embedding, names=names)
SVG(image)

在这里插入图片描述

ForceAtlas

通过力量定向算法 Atlas2 表示图的嵌入

from IPython.display import SVG

from sknetwork.data import karate_club
from sknetwork.embedding.force_atlas import ForceAtlas
from sknetwork.visualization import svg_graph

graph = karate_club(metadata=True)
adjacency = graph.adjacency
labels = graph.labels

forceatlas2 = ForceAtlas()
embedding = forceatlas2.fit_transform(adjacency)
image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

# 这里介绍不同设置下对图嵌入表示的影响

# 用对数吸引力代替线性吸引力（默认是线性吸引力）
forceatlas2 = ForceAtlas(lin_log = True)
embedding = forceatlas2.fit_transform(adjacency)
image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

# 设置重力和斥力常数(重力系数和斥力系数)来设置布局中每个力的重要性，将值保持在0.01和0.1之间
forceatlas2 = ForceAtlas(gravity_factor = 0.1)
embedding = forceatlas2.fit_transform(adjacency)
image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

# 设置摆动容许量，较低的摆动产生较低的速度和更高的精度
forceatlas2 = ForceAtlas(tolerance=1.5)
embedding = forceatlas2.fit_transform(adjacency)
image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述

# 设置近似范围，如果提供了正值，则仅在此距离内使用给定节点的节点来计算排斥力
forceatlas2 = ForceAtlas(approx_radius=2)
embedding = forceatlas2.fit_transform(adjacency)
image = svg_graph(adjacency, embedding, labels=labels)
SVG(image)

在这里插入图片描述