GCN学习（四）：使用numpy从底层一步步搭建GCN网络：Zachary数据集随机参数无训练实战

本文主要是介绍GCN学习（四）：使用numpy从底层一步步搭建GCN网络：Zachary数据集随机参数无训练实战，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

Zachary 空手道俱乐部是一个被广泛使用的社交网络，其中的节点代表空手道俱乐部的成员，边代表成员之间的相互关系。当年，Zachary 在研究空手道俱乐部的时候，管理员和教员发生了冲突，导致俱乐部一分为二。下图显示了该网络的图表征，其中的节点标注是根据节点属于俱乐部的哪个部分而得到的，「0」表示属于Mr. Hi部分的中心节点，[32」表示属于Officer阵营的中心节点
在这里插入图片描述

通过networkx调用karate club图

import networkx as nx
import numpy as np
#通过nx.to_numpy_array将图节点按照顺序转化成numpy的数组
zkc=nx.karate_club_graph()
order=list(zkc.nodes())
A=nx.to_numpy_array(zkc.nodes(),nodelist=order)

计算GCN的各项变量

具体算法原理见上一篇博客

#具体算法原理见上一篇博客
I=np.eye(A.shape[0])
A_hat=A+I
print('A_hat:',A_hat)
D_hat=np.sum(A_hat,axis=0)
D_hat=np.diag(D_hat)
print('D_hat:',D_hat)
D_hat_I=np.linalg.inv(D_hat)
D_hat_I_=D_hat_I**0.5
D_hat_I_=np.matrix(D_hat_I_)
A_hat=np.matrix(A_hat)
print('D_hat_I:',D_hat_I)
print('D_hat_I_:',D_hat_I_)
>>>A: [[0. 1. 1. ... 1. 0. 0.][1. 0. 1. ... 0. 0. 0.][1. 1. 0. ... 0. 1. 0.]...[1. 0. 0. ... 0. 1. 1.][0. 0. 1. ... 1. 0. 1.][0. 0. 0. ... 1. 1. 0.]]
A_hat: [[1. 1. 1. ... 1. 0. 0.][1. 1. 1. ... 0. 0. 0.][1. 1. 1. ... 0. 1. 0.]...[1. 0. 0. ... 1. 1. 1.][0. 0. 1. ... 1. 1. 1.][0. 0. 0. ... 1. 1. 1.]]
D_hat: [[17.  0.  0. ...  0.  0.  0.][ 0. 10.  0. ...  0.  0.  0.][ 0.  0. 11. ...  0.  0.  0.]...[ 0.  0.  0. ...  7.  0.  0.][ 0.  0.  0. ...  0. 13.  0.][ 0.  0.  0. ...  0.  0. 18.]]
D_hat_I: [[0.05882353 0.         0.         ... 0.         0.         0.        ][0.         0.1        0.         ... 0.         0.         0.        ][0.         0.         0.09090909 ... 0.         0.         0.        ]...[0.         0.         0.         ... 0.14285714 0.         0.        ][0.         0.         0.         ... 0.         0.07692308 0.        ][0.         0.         0.         ... 0.         0.         0.05555556]]
D_hat_I_: [[0.24253563 0.         0.         ... 0.         0.         0.        ][0.         0.31622777 0.         ... 0.         0.         0.        ][0.         0.         0.30151134 ... 0.         0.         0.        ]...[0.         0.         0.         ... 0.37796447 0.         0.        ][0.         0.         0.         ... 0.         0.2773501  0.        ][0.         0.         0.         ... 0.         0.         0.23570226]]

获得随机参数&生成GCN中两个隐层

这里未代入激活函数

W_1=np.random.normal(loc=0,scale=1,size=(A.shape[0],4))
W_2=np.random.normal(loc=0,scale=1,size=(W_1.shape[1],2))
def gcn_layer(W,H):return D_hat_I_*A_hat*D_hat_I_*H*W
H_1=gcn_layer(W_1,I)
H_2=gcn_layer(W_2,H_1)
print('W_1:',W_1)
print('W_2:',W_2)
print('H_1:',H_1)
print('H_2:',H_2)
>>>W_1: [[-0.83170794  0.32384612  0.19254748  0.70696413][-0.18471147  0.0883649  -1.11661952 -0.48318362][ 1.16053196  1.35436878  1.7325107  -0.81340677][-0.05643657  0.78313805  1.48633055 -0.78429642][ 2.04825991  0.75946907  0.7877478   0.40471074][-1.6825711   1.24341323 -0.13138839  0.09831662][ 1.20441677 -1.02081272 -0.15438911  1.03961703][ 0.85859398  1.04836695  0.54997693  0.34259851][-1.24704768 -0.72198946 -2.01097211  0.74801387][-0.69092111  0.52773092  0.28031613  0.25813498][-1.26664724 -1.49773084 -0.93544537 -0.285444  ][-0.24153454  1.91185276 -0.3330864   0.18437171][ 0.57581633  1.47301229  0.85280729  0.21404787][-0.73612301  0.0249905  -0.22220335  2.47315254][ 0.01006193  1.14992678  1.81193055  0.24425048][ 0.49826219  0.46537806  1.15559036  1.22559649][-0.17573175  0.7642652  -0.61541977  1.09116569][-2.0212443  -1.20003893  1.29472694  0.60905143][-0.15924997 -0.1955486   0.93153308 -0.54726901][ 0.10496633 -1.75949359 -0.57203004 -0.44890057][-1.55455233  0.60525928 -0.85878164 -0.17461178][ 2.09575314  1.26960615 -2.41258093  1.70626018][-0.4674859  -0.46671862 -0.08762951  0.49089521][ 0.47360112  0.7122978   1.4140279  -0.02709561][ 1.21027325 -0.58404666  0.69746025  0.25142965][ 0.94810688  1.5624341  -0.07637426 -2.13034201][ 0.36438514  0.6206908   0.0784685   0.25960684][ 1.21386557  0.29242271 -1.09378702 -0.08382282][-0.08687322  0.28939295 -1.42996523  0.96757856][ 0.89381163 -0.85629006  0.57127589 -0.35855218][-0.27673337  0.69421144  2.84473947  1.3983313 ][-0.3101751  -0.64610953 -0.90312309  2.52619311][ 0.41719548 -0.86331992  0.97754337 -0.1387886 ][ 0.83100378  0.35643724 -0.13823076  0.71158029]]
W_2: [[-0.36620028  0.10869551][ 0.20106848 -0.41626057][ 1.46492995  0.18866806][ 1.1037179  -0.59881204]]
H_1: [[-9.77573622e-03  4.47259336e-01 -2.68136684e-01  9.30080792e-01][ 3.91011566e-02  2.40576126e-01  4.02806554e-01  7.51832662e-01][-4.25046615e-02  4.02775288e-01 -1.98745516e-01  4.52892529e-01][ 1.83068787e-01  8.08970173e-01  5.38734247e-01  2.88551670e-01][ 3.63859541e-01 -3.73553995e-01 -4.80970347e-02  3.48014115e-01][-5.14446933e-01 -5.79242231e-02 -4.04343439e-01  5.22178309e-01][ 2.26788840e-01  4.46801019e-01 -1.90257319e-02  6.76501601e-01][ 2.02331834e-01  5.72293659e-01  4.57813658e-01 -1.65381793e-01][-7.06639358e-02  1.41736786e-01  5.13920070e-01  4.02601735e-01][ 8.48009367e-02  4.60180616e-01  3.76219287e-01  4.12828613e-02][-2.81690570e-01  1.32742319e-01 -4.29539179e-02  1.37532944e-01][-2.63404003e-01  1.01146553e+00 -1.33521581e-01  2.13429204e-01][ 6.31609004e-02  7.07246358e-01  6.35575053e-01 -8.03440067e-04][-1.47780407e-02  3.69488775e-01  2.67178037e-01  2.67142059e-01][ 1.83244009e-01  2.93572066e-01  7.41698242e-01  1.56026675e-01][ 3.45977430e-01  6.53891596e-02  5.22918177e-01  4.83142011e-01][-1.82036166e-01  3.12230272e-01 -2.78927357e-01  6.57535104e-01][-8.23934054e-01 -3.38532298e-01  2.54671788e-01  2.13795066e-01][ 1.26806708e-01 -1.54919725e-01  4.48232418e-01 -1.07813153e-01][-5.88853171e-03 -3.44623038e-01 -3.12501397e-01 -1.90306455e-02][-3.38294077e-01  1.12016234e-01 -1.48539155e-01  1.64059237e-02][ 5.48398429e-01  4.84682726e-01 -9.81097503e-01  5.79531317e-01][ 2.40613990e-02 -2.45309733e-01  1.08511554e-01  2.38241587e-01][ 7.84473937e-01  2.71245658e-01  2.22068174e-01 -4.67379303e-01][ 7.52406042e-01  1.87881340e-01 -2.59980935e-01 -1.10658173e-02][ 5.77650872e-01  2.67890814e-01  2.73234515e-01  2.14666589e-03][ 4.65328173e-01  3.43087536e-02  1.54848144e-01  9.07916513e-02][ 8.43947365e-01  2.78129762e-01  4.14405336e-01 -1.62742006e-04][ 1.92555623e-01  1.96430323e-01 -2.83270365e-01  6.80535120e-01][ 4.98655722e-01  4.95409797e-02  4.99359183e-01  4.81653435e-02][-1.69805316e-01 -4.99875404e-02  1.50560982e-01  4.05694340e-01][ 3.88690410e-01  1.18226973e-01 -1.74070779e-01  3.02309738e-01][-1.27975340e-01  2.30745593e-01  9.45281200e-01  6.41611149e-01][-1.76417968e-01  1.16101401e-01  3.56420570e-01  9.63796968e-01]]
H_2: [[ 0.80668705 -0.56944503][ 0.55274371 -0.38204191][ 1.06747189 -0.37504982][ 0.88372849 -0.32185238][ 0.33144136 -0.27353039][ 0.4203575  -0.47771249][ 0.39499527 -0.44329704][ 0.63488063 -0.28928895][ 0.85832425 -0.30308914][ 0.50031215 -0.20765919][ 0.2051401  -0.24015893][ 0.29462237 -0.43763181][ 0.71417285 -0.25166981][ 0.77168669 -0.35817718][ 0.99474094 -0.14773845][ 0.97309833 -0.18923361][ 0.37770452 -0.45453059][ 0.64819026 -0.20665704][ 0.73120033 -0.05334585][ 0.3788625  -0.21494375][ 0.5601559  -0.16956082][ 0.06696635 -0.42187805][ 0.69911044 -0.13496531][ 0.56439119 -0.01401422][-0.02490054 -0.03893154][-0.19040559  0.00897865][ 0.44032396 -0.04930899][ 0.07001811 -0.06985502][ 0.3120261  -0.31273757][ 0.5349575  -0.02366688][ 1.0258222  -0.2474404 ][ 0.42400361 -0.29460932][ 1.07155588 -0.15361521][ 1.08338933 -0.18341541]]

绘图

for i in range(A.shape[0]):if zkc.nodes[i]['club'] == 'Mr. Hi':plt.scatter(np.array(H_2)[i,0],np.array(H_2)[i,1] ,label=i,color = 'b',alpha=0.5,s = 250)plt.text(np.array(H_2)[i,0],np.array(H_2)[i,1] ,i, horizontalalignment='center',verticalalignment='center', fontdict={'color':'black'})else:plt.scatter(np.array(H_2)[i,0],np.array(H_2)[i,1] ,label = 'i',color = 'r',alpha=0.5,s = 250)plt.text(np.array(H_2)[i,0],np.array(H_2)[i,1] ,i, horizontalalignment='center',verticalalignment='center', fontdict={'color':'black'})
plt.show()