Created
February 14, 2016 01:26
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import numpy as np | |
from scipy import linalg,sparse,random | |
class RESCAL: | |
def __init__(self,r,lamb_A,lamb_R): | |
self.r = r | |
self.lamb_A = lamb_A | |
self.lamb_R = lamb_R | |
def fit(self,X,niter=30): | |
m = len(X) | |
n,_ = X[0].shape | |
self.A = random.randn(n,self.r) | |
self.R = [random.randn(self.r,self.r) for i in range(m)] | |
t = 0 | |
while True: | |
""" update A """ | |
AA = self.A.T.dot(self.A) | |
F = sum([X[k].dot(self.A).dot(self.R[k].T) + X[k].T.dot(self.A).dot(self.R[k]) for k in range(m)]) | |
S = sum([self.R[k].dot(AA).dot(self.R[k].T) + self.R[k].T.dot(AA).dot(self.R[k]) for k in range(m)]) | |
S += m * self.lamb_A * np.identity(self.r) | |
self.A = F.dot(linalg.inv(S)) | |
""" update R """ | |
Q,A_bar = linalg.qr(self.A,mode='economic') | |
Z = sparse.kron(A_bar,A_bar) | |
for k in range(m): | |
vec_Xk = Q.T.dot(X[k].dot(Q)).reshape(self.r**2,1) | |
self.R[k] = linalg.inv(Z.T.dot(Z) + self.lamb_R*np.identity(self.r**2)).dot(Z.T.dot(vec_Xk)).reshape(self.r,self.r) | |
t += 1 | |
if t >= niter: break | |
if __name__ == '__main__': | |
# Example graph from ICML'11 paper | |
m = 2 # number of edge types | |
X = [sparse.lil_matrix((5,5)) for i in range(m)] | |
X[0][0,1] = 1 # vicePresidentOf | |
X[0][2,3] = 1 # vicePresidentOf | |
X[1][0,4] = 1 # party | |
X[1][1,4] = 1 # party | |
X[1][2,4] = 1 # party | |
nodenames = {0:'Lyndon', 1:'John', 2:'AI', 3:'Bill', 4:'Party X'} | |
edgetypes = {0:'vicePresidentOf', 1:'party'} | |
# Parameters | |
r = 3 # number of latent component | |
lamb_A = 0.00001 # regularization | |
lamb_R = 0.00001 # regularization | |
rescal = RESCAL(r,lamb_A,lamb_R) | |
rescal.fit(X) | |
# TEST (link prediction) | |
X_bar = [rescal.A.dot(rescal.R[i]).dot(rescal.A.T) for i in range(m)] # reconstract X | |
estimated_facts = [] | |
for k in range(m): | |
indices = np.where(X_bar[k]>0.1) # triples with high likelihood | |
for i in range(indices[0].shape[0]): | |
if X[k][indices[0][i],indices[1][i]] == 0: # only for non-existence triples | |
estimated_facts.append((nodenames[indices[0][i]], edgetypes[k], nodenames[indices[1][i]])) | |
for f in estimated_facts: | |
print f |
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