Created
November 29, 2016 06:10
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import numpy as np | |
class Tucker: | |
def __init__(self,R,S,T,max_iter): | |
self.latent_size = (R,S,T) | |
self.max_iter=max_iter | |
def _calc_data_shape(self,X): | |
max_i = -1 | |
max_j = -1 | |
max_k = -1 | |
for i,j,k in X: | |
if max_i<i: max_i=i | |
if max_j<j: max_j=j | |
if max_k<k: max_k=k | |
return (max_i+1,max_j+1,max_k+1) | |
def _calc_core_tensor(self,X): | |
G = np.zeros(shape=self.latent_size) | |
for a in range(self.latent_size[0]): | |
for b in range(self.latent_size[1]): | |
for c in range(self.latent_size[2]): | |
for indices in X: | |
i,j,k = indices | |
G[a,b,c] += X[indices]*self.A[0][i,a]*self.A[1][j,b]*self.A[2][k,c] | |
return G | |
def _init_latent_vectors(self): | |
A = {} | |
for m in range(3): | |
A[m] = np.random.normal(loc=0, scale=0.1, size=(self.data_shape[m],self.latent_size[m])) | |
return A | |
def _loss(self,X): | |
G = self._calc_core_tensor(X) | |
return - (G**2).sum() / (G.shape[0]*G.shape[1]*G.shape[2]) | |
def _update(self,X,modes): | |
row = self.data_shape[modes[0]] | |
col = self.A[modes[1]].shape[1] * self.A[modes[2]].shape[1] | |
X_bar = np.zeros(shape=(row,col)) | |
for indices in X: | |
for a in range(self.latent_size[modes[1]]): | |
for b in range(self.latent_size[modes[2]]): | |
q = a*self.latent_size[modes[2]]+b | |
X_bar[indices[modes[0]],q] += X[indices] * self.A[modes[1]][indices[modes[1]],a] * self.A[modes[2]][indices[modes[2]],b] | |
U,s,V = np.linalg.svd(X_bar) | |
return U[:,:self.latent_size[modes[0]]] | |
def fit(self,X): | |
self.data_shape = self._calc_data_shape(X) | |
self.A = self._init_latent_vectors() | |
self._losses = [] | |
remained_iter = self.max_iter | |
while remained_iter>0: | |
self.A[0] = self._update(X,(0,1,2)) | |
self.A[1] = self._update(X,(1,2,0)) | |
self.A[2] = self._update(X,(2,0,1)) | |
remained_iter-=1 | |
l = self._loss(X) | |
self._losses.append(l) | |
self.G = self._calc_core_tensor(X) | |
return self | |
def predict(self,indices): | |
i,j,k = indices | |
ret = np.tensordot( | |
np.tensordot( | |
np.tensordot(self.G, | |
self.A[2][k], axes=(2,0)), | |
self.A[1][j], axes=(1,0)), | |
self.A[0][i], axes=(0,0)) | |
return ret |
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