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import numpy as np
class CPALS:
def __init__(self,k,lamb,max_iter):
self.k=k
self.lamb=lamb
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 _init_latent_vectors(self):
A = {}
for m in range(3): # 3rd-order tensor
A[m] = np.random.normal(loc=0, scale=0.1, size=(self.data_shape[m],self.k))
return A
def _loss(self,X):
L = 0
count = 0
for indices in X:
L += 0.5 * (X[indices]-self.predict(indices))**2
count += 1
return L/count
def _update(self,X,mode):
X_bar = np.zeros_like(self.A[mode])
for indices in X: # indices = (i,j,k)
X_bar[indices[mode]] += X[indices] * np.prod([self.A[m][indices[m]] for m in range(3) if m!=mode],axis=0)
K = np.prod([self.A[m].T.dot(self.A[m]) for m in range(3) if m!=mode],axis=0) + self.lamb*np.identity(self.k)
return np.dot(X_bar, np.linalg.inv(K))
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:
for m in range(3):
self.A[m] = self._update(X,m)
remained_iter-=1
self._losses.append(self._loss(X))
return self
def predict(self,indices):
return np.prod([self.A[m][indices[m]] for m in range(3)],axis=0).sum()
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