BINARY TENSOR FACTORIZATION

摘要

In factorization of binary matrices or tensors, training algorithms usually scale linearly with the number of training examples. For very unbalanced learning problems, the number of non-zero training examples can be much smaller than the number of zeros in the full dataset. For some problems where the squared norm can be efficiently computed, the training time complexity can be reduced. A method herein receives a binary tensor defined by matrices comprising elements in a database. A processing device determines an upper bound for non-quadratic losses associated with factorization of the binary tensor. The upper bound is based on a variation parameter. The processing device performs factorization of the binary tensor by alternately minimizing the upper bound with respect to the variation parameter and minimizing the upper bound with respect to the elements of the matrices using a gradient descent method.

主权项

1. A method comprising:
receiving, by a processing device, a tensor defined by matrices comprising elements in a database; and performing, by said processing device, factorization of said tensor, said factorization comprising:
identifying disjoint blocks of elements in said tensor;splitting ones of said disjoint blocks having maximal variance in the absolute values of a predicted value of said elements in said blocks;determining an upper bound on every one of said disjoint blocks of said tensor for losses associated with said factorization; andminimizing said upper bound with respect to a variation parameter and elements in said factorization using a gradient descent function.