Infinite Positive Semidefinite Tensor Factorization for Source Separation of Mixture Signals
Infinite Positive Semidefinite Tensor Factorization for Source Separation of Mixture Signals
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发表时间：
2013-06
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通讯作者：
Kazuyoshi Yoshii;Ryota Tomioka;D. Mochihashi;Masataka Goto
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作者：
Kazuyoshi Yoshii;Ryota Tomioka;D. Mochihashi;Masataka Goto
本文提出了一类新的张量分解，称为正半定张量分解(PSDTF)，它将一组正半定(PSD)矩阵分解成较少的PSD基矩阵的凸组合。PSDTF可以看作是非负矩阵分解的自然扩展。PSDTF的主要问题之一是应该预先给出适当数量的碱基。为了解决这个问题，我们提出了一个基于Gamma过程的非参数贝叶斯模型，该模型只能从假定存在的无限多个基中实例化有限数量的必要基。我们推导了闭合后验推断的变分贝叶斯算法和最大似然估计的乘法更新规则。我们从合成数据和真实音乐记录两个方面对PSDTF进行了评估，以显示其优越性。
This paper presents a new class of tensor factorization called positive semidefinite tensor factorization (PSDTF) that decomposes a set of positive semidefinite (PSD) matrices into the convex combinations of fewer PSD basis matrices. PSDTF can be viewed as a natural extension of nonnegative matrix factorization. One of the main problems of PSDTF is that an appropriate number of bases should be given in advance. To solve this problem, we propose a nonparametric Bayesian model based on a gamma process that can instantiate only a limited number of necessary bases from the infinitely many bases assumed to exist. We derive a variational Bayesian algorithm for closed-form posterior inference and a multiplicative update rule for maximum-likelihood estimation. We evaluated PSDTF on both synthetic data and real music recordings to show its superiority.