基于随机变量相似度的ICA方法

从随机变量(微分)熵的概念出发，定义了随机变量的相似度，讨论了用求相似度极点的方法实现观测数据线性组合非高斯性最大化，从而串行估计独立分量分析(ICA)模型中的独立分量的原理和算法。对非多项式矩定理进行了更为一般化的证明，以此定理为根据阐明了以一般的非二次型光滑偶函数的数学期望近似代替相似度的可行性。给出梯度算法中的符号因子计算公式，避免了现有的相应算法中符号因子计算公式与目标函数之间的矛盾。通过与极大似然ICA方法对比，表明所定义的相似度就是在预白化条件下单个源变量的极大似然函数。

Random Variable Analogy Based ICA Method

This paper defines analogy measure of two random variables, and discusses the principle and algorithm of maximizing non-Gaussianity of observed data with a linear transformation to estimate independent components serially. It also proves the non-polynomial moment theorem by a generalized way, and states the feasibility that substitutes the analogy with the expectation of a non-quadratic smooth even function based on the theorem. A formula to compute sign of above algorithm is given. The algorithm overcomes the contradiction between the objective function and the sign computation formula.Comparing with Maximum likelihood ICA, the analogy is Maximum likelihood function of single source under pre-whited.