光电工程, 2009, 36 (9): 104, 网络出版: 2010-01-31
ICA 的梯度下降算法框架
Framework of Gradient Descent Algorithms for ICA
盲信号处理 独立分量分析 梯度下降算法 串行矩阵更新 等变自适应分离 blind signal processing independent component analysis gradient descent algorithm serial matrix updating equivariant adaptive separation
摘要
为了设计更多有效的独立分量分析(ICA)算法,本文提出了ICA 梯度下降算法(GDA)的一般框架,覆盖了许多目前流行的算法,如Infomax,MMI,MLE 等等。该框架由一种新的基于II 类超加(减)性函数的参比函数理论导出,并采用推广的EASI 形式作为更新规则来获得更好的性能。同时本文也展示了一个基于二次熵函数的框架使用例子,并提出了其梯度的快速计算方法,最后仿真证明了它的有效性。实验结果表明,该框架非常实用,可作为开发更多有效ICA 算法的有利工具。
Abstract
To design more effective algorithms for Independent Component Analysis (ICA), a general framework of Gradient Descent Algorithms (GDAs) for ICA was proposed, which covers many popular algorithms such as Infomax, Minimization of Mutual Information (MMI), Maximum Likelihood Estimation (MLE) and so on. This framework was derived from a new theory of the contrast functions for ICA based on the superadditive (or subadditive) function of class II. For better performances, the Equivariant Adaptive Separation via Independence (EASI) form was generalized and used as the updating rule. An example of using the framework was also shown based on the quadratic entropy. Furthermore, a fast method of computing the gradient in the example was proposed and the simulation proved its validity. The results demonstrate that this framework is a useful tool to discover more effective algorithms for ICA.
罗一涵, 付承毓, 舒勤. ICA 的梯度下降算法框架[J]. 光电工程, 2009, 36(9): 104. LUO Yi-han, FU Cheng-yu, SHU Qin. Framework of Gradient Descent Algorithms for ICA[J]. Opto-Electronic Engineering, 2009, 36(9): 104.