基于核函数的主分量分析法源代码

+------------+ | Kernel ICA | +------------+ Version 1.1 - May 13th, 2002 ------------------------------ Description ----------- The kernel-ica package is a Matlab program that implements the Kernel ICA algorithm for independent component analysis (ICA). The Kernel ICA algorithm is based on the minimization of a contrast function based on kernel ideas. A contrast function measures the statistical dependence between components, thus when applied to estimated components and minimized over possible demixing matrices, components that are as independent as possible are found. For more information, please read the following paper: Francis R. Bach, Michael I. Jordan (2001). Kernel Independent Component Analysis, Technical Report UCB//CSD-01-1166, University of California, Berkeley. The kernel-ica package is Copyright (c) 2002 by Francis Bach. If you have any questions or comments regarding this package, or if you want to report any bugs, please send me an e-mail to fbach@cs.berkeley.edu. The current version 1.0 has been released on March, 19th 2002. It has been tested on both matlab 5 and matlab 6. Check regularly the following for newer versions: http://www.cs.berkeley.edu/~fbach Installation ------------ 1. Unzip all the .m files in the same directory 2. (Optional) if you want a faster implementation which uses pieces of C code: at the matlab prompt, in the directory where the package is installed, type: >> mex chol_gauss.c and >> mex chol_hermite.c It should create compiled files whose extensions depends on the platform you are using: Windows: chol_gauss.dll and chol_hermite.dll Solaris: chol_gauss.mexsol and chol_hermite.dll Linux : chol_gauss.mexglx and chol_hermite.dll To check if the file was correcly compiled, type >> which chol_gauss >> which chol_hermite and the name of the compiled versions should appear. If you have any problems with the C file of if you are using a platform i did not mention, please e-mail me. How to use the kernel-ica package --------------------------------- The function that you should use to run the ICA algorithm is 'kernel_ica'. a detailed description of its options are described inside the file and can be reached by simply typing 'help kernel_ica' at the matlab prompt. A simple demonstration script is provided : 'demo_kernel_ica'. NB: all the data should be given in columns, that is, if you have m components and N samples, the matrix should be m x N. If you wish to investigate the tools and methods we used for this algorithms, you will find the following files useful: -contrast_ica.m : computation of the contrast functions based on Kernel canonical correlations -chol_gauss.c/.m : incomplete cholesky decomposition with Gaussian kernel in one or higher dimensions -chol_hermite.c/.m : incomplete cholesky decomposition with Hermite polynomial kernel in (currently) only one dimension Package file list ----------------- amari_distance.m : Amari distance between two square matrices chol_gauss.c : incomplete cholesky (Gaussian kernel) - C source chol_gauss.m : incomplete cholesky (Gaussian kernel) - M file chol_hermite.c : incomplete cholesky (Hermite kernel) - C source chol_hermite.m : incomplete cholesky (Hermite kernel) - M file chol_poly.c : incomplete cholesky (Polyn. kernel) - C source chol_poly.m : incomplete cholesky (Polyn. kernel) - M file contrast_emp_grad.m : derivative of m-way contrast functions contrast_emp_grad_oneunit.m : derivative of the one-unit contrast functions contrast_ica.m : m-way contrast functions contrast_update_oneunit.m : one-unit contrast function demo_kernel_ica.m : demonstration script empder_search.m : local search (reaches a local minimum) - full contrast empder_search_oneunit.m : local search (reaches a local minimum) - one-unit contrast global_mini.m : global minimization with random restarts - full contrast global_mini_oneunit.m : global minimization with random restarts - one-unit contrast global_mini_sequential.m : global minimization with random restarts one-unit contrast + deflation scheme kernel_ica.m : performs ICA using the kernel ICA algorithm rand_orth.m : generates random matrix with orthogonal columns update_contrast.m : used for efficient computation of empirical gradient