Kernel Principal Component Analysis (KPCA)matlab代码.zip

<p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/helix.png"> </p> <h3 align="center">Kernel Principal Component Analysis (KPCA)</h3> <p align="center">MATLAB code for dimensionality reduction, fault detection, and fault diagnosis using KPCA</p> <p align="center">Version 2.2, 14-MAY-2021</p> <p align="center">Email: [email protected]</p> <div align=center> [](https://ww2.mathworks.cn/matlabcentral/fileexchange/69378-kernel-principal-component-analysis-kpca) <img src="https://img.shields.io/github/v/release/iqiukp/Kernel-Principal-Component-Analysis-KPCA?label=version" /> <img src="https://img.shields.io/github/repo-size/iqiukp/Kernel-Principal-Component-Analysis-KPCA" /> <img src="https://img.shields.io/github/languages/code-size/iqiukp/Kernel-Principal-Component-Analysis-KPCA" /> <img src="https://img.shields.io/github/languages/top/iqiukp/Kernel-Principal-Component-Analysis-KPCA" /> <img src="https://img.shields.io/github/stars/iqiukp/Kernel-Principal-Component-Analysis-KPCA" /> <img src="https://img.shields.io/github/forks/iqiukp/Kernel-Principal-Component-Analysis-KPCA" /> </div> <hr /> ## Main features - Easy-used API for training and testing KPCA model - Support for dimensionality reduction, data reconstruction, fault detection, and fault diagnosis - Multiple kinds of kernel functions (linear, gaussian, polynomial, sigmoid, laplacian) - Visualization of training and test results - Component number determination based on given explained level or given number ## Notices - Only fault diagnosis of Gaussian kernel is supported. - This code is for reference only. ## How to use ### 01. Kernel funcions A class named ***Kernel*** is defined to compute kernel function matrix. ``` %{ type - linear : k(x,y) = x'*y polynomial : k(x,y) = (γ*x'*y+c)^d gaussian : k(x,y) = exp(-γ*||x-y||^2) sigmoid : k(x,y) = tanh(γ*x'*y+c) laplacian : k(x,y) = exp(-γ*||x-y||) degree - d offset - c gamma - γ %} kernel = Kernel('type', 'gaussian', 'gamma', value); kernel = Kernel('type', 'polynomial', 'degree', value); kernel = Kernel('type', 'linear'); kernel = Kernel('type', 'sigmoid', 'gamma', value); kernel = Kernel('type', 'laplacian', 'gamma', value); ``` For example, compute the kernel matrix between **X** and **Y** ``` X = rand(5, 2); Y = rand(3, 2); kernel = Kernel('type', 'gaussian', 'gamma', 2); kernelMatrix = kernel.computeMatrix(X, Y); >> kernelMatrix kernelMatrix = 0.5684 0.5607 0.4007 0.4651 0.8383 0.5091 0.8392 0.7116 0.9834 0.4731 0.8816 0.8052 0.5034 0.9807 0.7274 ``` ### 02. Simple KPCA model for dimensionality reduction ``` clc clear all close all addpath(genpath(pwd)) load('.\data\helix.mat', 'data') kernel = Kernel('type', 'gaussian', 'gamma', 2); parameter = struct('numComponents', 2, ... 'kernelFunc', kernel); % build a KPCA object kpca = KernelPCA(parameter); % train KPCA model kpca.train(data); %　mapping data mappingData = kpca.score; % Visualization kplot = KernelPCAVisualization(); % visulize the mapping data kplot.score(kpca) ``` The training results (dimensionality reduction): ``` *** KPCA model training finished *** running time = 0.2798 seconds kernel function = gaussian number of samples = 1000 number of features = 3 number of components = 2 number of T2 alarm = 135 number of SPE alarm = 0 accuracy of T2 = 86.5000% accuracy of SPE = 100.0000% ``` <p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/helix.png"> </p> Another application using banana-shaped data: <p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/banana.png"> </p> ### 03. Simple KPCA model for reconstruction ``` clc clear all close all addpath(genpath(pwd)) load('.\data\circle.mat', 'data') kernel = Kernel('type', 'gaussian', 'gamma', 0.2); parameter = struct('numComponents', 2, ... 'kernelFunc', kernel); % build a KPCA object kpca = KernelPCA(parameter); % train KPCA model kpca.train(data); %　reconstructed data reconstructedData = kpca.newData; % Visualization kplot = KernelPCAVisualization(); kplot.reconstruction(kpca) ``` <p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/circle.png"> </p> ### 04. Component number determination The Component number can be determined based on given explained level or given number. ***Case 1*** The number of components is determined by the given explained level. The given explained level should be 0 < explained level < 1. For example, when explained level is set to 0.75, the parameter should be set as: ``` parameter = struct('numComponents', 0.75, ... 'kernelFunc', kernel); ``` The code is ``` clc clear all close all addpath(genpath(pwd)) load('.\data\TE.mat', 'trainData') kernel = Kernel('type', 'gaussian', 'gamma', 1/128^2); parameter = struct('numComponents', 0.75, ... 'kernelFunc', kernel); % build a KPCA object kpca = KernelPCA(parameter); % train KPCA model kpca.train(trainData); % Visualization kplot = KernelPCAVisualization(); kplot.cumContribution(kpca) ``` <p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/cumContirb.png"> </p> As shown in the image, when the number of components is 21, the cumulative contribution rate is 75.2656%，which exceeds the given explained level (0.75）. ***Case 2*** The number of components is determined by the given number. For example, when the given number is set to 24, the parameter should be set as: ``` parameter = struct('numComponents', 24, ... 'kernelFunc', kernel); ``` The code is ``` clc clear all close all addpath(genpath(pwd)) load('.\data\TE.mat', 'trainData') kernel = Kernel('type', 'gaussian', 'gamma', 1/128^2); parameter = struct('numComponents', 24, ... 'kernelFunc', kernel); % build a KPCA object kpca = KernelPCA(parameter); % train KPCA model kpca.train(trainData); % Visualization kplot = KernelPCAVisualization(); kplot.cumContribution(kpca) ``` <p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/components.png"> </p> As shown in the image, when the number of components is 24, the cumulative contribution rate is 80.2539%. ### 05. Fault detection Demonstration of fault detection using KPCA (TE process data) ``` clc clear all close all addpath(genpath(pwd)) load('.\data\TE.mat', 'trainData', 'testData') kernel = Kernel('type', 'gaussian', 'gamma', 1/128^2); parameter = struct('numComponents', 0.65, ... 'kernelFunc', kernel); % build a KPCA object kpca = KernelPCA(parameter); % train KPCA model kpca.train(trainData); % test KPCA model results = kpca.test(testData); % Visualization kplot = KernelPCAVisualization(); kplot.cumContribution(kpca) kplot.trainResults(kpca) kplot.testResults(kpca, results) ``` The training results are ``` *** KPCA model training finished *** running time = 0.0986 seconds kernel function = gaussian number of samples = 500 number of features = 52 number of components = 16 number of T2 alarm = 16 number of SPE alarm = 17 accuracy of T2 = 96.8000% accuracy of SPE = 96.6000% ``` <p align="center"> <img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/FD_train.png"> </p> The test results are ``` *** KPCA model test finished *** running time = 0.0312 seconds number of test data = 960 number of T2 alarm = 799 number of SPE alarm