Kernel Principal Component Analysis (KPCA)

版本 2.2.1 (988.3 KB) 作者: Kepeng Qiu

MATLAB code for dimensionality reduction, fault detection, and fault diagnosis using KPCA.

https://github.com/iqiukp/KPCA-MATLAB

关注

5.0

(10)

3.3K 次下载

更新时间 2022/2/21

在 GitHub 上查看许可证

Kernel Principal Component Analysis (KPCA)

MATLAB code for dimensionality reduction, fault detection, and fault diagnosis using KPCA

Version 2.2, 14-MAY-2021

Email: iqiukp@outlook.com

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%

Another application using banana-shaped data:

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)

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)

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)

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%

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     = 851

06. Fault diagnosis

Notice

If you want to calculate CPS of a certain time, you should set starting time equal to ending time. For example, 'diagnosis', [500, 500]
If you want to calculate the average CPS of a period of time, starting time and ending time should be set respectively. 'diagnosis', [300, 500]
The fault diagnosis module is only supported for gaussian kernel function and it may still take a long time when the number of the training data is large.

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,...
                   'diagnosis', [300, 500]);
               
% 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)
kplot.diagnosis(results)

Diagnosis results:

*** Fault diagnosis ***
Fault diagnosis start...
Fault diagnosis finished.
running time            = 18.2738 seconds
start point             = 300 
ending point            = 500 
fault variables (T2)    = 44   1   4 
fault variables (SPE)   = 1  44  18

引用格式

Kepeng Qiu (2024). Kernel Principal Component Analysis (KPCA) (https://github.com/iqiukp/KPCA-MATLAB), GitHub. 检索时间: 2024/11/22.

MATLAB 版本兼容性

创建方式 R2021b

与 R2016b 及更高版本兼容

平台兼容性

Windows macOS Linux

类别

Signal Processing > DSP System Toolbox > Filter Design and Analysis > Filter Design >

在 Help Center 和 MATLAB Answers 中查找有关 Filter Design 的更多信息

标签添加标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

KernelPCA

无法下载基于 GitHub 默认分支的版本

版本	已发布	发行说明
2.2.1	2022/2/21	* Added descriptions
2.2	2021/5/24	Please visit https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA for detailed information.
2.1.2	2021/5/8	1. Added some descriptions
2.1.1	2021/3/25	1. Added some descriptions
2.1	2020/4/10	1. added support for data reconstruction
2.0	2019/11/16	1. Used OOP to rewrite some modules. 2. Added support for multiple kernel functions. 3. Fixed some bugs. 4. Accelerated the running speed of the fault diagnosis module.
1.2	2019/4/18	1. Fixed some errors 2. Added Dynamic KPCA(DKPCA)
1.1.1	2019/4/11	1. Fixed some errors 2. Added fault diagnosis
1.1	2019/4/11	1. Fixed some errors 2. Added fault diagnosis
1.0.0	2018/11/9

要查看或报告此来自 GitHub 的附加功能中的问题，请访问其 GitHub 仓库。

Kernel Principal Component Analysis (KPCA)

Kernel Principal Component Analysis (KPCA)

Main features

Notices

How to use

01. Kernel funcions

02. Simple KPCA model for dimensionality reduction

03. Simple KPCA model for reconstruction

04. Component number determination

05. Fault detection

06. Fault diagnosis

引用格式

MATLAB 版本兼容性

平台兼容性

类别

标签 添加标签

Community Treasure Hunt

探索实时编辑器

KernelPCA

标签添加标签