Matlab实现RVM-Adaboost时间序列预测（完整源码和数据）

<p align="center"> <img src="https://z3.ax1x.com/2021/10/16/5JSTRU.png"> </p> <h3 align="center">Relevance Vector Machine (RVM)</h3> <p align="center">MATLAB code for Relevance Vector Machine</p> <p align="center">Version 2.1, 31-AUG-2021</p> <p align="center">Email: iqiukp@outlook.com</p> <div align=center> [](https://www.mathworks.com/matlabcentral/fileexchange/69407-relevance-vector-machine-rvm) <img src="https://img.shields.io/github/v/release/iqiukp/Relevance-Vector-Machine-RVM?label=version" /> <img src="https://img.shields.io/github/repo-size/iqiukp/Relevance-Vector-Machine-RVM" /> <img src="https://img.shields.io/github/languages/code-size/iqiukp/Relevance-Vector-Machine-RVM" /> <img src="https://img.shields.io/github/languages/top/iqiukp/Relevance-Vector-Machine-RVM" /> <img src="https://img.shields.io/github/stars/iqiukp/Relevance-Vector-Machine-RVM" /> <img src="https://img.shields.io/github/forks/iqiukp/Relevance-Vector-Machine-RVM" /> </div> <hr /> ## Main features - RVM model for binary classification (RVC) or regression (RVR) - Multiple kinds of kernel functions (linear, gaussian, polynomial, sigmoid, laplacian) - Hybrid kernel functions (K =w1×K1+w2×K2+...+wn×Kn) - Parameter Optimization using Bayesian optimization, Genetic Algorithm, and Particle Swarm Optimization ## Notices - This version of the code is not compatible with the versions lower than R2016b. - Detailed applications please see the demonstrations. - This code is for reference only. ## Citation ``` @article{tipping2001sparse, title={Sparse Bayesian learning and the relevance vector machine}, author={Tipping, Michael E}, journal={Journal of machine learning research}, volume={1}, number={Jun}, pages={211--244}, year={2001} } ``` ``` @article{qiu2021soft, title={Soft sensor development based on kernel dynamic time warping and a relevant vector machine for unequal-length batch processes}, author={Qiu, Kepeng and Wang, Jianlin and Wang, Rutong and Guo, Yongqi and Zhao, Liqiang}, journal={Expert Systems with Applications}, volume={182}, pages={115223}, year={2021}, publisher={Elsevier} } ``` ## How to use ### 01. Classification using RVM (RVC) A demo for classification using RVM ```MATLAB clc clear all close all addpath(genpath(pwd)) % use fisheriris dataset load fisheriris inds = ~strcmp(species, 'setosa'); data_ = meas(inds, 3:4); label_ = species(inds); cvIndices = crossvalind('HoldOut', length(data_), 0.3); trainData = data_(cvIndices, :); trainLabel = label_(cvIndices, :); testData = data_(~cvIndices, :); testLabel = label_(~cvIndices, :); % kernel function kernel = Kernel('type', 'gaussian', 'gamma', 0.2); % parameter parameter = struct( 'display', 'on',... 'type', 'RVC',... 'kernelFunc', kernel); rvm = BaseRVM(parameter); % RVM model training, testing, and visualization rvm.train(trainData, trainLabel); results = rvm.test(testData, testLabel); rvm.draw(results) ``` results: ```MATLAB *** RVM model (classification) train finished *** running time = 0.1604 seconds iterations = 20 number of samples = 70 number of RVs = 2 ratio of RVs = 2.8571% accuracy = 94.2857% *** RVM model (classification) test finished *** running time = 0.0197 seconds number of samples = 30 accuracy = 96.6667% ``` <p align="center"> <img src="https://z3.ax1x.com/2021/10/16/5JSzi6.png"> <img src="https://z3.ax1x.com/2021/10/16/5JpSJK.png"> </p> ### 02. Regression using RVM (RVR) A demo for regression using RVM ```MATLAB clc clear all close all addpath(genpath(pwd)) % sinc funciton load sinc_data trainData = x; trainLabel = y; testData = xt; testLabel = yt; % kernel function kernel = Kernel('type', 'gaussian', 'gamma', 0.1); % parameter parameter = struct( 'display', 'on',... 'type', 'RVR',... 'kernelFunc', kernel); rvm = BaseRVM(parameter); % RVM model training, testing, and visualization rvm.train(trainData, trainLabel); results = rvm.test(testData, testLabel); rvm.draw(results) ``` results: ```MATLAB *** RVM model (regression) train finished *** running time = 0.1757 seconds iterations = 76 number of samples = 100 number of RVs = 6 ratio of RVs = 6.0000% RMSE = 0.1260 R2 = 0.8821 MAE = 0.0999 *** RVM model (regression) test finished *** running time = 0.0026 seconds number of samples = 50 RMSE = 0.1424 R2 = 0.8553 MAE = 0.1106 ``` <p align="center"> <img src="https://z3.ax1x.com/2021/10/16/5JpPQe.png"> </p> ### 03. Kernel funcions A class named ***Kernel*** is defined to compute kernel function matrix. ```MATLAB %{ 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** ```MATLAB 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 ``` ### 04. Hybrid kernel A demo for regression using RVM with hybrid_kernel (K =w1×K1+w2×K2+...+wn×Kn) ```MATLAB clc clear all close all addpath(genpath(pwd)) % sinc funciton load sinc_data trainData = x; trainLabel = y; testData = xt; testLabel = yt; % kernel function kernel_1 = Kernel('type', 'gaussian', 'gamma', 0.3); kernel_2 = Kernel('type', 'polynomial', 'degree', 2); kernelWeight = [0.5, 0.5]; % parameter parameter = struct( 'display', 'on',... 'type', 'RVR',... 'kernelFunc', [kernel_1, kernel_2],... 'kernelWeight', kernelWeight); rvm = BaseRVM(parameter); % RVM model training, testing, and visualization rvm.train(trainData, trainLabel); results = rvm.test(testData, testLabel); rvm.draw(results) ``` ### 05. Parameter Optimization for single-kernel-RVM A demo for RVM model with Parameter Optimization ```MATLAB clc clear all close all addpath(genpath(pwd)) % use fisheriris dataset load fisheriris inds = ~strcmp(species, 'setosa'); data_ = meas(inds, 3:4); label_ = species(inds); cvIndices = crossvalind('HoldOut', length(data_), 0.3); trainData = data_(cvIndices, :); trainLabel = label_(cvIndices, :); testData = data_(~cvIndices, :); testLabel = label_(~cvIndices, :); % kernel function kernel = Kernel('type', 'gaussian', 'gamma', 5); % parameter optimization opt.method = 'bayes'; % bayes, ga, pso opt.display = 'on'; opt.iteration = 20; % parameter parameter = struct( 'display', 'on',... 'type', 'RVC',... 'kernelFunc', kernel,... 'optimization', opt); rvm = BaseRVM(parameter); % RVM model training, testing, and visualization rvm.train(trainData, trainLabel); results = rvm.test(trainData, trainLabel); rvm.draw(results) ``` results: ```MATLAB *** RVM model (classification) train finished *** running time = 13.3356 seconds iterations = 88 number of samples = 70 number of RVs = 4 ratio of RVs