基于PSO优化LSSVM的时序预测MATLAB实战

news2024/9/28 15:28:37

今天给大家分享PSO优化LSSVM的时序预测代码实战，主要从算法原理和代码实战展开。需要了解更多算法代码的，可以点击文章左下角的阅读全文，进行获取哦~需要了解智能算法、机器学习、深度学习和信号处理相关理论的可以后台私信哦，下一期分享的内容就是你想了解的内容~

一、算法原理

支持向量机是针对小样本问题，基于结构风险最小化，较好地解决了以往机器学习模型中的过学习、非线性、维数灾难以及局部极小值等问题，具有较好的泛化能力；然而，该方法在大规模训练样本时，存在训练速度慢、稳定性差等缺陷，从而制约了其使用范围（学习过程中需要求解二次规划问题）。为加快支持向量机的训练速度和简化计算复杂度，最小二乘支持向量机（Least Square Support Vector Machine, LSSVM）被提出。最小二乘支持向量机（LSSVM）是标准支持向量机的一种扩展，该算法将支持向量机的求解从二次规划问题转化为线性方程组。它与支持向量机的不同之处在于它把不等式约束改成等式约束，并把经验风险由偏差的一次方改为二次方。

本文分享的实战为时序预测问题是一类回归问题，因此接下来介绍的算法原理为最小二乘支持向量回归算法（LSSVR）。

（1）构建LSSVR的优化问题的目标函数：

(2) 将传统SVM的不等式约束转换为等式约束：

（3）构造拉格朗日函数：

（4）进行KKT转换，得到最优对应的约束条件：

（5）得到对应的线性方程系统为：

（6）最终求解得到：

关于粒子群算法的原理可以参考我以前的文章：

matlab编程第五期--粒子群优化算法实战

二、代码实战

%% 文件说明% main.m   : 主文件，进行预测，将生成的网络保存到 'nets.mat'中% main_back.m : 使用'nets.mat'重现结果% nets.mat : 保存 3 * 48 个grnn网络，用于结果重现% QLD1.csv : 原始数据(用的什么时候的数据你点开看一下就明白了)% QLD1.mat : 导成matlab格式的数据% adaboost : 组合算法, 输出结果的第一个数是组合后的mape%% 原理% 输入前一个周7个相同时间点的数据 得到本周7个相同时间点的数据% 不用执行本文件，运行`main_back.m`即可看到结果% net1MeanMape =%    0.0165        <- grnn1% net2MeanMape =%    0.0168        <- grnn2% net3MeanMape =%    0.0168        <- grnn3% combineMeanMapes =%    0.0157        <- adaboostclc;close;clear;testWeekNum  = 1;%% 训练数据周数trainWeekNum = 228;load QLD1;QLD1 = reshape(QLD1, 48, length(QLD1)/48);testWeekInd  = 1;trainWeekInd = 1 + (1:trainWeekNum);testWeekX = [];testWeekY = [];for yWeekInd = testWeekInd    yWeekDayInd = (yWeekInd*7-6):(yWeekInd*7);    xWeekDayStart = yWeekInd * 7 + 1;    xWeekDayEnd = (yWeekInd + 1) * 7;    xWeekDayInd = xWeekDayStart:xWeekDayEnd;    yDayData = QLD1(:, yWeekDayInd);    xDayData = QLD1(:, xWeekDayInd);        testWeekY = [testWeekY yDayData'];    testWeekX = [testWeekX xDayData'];endtrainWeekX = [];trainWeekY = [];for yWeekInd = trainWeekInd    yWeekDayInd = (yWeekInd*7-6):(yWeekInd*7);    xWeekDayStart = yWeekInd * 7 + 1;    xWeekDayEnd = (yWeekInd + 1) * 7;    xWeekDayInd = xWeekDayStart:xWeekDayEnd;    yDayData = QLD1(:, yWeekDayInd);    xDayData = QLD1(:, xWeekDayInd);        trainWeekY = [trainWeekY yDayData'];    trainWeekX = [trainWeekX xDayData'];endnets = {};netMapes = [];for time = 1:48    disp([' time:', num2str(time)]);    testInd  = (0:(testWeekNum-1))  * 48 + time;    trainInd = (0:(trainWeekNum-1)) * 48 + time;    global trainX trainY xmap ymap testX testY;    testX  = testWeekX(:, testInd);    testY  = testWeekY(:, testInd);    trainX = trainWeekX(:,trainInd);    trainY = trainWeekY(:,trainInd);    [trainX, xmap] = mapminmax(trainX, 0.0000001, 1);    [trainY, ymap] = mapminmax(trainY, 0.0000001, 1);    testX = mapminmax('apply', testX, xmap);    [bestGam, bestSig2] = optimizeLSSVM();    rand('seed', 2);    net = initlssvm(trainX', trainY', 'function estimation', bestGam, bestSig2, 'RBF_kernel');    net = trainlssvm(net);    ySim = simlssvm(net, testX')';    ySim = mapminmax('reverse', ySim, ymap);    mape_ = mape(testY, ySim);    nets{time, 1} = net;    netMapes = [netMapes mape_];endmeanMape = mean(netMapes)save nets nets;

%% 48 7 -> 7clc;close;clear;testWeekNum  = 1;  trainWeekNum = 228;load QLD1;load nets;QLD1 = reshape(QLD1, 48, length(QLD1)/48);netMapes = [];testWeekInd  = 1;trainWeekInd = 1 + (1:trainWeekNum);testWeekX = [];testWeekY = [];for yWeekInd = testWeekInd    yWeekDayInd = (yWeekInd*7-6):(yWeekInd*7);    xWeekDayStart = yWeekInd * 7 + 1;    xWeekDayEnd = (yWeekInd + 1) * 7;    xWeekDayInd = xWeekDayStart:xWeekDayEnd;    yDayData = QLD1(:, yWeekDayInd);    xDayData = QLD1(:, xWeekDayInd);        testWeekY = [testWeekY yDayData'];    testWeekX = [testWeekX xDayData'];endtrainWeekX = [];trainWeekY = [];for yWeekInd = trainWeekInd    yWeekDayInd = (yWeekInd*7-6):(yWeekInd*7);    xWeekDayStart = yWeekInd * 7 + 1;    xWeekDayEnd = (yWeekInd + 1) * 7;    xWeekDayInd = xWeekDayStart:xWeekDayEnd;    yDayData = QLD1(:, yWeekDayInd);    xDayData = QLD1(:, xWeekDayInd);        trainWeekY = [trainWeekY yDayData'];    trainWeekX = [trainWeekX xDayData'];endfor time = 1:48    disp([' time:', num2str(time)]);    testInd  = (0:(testWeekNum-1))  * 48 + time;    trainInd = (0:(trainWeekNum-1)) * 48 + time;    global trainX trainY xmap ymap testX testY;    testX  = testWeekX(:, testInd);    testY  = testWeekY(:, testInd);    trainX = trainWeekX(:,trainInd);    trainY = trainWeekY(:,trainInd);    [trainX, xmap] = mapminmax(trainX, 0.0000001, 1);    [trainY, ymap] = mapminmax(trainY, 0.0000001, 1);    testX = mapminmax('apply', testX, xmap);    net = nets{time, 1};    ySim = simlssvm(net, testX')';    ySim = mapminmax('reverse', ySim, ymap);    mape_ = mape(testY, ySim);    netMapes = [netMapes mape_];end  % end timemeanMape = mean(netMapes)figure(1)plot(ySim,'r');hold on plot(testY,'b');