💥1 概述
极限学习机（Extreme Learning Machine,ELM）作为前馈神经网络学习中一种全新的训练框架,在行为识别、情感识别和故障诊断等方面被广泛应用,引起了各个领域的高度关注和深入研究.ELM最初是针对单隐层前馈神经网络的学习速度而提出的,之后又被众多学者扩展到多隐层前馈神经网络中.该算法的核心思想是随机选取网络的输入权值和隐层偏置,在训练过程中保持不变,仅需要优化隐层神经元个数.网络的输出权值则是通过最小化平方损失函数,来求解Moore-Penrose广义逆运算得到最小范数最小二乘解.相比于其它传统的基于梯度的前馈神经网络学习算法,ELM具有实现简单,学习速度极快和人为干预较少等显著优势,已成为当前人工智能领域最热门的研究方向之一.ELM的学习理论表明,当隐层神经元的学习参数独立于训练样本随机生成,只要前馈神经网络的激活函数是非线性分段连续的,就可以逼近任意连续目标函数或分类任务中的任何复杂决策边界.近年来,随机神经元也逐步在越来越多的深度学习中使用,而ELM可以为其提供使用的理论基础.
运行脚本的说明：
- 打开 ELM_run.m 脚本并更改脚本参数的值。
- 运行脚本
📚2 运行结果
🎉3 参考文献
[1]徐睿,梁循,齐金山,李志宇,张树森.极限学习机前沿进展与趋势[J].计算机学报,2019,42(07):1640-1670.
👨💻4 Matlab代码
主函数部分代码：
%%Introduction to the ELM run script %Please the change the arguments according to your needs %% important arguments for the script activationFunction = 'linear'; dataFile = 'newstocks.txt'; rowsToSkip = 1; columnsToSkipFromLeft = 1; columnsToSkipFromRight = 1; hiddenLayerSize = 10; trainingPercentage = 50; daysToPredict = 5; %% data loading and preprocessing % load data pureData = csvread(dataFile,rowsToSkip,columnsToSkipFromLeft); % acquire X X = pureData(daysToPredict:end,1:end - columnsToSkipFromRight); % get number of entries and features [nEntries, nFeatures] = size(X); % acquire Y Y = pureData(1:nEntries,1:nFeatures); % finding split points in data percTraining = trainingPercentage/100; endTraining = ceil(percTraining * nEntries); % dividing X and Y % training data trainX = X(1:endTraining,:); trainY = Y(1:endTraining,:); % testing data testX = X(endTraining+1:end,:); testY = Y(endTraining+1:end,:); %% creation and training of ELM model % create ELM ELM = ELM_MatlabClass(nFeatures,hiddenLayerSize,activationFunction); % train ELM on the training dataset ELM = train(ELM,trainX,trainY); %% validation of ELM model predictionTest = predict(ELM,testX); disp('Statistics when predicting on testing data'); fprintf('Testing Rsquare(close to 1 means nice prediction) = %3.3f\n',computeR2(testX,predictionTest)); fprintf('Testing Root mean square error of open price = %3.3f\n',computeRMSE(testX(:,1),predictionTest(:,1))); fprintf('Testing Root mean square error of high price = %3.3f\n',computeRMSE(testX(:,2),predictionTest(:,2))); fprintf('Testing Root mean square error of low price = %3.3f\n',computeRMSE(testX(:,3),predictionTest(:,3))); fprintf('Testing Root mean square error of close price = %3.3f\n',computeRMSE(testX(:,4),predictionTest(:,4))); % compute and report accuracy on training dataset predictionTrain = predict(ELM,trainX); disp('Statistics when predicting on training data'); fprintf('Training Rsquare(close to 1 means nice prediction) = %3.3f\n',computeR2(trainX,predictionTrain)); fprintf('Training Root mean square error of open price = %3.3f\n',computeRMSE(trainX(:,1),predictionTrain(:,1))); fprintf('Training Root mean square error of high price = %3.3f\n',computeRMSE(trainX(:,2),predictionTrain(:,2))); fprintf('Training Root mean square error of low price = %3.3f\n',computeRMSE(trainX(:,3),predictionTrain(:,3))); fprintf('Training Root mean square error of close price = %3.3f\n',computeRMSE(trainX(:,4),predictionTrain(:,4))); %% sensitivity analysis on number of hidden neurons hiddenLayerSize = 1:10:100; trainR2 = zeros(size(hiddenLayerSize)); testR2 = zeros(size(hiddenLayerSize)); for i = 1 : numel(hiddenLayerSize) % create ELM for classification ELM = ELM_MatlabClass(nFeatures,hiddenLayerSize(i),activationFunction); % train ELM on the training dataset ELM = train(ELM,trainX,trainY); Yhat = predict(ELM,trainX); trainR2(i) = computeR2(trainX,Yhat); % validation of ELM model Yhat = predict(ELM,testX); testR2(i) = computeR2(testX,Yhat); end % plot results of accuracy with different sizes of the hidden layer figure; plot(hiddenLayerSize,[trainR2;testR2],'-o'); xlabel('Number of Hidden Neurons'); ylabel('R square error'); legend({'training','testing'},'Location','southeast');
