【RELM分类】基于鲁棒极限学习机RELM实现数据分类附matlab代码

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本文介绍了鲁棒极限学习机(RELM)，一种改进的ELM算法，通过引入鲁棒损失函数增强对噪声和异常值的抵抗能力。文章详细阐述了RELM的实现步骤，包括数据预处理、权重初始化、隐藏层输出计算和输出权重求解，以及模型的训练和测试过程。

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❤️ 内容介绍

鲁棒极限学习机（Robust Extreme Learning Machine, RELM）是一种基于极限学习机（Extreme Learning Machine, ELM）的算法，用于实现数据分类任务。RELM通过引入鲁棒损失函数，提高了ELM在面对噪声和异常值时的鲁棒性能。

RELM的实现步骤如下：

数据预处理：对原始数据进行预处理，包括数据清洗、特征选择和特征缩放等操作。
构建输入矩阵：将预处理后的数据按照矩阵的形式表示，其中每一行代表一个样本的特征，每一列代表一个特征。
随机初始化输入权重：随机生成输入层到隐藏层的权重矩阵，其中隐藏层的节点数可以根据经验或者交叉验证进行选择。
计算隐藏层输出：使用ReLU（Rectified Linear Unit）激活函数计算隐藏层的输出，即将输入矩阵与输入权重矩阵相乘，并将结果进行非线性变换。
求解输出权重：使用最小二乘法或者正则化方法求解输出权重矩阵，将隐藏层输出与样本的标签进行拟合。
预测分类结果：使用求解得到的输出权重矩阵，将测试样本的特征与隐藏层输出进行相乘，并通过激活函数得到预测的分类结果。
模型评估：使用评估指标（如准确率、精确率、召回率等）对模型进行评估，可以使用交叉验证等方法进行评估结果的稳定性。

通过以上步骤，可以使用RELM实现数据的分类任务。相比于传统的ELM算法，RELM在面对噪声和异常值时具有更好的鲁棒性能，可以提高分类模型的准确性和稳定性。

🔥核心代码

function [TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] = elm(TrainingData_File, TestingData_File, Elm_Type, NumberofHiddenNeurons, ActivationFunction)% Usage: elm(TrainingData_File, TestingData_File, Elm_Type, NumberofHiddenNeurons, ActivationFunction)% OR:    [TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] = elm(TrainingData_File, TestingData_File, Elm_Type, NumberofHiddenNeurons, ActivationFunction)%% Input:% TrainingData_File     - Filename of training data set% TestingData_File      - Filename of testing data set% Elm_Type              - 0 for regression; 1 for (both binary and multi-classes) classification% NumberofHiddenNeurons - Number of hidden neurons assigned to the ELM% ActivationFunction    - Type of activation function:%                           'sig' for Sigmoidal function%                           'sin' for Sine function%                           'hardlim' for Hardlim function%                           'tribas' for Triangular basis function%                           'radbas' for Radial basis function (for additive type of SLFNs instead of RBF type of SLFNs)%% Output: % TrainingTime          - Time (seconds) spent on training ELM% TestingTime           - Time (seconds) spent on predicting ALL testing data% TrainingAccuracy      - Training accuracy: %                           RMSE for regression or correct classification rate for classification% TestingAccuracy       - Testing accuracy: %                           RMSE for regression or correct classification rate for classification%% MULTI-CLASSE CLASSIFICATION: NUMBER OF OUTPUT NEURONS WILL BE AUTOMATICALLY SET EQUAL TO NUMBER OF CLASSES% FOR EXAMPLE, if there are 7 classes in all, there will have 7 output% neurons; neuron 5 has the highest output means input belongs to 5-th class%% Sample1 regression: [TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] = elm('sinc_train', 'sinc_test', 0, 20, 'sig')% Sample2 classification: elm('diabetes_train', 'diabetes_test', 1, 20, 'sig')%    %%%%    Authors:    MR QIN-YU ZHU AND DR GUANG-BIN HUANG    %%%%    NANYANG TECHNOLOGICAL UNIVERSITY, SINGAPORE    %%%%    EMAIL:      EGBHUANG@NTU.EDU.SG; GBHUANG@IEEE.ORG    %%%%    WEBSITE:    http://www.ntu.edu.sg/eee/icis/cv/egbhuang.htm    %%%%    DATE:       APRIL 2004%%%%%%%%%%% Macro definitionREGRESSION=0;CLASSIFIER=1;%%%%%%%%%%% Load training datasettrain_data=load(TrainingData_File);T=train_data(:,1)';P=train_data(:,2:size(train_data,2))';clear train_data;                                   %   Release raw training data array%%%%%%%%%%% Load testing datasettest_data=load(TestingData_File);TV.T=test_data(:,1)';TV.P=test_data(:,2:size(test_data,2))';clear test_data;                                    %   Release raw testing data arrayNumberofTrainingData=size(P,2);NumberofTestingData=size(TV.P,2);NumberofInputNeurons=size(P,1);if Elm_Type~=REGRESSION    %%%%%%%%%%%% Preprocessing the data of classification    sorted_target=sort(cat(2,T,TV.T),2);    label=zeros(1,1);                               %   Find and save in 'label' class label from training and testing data sets    label(1,1)=sorted_target(1,1);    j=1;    for i = 2:(NumberofTrainingData+NumberofTestingData)        if sorted_target(1,i) ~= label(1,j)            j=j+1;            label(1,j) = sorted_target(1,i);        end    end    number_class=j;    NumberofOutputNeurons=number_class;           %%%%%%%%%% Processing the targets of training    temp_T=zeros(NumberofOutputNeurons, NumberofTrainingData);    for i = 1:NumberofTrainingData        for j = 1:number_class            if label(1,j) == T(1,i)                break;             end        end        temp_T(j,i)=1;    end    T=temp_T*2-1;    %%%%%%%%%% Processing the targets of testing    temp_TV_T=zeros(NumberofOutputNeurons, NumberofTestingData);    for i = 1:NumberofTestingData        for j = 1:number_class            if label(1,j) == TV.T(1,i)                break;             end        end        temp_TV_T(j,i)=1;    end    TV.T=temp_TV_T*2-1;end                                                 %   end if of Elm_Type%%%%%%%%%%% Calculate weights & biasesstart_time_train=cputime;%%%%%%%%%%% Random generate input weights InputWeight (w_i) and biases BiasofHiddenNeurons (b_i) of hidden neuronsInputWeight=rand(NumberofHiddenNeurons,NumberofInputNeurons)*2-1;BiasofHiddenNeurons=rand(NumberofHiddenNeurons,1);tempH=InputWeight*P;clear P;                                            %   Release input of training data ind=ones(1,NumberofTrainingData);BiasMatrix=BiasofHiddenNeurons(:,ind);              %   Extend the bias matrix BiasofHiddenNeurons to match the demention of HtempH=tempH+BiasMatrix;%%%%%%%%%%% Calculate hidden neuron output matrix Hswitch lower(ActivationFunction)    case {'sig','sigmoid'}        %%%%%%%% Sigmoid         H = 1 ./ (1 + exp(-tempH));    case {'sin','sine'}        %%%%%%%% Sine        H = sin(tempH);        case {'hardlim'}        %%%%%%%% Hard Limit        H = double(hardlim(tempH));    case {'tribas'}        %%%%%%%% Triangular basis function        H = tribas(tempH);    case {'radbas'}        %%%%%%%% Radial basis function        H = radbas(tempH);        %%%%%%%% More activation functions can be added here                endclear tempH;                                        %   Release the temparary array for calculation of hidden neuron output matrix H%%%%%%%%%%% Calculate output weights OutputWeight (beta_i)OutputWeight=pinv(H') * T';                        % implementation without regularization factor //refer to 2006 Neurocomputing paper%OutputWeight=inv(eye(size(H,1))/C+H * H') * H * T';   % faster method 1 //refer to 2012 IEEE TSMC-B paper%implementation; one can set regularizaiton factor C properly in classification applications %OutputWeight=(eye(size(H,1))/C+H * H') \ H * T';      % faster method 2 //refer to 2012 IEEE TSMC-B paper%implementation; one can set regularizaiton factor C properly in classification applications%If you use faster methods or kernel method, PLEASE CITE in your paper properly: %Guang-Bin Huang, Hongming Zhou, Xiaojian Ding, and Rui Zhang, "Extreme Learning Machine for Regression and Multi-Class Classification," submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence, October 2010. end_time_train=cputime;TrainingTime=end_time_train-start_time_train        %   Calculate CPU time (seconds) spent for training ELM%%%%%%%%%%% Calculate the training accuracyY=(H' * OutputWeight)';                             %   Y: the actual output of the training dataif Elm_Type == REGRESSION    TrainingAccuracy=sqrt(mse(T - Y))               %   Calculate training accuracy (RMSE) for regression caseendclear H;%%%%%%%%%%% Calculate the output of testing inputstart_time_test=cputime;tempH_test=InputWeight*TV.P;clear TV.P;             %   Release input of testing data             ind=ones(1,NumberofTestingData);BiasMatrix=BiasofHiddenNeurons(:,ind);              %   Extend the bias matrix BiasofHiddenNeurons to match the demention of HtempH_test=tempH_test + BiasMatrix;switch lower(ActivationFunction)    case {'sig','sigmoid'}        %%%%%%%% Sigmoid         H_test = 1 ./ (1 + exp(-tempH_test));    case {'sin','sine'}        %%%%%%%% Sine        H_test = sin(tempH_test);            case {'hardlim'}        %%%%%%%% Hard Limit        H_test = hardlim(tempH_test);            case {'tribas'}        %%%%%%%% Triangular basis function        H_test = tribas(tempH_test);            case {'radbas'}        %%%%%%%% Radial basis function        H_test = radbas(tempH_test);                %%%%%%%% More activation functions can be added here        endTY=(H_test' * OutputWeight)';                       %   TY: the actual output of the testing dataend_time_test=cputime;TestingTime=end_time_test-start_time_test           %   Calculate CPU time (seconds) spent by ELM predicting the whole testing dataif Elm_Type == REGRESSION    TestingAccuracy=sqrt(mse(TV.T - TY))            %   Calculate testing accuracy (RMSE) for regression caseendif Elm_Type == CLASSIFIER%%%%%%%%%% Calculate training & testing classification accuracy    MissClassificationRate_Training=0;    MissClassificationRate_Testing=0;    for i = 1 : size(T, 2)        [x, label_index_expected]=max(T(:,i));        [x, label_index_actual]=max(Y(:,i));        if label_index_actual~=label_index_expected            MissClassificationRate_Training=MissClassificationRate_Training+1;        end    end    TrainingAccuracy=1-MissClassificationRate_Training/size(T,2)    for i = 1 : size(TV.T, 2)        [x, label_index_expected]=max(TV.T(:,i));        [x, label_index_actual]=max(TY(:,i));        if label_index_actual~=label_index_expected            MissClassificationRate_Testing=MissClassificationRate_Testing+1;        end    end    TestingAccuracy=1-MissClassificationRate_Testing/size(TV.T,2)  end