function [V,X] = S2DLDAL1(X,Y,v0,sigma,delta,p,dim) % % % close all; clear variables; % Useage: % Input - X: the trainig data, is a 3-dimensional data of size d1*d2*N % Y： the label vector corresponding to X % v0: the initialization projection vector % sigma: the L2-norm regularization term parameter % delta: the Lp-norm regularization term parameter % p: in the Lp-norm % dim: the reduced dimension % Output - V: the projection matrix % % % % % Examples % for i = 1:10 % X(:,:,i) = rand(32,32); % end % Y = [ones(5,1);-ones(5,1)]; % v0 = ones(32,1); % sigma = 10^4; % delta = 10^-3 % p = 1; % dim = 10; % [V,X] = S2DLDAL1(X,Y,v0,sigma,delta,p,dim); % % % Reference: % Chun-Na Li, Meng-Qi Shang, Yuan-Hai Shao, and Nai-Yang Deng, % "Sparse L1-norm two dimensional linear discriminant analysis via the generalized elastic net regularization", submitted 2018 % Version 1.0 -- 15.April/2018 % % Written by Meng-Qi Shang,17858527466@163.com %输入：数据矩阵，标签数据，初始值w，s投影纬度，每个图像矩阵参数行和列 %输出投影矩阵，与更新后的原始数据 A = X; V = zeros(size(X,2),dim); d=1; while d <= dim [v1] = main2(X,Y,v0,sigma,delta,p); V(:,d) = v1; X = updata(A,V); clc fprintf('The %d-the dimension is done\n',d) d = d+1; end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [v] = main2(X,Y,v,sigma,delta,p) %输入：训练数据集，初始w，每个数据矩阵的行列 %输出：收敛的w maxiter = 0; v0 = 0; while max(abs(v-v0))>0.0001 && maxiter<100%检测目标值是否收敛合格 v0 = v; new_v = main1(X,Y,v,sigma,delta,p); v = new_v; maxiter = maxiter+1; end v = v./sqrt(v'*v); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [v]=main1(X,lable,v0,sigma,delta,p) class = unique(lable); c = length(class); matrix1 = mean(X,3);%总均值矩阵 [m,n,~] = size(X); h = 0;H = zeros(n); for i=1:c [data1,matrix2,num] = find_matrix(X,lable,class(i)); Y = matrix2 - matrix1; h = h + sum(num*(ones(n,1)*sign(Y*v0)').*Y',2); for j=1:num matrix4 = data1(:,:,j); for k=1:m Z = matrix4(k,:)-matrix2(k,:); if abs(Z*v0) <= 10^-4 v0 = v0+0.0002*ones(n,1); H = H+(Z'*Z/abs(Z*v0)); else H = H+(Z'*Z/abs(Z*v0)); end end end end H = H+sigma*eye(n); G = delta*((abs(v0)).^(p-1).*sign(v0)); v = ((h'/H*G+1)*H\h)/(h'/H*h)-H\G; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [sample_data,mean_data,num]=find_matrix(X,Y,C) %输入：X样本数据，Y为样本标签，C为类别 %输出：x1为第c类样本数据，x2为第c类样本均值，num为c类样本数量 sample_data = X(:,:,Y == C); mean_data = mean(sample_data,3); num = length(sample_data(1,1,:)); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [newX] = updata(X,V) %更新原始数据 [~,m,n]=size(X); newX = zeros(size(X)); for i=1:n newX(:,:,i) = X(:,:,i)*(eye(m)-V*V'); end end