function [U, S, V, P,P_res, L,L_res] = cca_fun_static(X,Y) % CCA calculate canonical correlations % % [U, S, V, P, L] = cca(Y_tr,U_tr) where P and L contains the canonical correlation % matrices as columns and S is a matrix with corresponding canonical % correlations. The correlations are sorted in descending order. Y_tr and % U_tr are matrices where each column is a sample. Hence, Y_tr and U_tr must have % the same number of columns. % % Example: If Y is M*K and U_tr is L*K there are rank=MIN(M,L) solutions. U is % then M*M, V is L*L and S is M*L. P is M*rank, L is L*rank. % % % ? 2014 Zhiwen Chen, Duisburg-Essen universitet % --- Calculate covariance matrices --- [l,n_s]=size(Y); [m,~]=size(X); %% %CVA decomposition [U,S,V]=svd((X*X')^(-0.5)*(X*Y')*(Y*Y')^(-0.5)); %%%%%%%%%%%%%%%%%%%%%%%% Determine the order n_o = rank(S); S = S(1:n_o,1:n_o); % for i=1:size(S,2) % if sum(sum(S(1:i,1:i)))/sum(sum(S))>0.8 % n_o=i; % break % end % end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Get L,P,X,Q,Omega,X P=(X*X')^(-0.5)*U(:,1:n_o); P_res = (X*X')^(-0.5)*U(:,n_o+1:end); L=(Y*Y')^(-0.5)*V(:,1:n_o); L_res=(Y*Y')^(-0.5)*V(:,n_o+1:end); end
时间: 2024-04-03 08:32:12 浏览: 61
这段代码实现了CCA(Canonical Correlation Analysis,典型相关分析)算法。该算法可以用于分析两个不同数据集之间的相关性,并找到它们之间的线性关系。该算法的输入是两个矩阵X和Y,它们分别表示两个数据集,每一列为一个样本,X的大小为m*n_s,Y的大小为l*n_s。其中,m和l分别为两个数据集的维数,n_s为样本数量。输出是四个矩阵U、S、V和P,以及两个残差矩阵P_res和L_res。
算法的主要步骤如下:
1. 计算两个数据集的协方差矩阵;
2. 对协方差矩阵进行SVD分解;
3. 根据SVD分解的结果,计算出CCA的解;
4. 求解P、L和残差矩阵P_res和L_res。
其中,U、S和V分别表示SVD分解得到的左奇异矩阵、奇异值矩阵和右奇异矩阵,P和L表示两个数据集之间的映射矩阵,P_res和L_res表示P和L的残差矩阵。最后返回这些矩阵作为函数的输出。
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