Matlab实现基于LFDA基于局部费歇尔判别的分类数据降维可视化（完整程序和数据）

function [T, Z] = LFDA(p_train, t_train, r, metric, kNN) %% 用于监督降维的局部 Fisher 判别分析 % Input: % p_train:num_d x num_s matrix of original samples % num_d --- dimensionality of original samples % num_s --- the number of samples % t_train:num_s dimensional vector of class labels % r: dimensionality of reduced space (default: num_d) % metric: type of metric in the embedding space (default: 'weighted') % 'weighted' --- weighted eigenvectors % 'orthonormalized' --- orthonormalized % 'plain' --- raw eigenvectors % kNN: parameter used in local scaling method (default: 7) % % Output: % T: num_d x r transformation matrix % Z: r x num_s matrix of dimensionality reduced samples % 获取数据的样本数目和维度 [num_d, num_s] = size(p_train); % 参数输入检查，默认参数设置 if nargin < 3 r = num_d; end if nargin < 4 metric = 'weighted'; end if nargin < 5 kNN = 7; end % 参数的初始化 tSb = zeros(num_d, num_d); tSw = zeros(num_d, num_d); % 获取不同参数类别 for c = unique(t_train') % 获取该类别样本的输入和数目 Xc = p_train(:, t_train == c); nc = size(Xc, 2); % 定义类亲和矩阵 Xc2 = sum(Xc .^ 2, 1); distance2 = repmat(Xc2, nc, 1) + repmat(Xc2', 1, nc) - 2 * (Xc' * Xc); [sorted, ~] = sort(distance2); kNNdist2 = sorted(kNN + 1, :); sigma = sqrt(kNNdist2); localscale = sigma' * sigma; flag = (localscale ~= 0); A = zeros(nc, nc); A(flag) = exp(-distance2(flag) ./ localscale(flag)); Xc1 = sum(Xc, 2); G = Xc * (repmat(sum(A, 2), [1, num_d]) .* Xc') - Xc * A * Xc'; tSb = tSb + G / num_s + Xc * Xc' * (1 - nc / num_s) + Xc1 * Xc1' / num_s; tSw = tSw + G / nc; end X1 = sum(p_train, 2); tSb = tSb - X1 * X1' / num_s - tSw; tSb = (tSb + tSb') / 2; tSw = (tSw + tSw') / 2; if r == num_d [eigvec, eigval_matrix] = eig(tSb, tSw); else opts.disp = 0; [eigvec, eigval_matrix] = eigs(tSb, tSw, r, 'la', opts); end eigval = diag(eigval_matrix); [sort_eigval, sort_eigval_index] = sort(eigval); T0 = eigvec(:, sort_eigval_index(end: -1: 1)); % 确定嵌入空间中的度量 switch metric % 加权特征向量 case 'weighted' T = T0 .* repmat(sqrt(sort_eigval(end: -1: 1))', [num_d, 1]); % 正交归一化 case 'orthonormalized' [T, ~] = qr(T0, 0); % 原始特征向量 case 'plain' T = T0; end % 获取转移矩阵 Z = T' * p_train;