XQDA.rar_XQDA_XQDA 度量学习_度量学习_行人重识别

function [W, M, inCov, exCov] = XQDA(galX, probX, galLabels, probLabels, options) lambda = 0.001; qdaDims = -1; verbose = false; if nargin >= 5 && ~isempty(options) if isfield(options,'lambda') && ~isempty(options.lambda) && isscalar(options.lambda) && isnumeric(options.lambda) lambda = options.lambda; end if isfield(options,'qdaDims') && ~isempty(options.qdaDims) && isscalar(options.qdaDims) && isnumeric(options.qdaDims) && options.qdaDims > 0 qdaDims = options.qdaDims; end if isfield(options,'verbose') && ~isempty(options.verbose) && isscalar(options.verbose) && islogical(options.verbose) verbose = options.verbose; end end if verbose == true fprintf('options.lambda = %g.\n', lambda); fprintf('options.qdaDims = %d.\n', qdaDims); fprintf('options.verbose = %d.\n', verbose); end [numGals, d] = size(galX); % n numProbs = size(probX, 1); % m % If d > numGals + numProbs, it is not necessary to apply XQDA on the high dimensional space. % In this case we can apply XQDA on QR decomposed space, achieving the same performance but much faster. if d > numGals + numProbs if verbose == true fprintf('\nStart to apply QR decomposition.\n'); end t0 = tic; [W, X] = qr([galX', probX'], 0); % [d, n] galX = X(:, 1:numGals)'; probX = X(:, numGals+1:end)'; d = size(X,1); clear X; if verbose == true fprintf('QR decomposition time: %.3g seconds.\n', toc(t0)); end end labels = unique([galLabels; probLabels]); c = length(labels); if verbose == true fprintf('#Classes: %d\n', c); fprintf('Compute intra/extra-class covariance matrix...'); end t0 = tic; galW = zeros(numGals, 1); galClassSum = zeros(c, d); probW = zeros(numProbs, 1); probClassSum = zeros(c, d); ni = 0; for k = 1 : c galIndex = find(galLabels == labels(k)); nk = length(galIndex); galClassSum(k, :) = sum( galX(galIndex, :), 1 ); probIndex = find(probLabels == labels(k)); mk = length(probIndex); probClassSum(k, :) = sum( probX(probIndex, :), 1 ); ni = ni + nk * mk; galW(galIndex) = sqrt(mk); probW(probIndex) = sqrt(nk); end galSum = sum(galClassSum, 1); probSum = sum(probClassSum, 1); galCov = galX' * galX; probCov = probX' * probX; galX = bsxfun( @times, galW, galX ); probX = bsxfun( @times, probW, probX ); inCov = galX' * galX + probX' * probX - galClassSum' * probClassSum - probClassSum' * galClassSum; exCov = numProbs * galCov + numGals * probCov - galSum' * probSum - probSum' * galSum - inCov; ne = numGals * numProbs - ni; inCov = inCov / ni; exCov = exCov / ne; inCov = inCov + lambda * eye(d); if verbose == true fprintf(' %.3g seconds.\n', toc(t0)); fprintf('#Intra: %d, #Extra: %d\n', ni, ne); fprintf('Compute eigen vectors...'); end t0 = tic; [V, S] = svd(inCov \ exCov); if verbose == true fprintf(' %.3g seconds.\n', toc(t0)); end latent = diag(S); [latent, index] = sort(latent, 'descend'); energy = sum(latent); minv = latent(end); r = sum(latent > 1); energy = sum(latent(1:r)) / energy; if qdaDims > r qdaDims = r; end if qdaDims <= 0 qdaDims = max(1,r); end if verbose == true fprintf('Energy remained: %f, max: %f, min: %f, all min: %f, #opt-dim: %d, qda-dim: %d.\n', energy, latent(1), latent(max(1,r)), minv, r, qdaDims); end V = V(:, index(1:qdaDims)); if ~exist('W', 'var'); W = V; else W = W * V; end if verbose == true fprintf('Compute kernel matrix...'); end t0 = tic; inCov = V' * inCov * V; exCov = V' * exCov * V; M = inv(inCov) - inv(exCov); if verbose == true fprintf(' %.3g seconds.\n\n', toc(t0)); end