正态分布有关计算,在线计算,在线计算器,计算器在线计算

2024-07-12 00:39| 来源: 网络整理| 查看: 265

function varargout = gmm(X, K_or_centroids) % ============================================================ % Expectation-Maximization iteration implementation of % Gaussian Mixture Model. % % PX = GMM(X, K_OR_CENTROIDS) % [PX MODEL] = GMM(X, K_OR_CENTROIDS) % % - X: N-by-D data matrix. % - K_OR_CENTROIDS: either K indicating the number of % components or a K-by-D matrix indicating the % choosing of the initial K centroids. % % - PX: N-by-K matrix indicating the probability of each % component generating each point. % - MODEL: a structure containing the parameters for a GMM: % MODEL.Miu: a K-by-D matrix. % MODEL.Sigma: a D-by-D-by-K matrix. % MODEL.Pi: a 1-by-K vector. % ============================================================

threshold = 1e-15; [N, D] = size(X); if isscalar(K_or_centroids) K = K_or_centroids; % randomly pick centroids rndp = randperm(N); centroids = X(rndp(1:K), :); else K = size(K_or_centroids, 1); centroids = K_or_centroids; end % initial values [pMiu pPi pSigma] = init_params(); Lprev = -inf; while true Px = calc_prob(); % new value for pGamma pGamma = Px .* repmat(pPi, N, 1); pGamma = pGamma ./ repmat(sum(pGamma, 2), 1, K); % new value for parameters of each Component Nk = sum(pGamma, 1); pMiu = diag(1./Nk) * pGamma' * X; pPi = Nk/N; for kk = 1:K Xshift = X-repmat(pMiu(kk, :), N, 1); pSigma(:, :, kk) = (Xshift' * ... (diag(pGamma(:, kk)) * Xshift)) / Nk(kk); end % check for convergence L = sum(log(Px*pPi')); if L-Lprev < threshold break; end Lprev = L; end if nargout == 1 varargout = {Px}; else model = []; model.Miu = pMiu; model.Sigma = pSigma; model.Pi = pPi; varargout = {Px, model}; end function [pMiu pPi pSigma] = init_params() pMiu = centroids; pPi = zeros(1, K); pSigma = zeros(D, D, K); % hard assign x to each centroids distmat = repmat(sum(X.*X, 2), 1, K) + ... repmat(sum(pMiu.*pMiu, 2)', N, 1) - ... 2*X*pMiu'; [dummy labels] = min(distmat, [], 2); for k=1:K Xk = X(labels == k, :); pPi(k) = size(Xk, 1)/N; pSigma(:, :, k) = cov(Xk); end end function Px = calc_prob() Px = zeros(N, K); for k = 1:K Xshift = X-repmat(pMiu(k, :), N, 1); inv_pSigma = inv(pSigma(:, :, k)); tmp = sum((Xshift*inv_pSigma) .* Xshift, 2); coef = (2*pi)^(-D/2) * sqrt(det(inv_pSigma)); Px(:, k) = coef * exp(-0.5*tmp); end end

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