K-Means和图片压缩

K-Means的核心思想

初始化簇中心

代价函数

代码实现

J = zeros(100,1);

M = size(X,1);

min = inf;

for i = 1:100

    %随机取k个样本点作为簇中心

    randidx = randperm(M);

    initial_centroids = X(randidx(1:K),:);

    %将所得的中心点进行训练

    [centroids0, idx] = runkMeans(X, initial_centroids,10);

    for k = 1:M

       J(i) = J(i) + sum((X(k,:) - centroids0(idx(M),:)).^2);

    end

    %取最小代价为样本中心点

    if(min > J(i))

        centroids =centroids0;

    end

end

簇分配

tmp = zeros(K,1);

for i = 1:size(X,1)

    for j = 1:K

        tmp(j) = sum((X(i,:) - centroids(j,:)).^2);

    end

    [mins,index]=min(tmp);

    idx(i) = index;

end

簇中心移动

for i = 1:m

    centroids(idx(i),:) = centroids(idx(i),:) + X(i,:);

end

for j = 1:K

    centroids(j,:) = centroids(j,:)/sum(idx == j);

end

图片压缩

%  加载图片

A = double(imread('dragonfly.jpg'));

% 特征缩减

A = A / 255;

img_size = size(A);

X = reshape(A, img_size(1) * img_size(2), 3);

K = 16;

max_iters = 10;

%开始训练模型

initial_centroids = kMeansInitCentroids(X, K);

[centroids, idx] = runkMeans(X, initial_centroids, max_iters);

%开始压缩图片

idx = findClosestCentroids(X, centroids);

X_recovered = centroids(idx,:);

X_recovered = reshape(X_recovered, img_size(1), img_size(2), 3);

%输出所压缩的图片

subplot(1, 2, 2);

imagesc(X_recovered)