筆記：

核心步驟：

那我們就實現這兩個函式就行啦：

findClosestCentroids.m（把每個點染色）：

function idx = findClosestCentroids(X, centroids)
%FINDCLOSESTCENTROIDS computes the centroid memberships for every example
%   idx = FINDCLOSESTCENTROIDS (X, centroids) returns the closest centroids
%   in idx for a dataset X where each row is a single example. idx = m x 1 
 

%   vector of centroid assignments (i.e. each entry in range [1..K])
%

% Set K
K = size(centroids, 1);

% You need to return the following variables correctly.
idx = zeros(size(X,1), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Go over every example, find its closest centroid, and store
 

%               the index inside idx at the appropriate location.
%               Concretely, idx(i) should contain the index of the centroid
%               closest to example i. Hence, it should be a value in the 
%               range 1..K
%
% Note: You can use a for-loop over the examples to compute this.
 

%

m = size(X,1);
dis = zeros(m,K);       %(m,k)位置表示第m個樣本和第K個聚類中心的距離的平方
for i=1:m
    for j=1:K
        dis(i,j) = X(i,:)*X(i,:)' + centroids(j,:)*centroids(j,:)' - ...
            X(i,:)*centroids(j,:)'*2;
    end
end
[~, idx] = min(dis,[],2);       %尋找每一行中最小的元素索引

% =============================================================

end

computeCentroids.m（更新聚類中心）：

function centroids = computeCentroids(X, idx, K)
%COMPUTECENTROIDS returns the new centroids by computing the means of the 
%data points assigned to each centroid.
%   centroids = COMPUTECENTROIDS(X, idx, K) returns the new centroids by 
%   computing the means of the data points assigned to each centroid. It is
%   given a dataset X where each row is a single data point, a vector
%   idx of centroid assignments (i.e. each entry in range [1..K]) for each
%   example, and K, the number of centroids. You should return a matrix
%   centroids, where each row of centroids is the mean of the data points
%   assigned to it.
%

% Useful variables
[m n] = size(X);

% You need to return the following variables correctly.
centroids = zeros(K, n);

% ====================== YOUR CODE HERE ======================
% Instructions: Go over every centroid and compute mean of all points that
%               belong to it. Concretely, the row vector centroids(i, :)
%               should contain the mean of the data points assigned to
%               centroid i.
%
% Note: You can use a for-loop over the centroids to compute this.
%

for i=1:K
    index = find(idx == i);
    centroids(i,:) = mean(X(index,:));
end

% =============================================================

end

看看聚類中心是怎麼變化的吧~

剩下的基本不怎麼變啦~

還有一點需要注意：聚類中心的隨機初始化：

Code（kMeansInitCentroids.m）：

function centroids = kMeansInitCentroids(X, K)
%KMEANSINITCENTROIDS This function initializes K centroids that are to be 
%used in K-Means on the dataset X
%   centroids = KMEANSINITCENTROIDS(X, K) returns K initial centroids to be
%   used with the K-Means on the dataset X
%

% You should return this values correctly
centroids = zeros(K, size(X, 2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should set centroids to randomly chosen examples from
%               the dataset X
%

% Randomly reorder the indices of examples
randidx = randperm(size(X, 1));
% Take the first K examples as centroids
centroids = X(randidx(1:K), :);

% =============================================================

end

另外最後還給了個例子，是關於影象顏色壓縮的，也是用的K-means演算法，並不是很難，自己看看了解一下就好~