原
吴恩达机器学习 - 无监督学习——K-means算法
笔记：
核心步骤：
那我们就实现这两个函数就行啦：
findClosestCentroids.m（把每个点染色）：
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个样本和第K个聚类中心的距离的平方
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); %寻找每一行中最小的元素索引
% =============================================================
end
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computeCentroids.m（更新聚类中心）：
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
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看看聚类中心是怎么变化的吧~
剩下的基本不怎么变啦~
还有一点需要注意：聚类中心的随机初始化：
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
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另外最后还给了个例子，是关于图像颜色压缩的，也是用的K-means算法，并不是很难，自己看看了解一下就好~