机器学习--- K均值（K-Means）
假定我们有如下8个点
A1(2, 10) A2(2, 5) A3(8, 4) A4(5, 8) A5(7, 5) A6(6, 4) A7(1, 2) A8(4, 9)
希望分成3个聚类
初始化选择 A1(2, 10), A4(5, 8) ，A7(1, 2)为聚类中心点，两点距离定义为ρ(a, b) = |x2 – x1| + |y2 – y1| .
第一步
Iteration 1
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(2, 10) |
(5, 8) |
(1, 2) |
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Point |
Dist Mean cluster 1 |
Dist Mean cluster2 |
Dist Mean cluster 3 |
Cluster |
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A1 |
(2, 10) |
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A2 |
(2, 5) |
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A3 |
(8, 4) |
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A4 |
(5, 8) |
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A5 |
(7, 5) |
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A6 |
(6, 4) |
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A7 |
(1, 2) |
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A8 |
(4, 9) |
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对A1点，计算其到每个cluster 的距离
A1->class1 = |2-2|+|10-10}=0
A1->class2 = |2-5|+|10-8|=5
A1->class3 = |2-1|+|10-2|=9
因此A1 属于cluster1
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(2, 10) |
(5, 8) |
(1, 2) |
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Point |
Dist Mean cluster 1 |
Dist Mean cluster 2 |
Dist Mean cluster 3 |
Cluster |
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A1 |
(2, 10) |
0 |
5 |
9 |
1 |
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A2 |
(2, 5) |
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A3 |
(8, 4) |
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A4 |
(5, 8) |
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A5 |
(7, 5) |
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A6 |
(6, 4) |
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A7 |
(1, 2) |
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A8 |
(4, 9) |
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余下继续计算，直到
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(2, 10) |
(5, 8) |
(1, 2) |
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Point |
Dist Mean cluster 1 |
Dist Mean cluster 2 |
Dist Mean cluster 3 |
Cluster |
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A1 |
(2, 10) |
0 |
5 |
9 |
1 |
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A2 |
(2, 5) |
5 |
6 |
4 |
3 |
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A3 |
(8, 4) |
12 |
7 |
9 |
2 |
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A4 |
(5, 8) |
5 |
0 |
10 |
2 |
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A5 |
(7, 5) |
10 |
5 |
9 |
2 |
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A6 |
(6, 4) |
10 |
5 |
7 |
2 |
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A7 |
(1, 2) |
9 |
10 |
0 |
3 |
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A8 |
(4, 9) |
3 |
2 |
10 |
2 |
重新计算中心点
cluster1只有1个点，因此A1为中心点
cluster2的中心点为 ( (8+5+7+6+4)/5,(4+8+5+4+9)/5 )=（6,6）。注意：这个点并不实际存在。
cluster3的中心点为( (2+1)/2, (5+2)/2 )= (1.5, 3.5)
图形化的过程如下：
持续迭代，直到前后两次迭代不发生变化为止，如下：
