k-means算法的简单示例备课讲稿

9

Example

E

C

D

P(1.6,4.8)

A

B

F

G

H

Q(4.8,1.6)

I

J

A dPA 1

<

< B dPB 0.89

< C dPC 0.63 < D dPD 0.45

< E dPE 1.26 > F dPF 3.69

> G dPG 4.40 > H dPH 5.22

> I dPI 4.49 > J dPJ 5.10
3. Each cluster's center is recomputed as the average of the points in that cluster.
4. Iterate step 2 or more until the new center of cluster equals to the original center of cluster or less than a specified threshold,then clustering finished.

α , β as the centre and K=2.
Step 2 again.

So,we classify A,B,C,D,E as a cluster and F,G,H,I,J as another cluster.

8

Example

E

C

D

α(1,4.5)

A

B

cluster 1

β(3.75,2.875)

F

G

H

I

J

cluster 2

α , β as the centre and K=2.

Step 3 again.

cente(rxi ,yj)
ij
PA,B,C,D,E(1.6,4.8)
new center
Q F,G,H,I,J(4.8,1.6)
The new centers of the two clusters are P(1.6,4.8) and Q(4.8,1.6)
k-means算法的简单示例

3
Algorithm Procedure
1. Randomly select K points from complete samples as the initial center.(That's what k means in K-means)
2. Each point in the dataset is assigned to the closed cluster,based upon the Euclidean distance between each point and each cluster center.

The new centers of the two clusters are (1,4.5) and (3.75,2.875)

7

Example

E

C

D

α(1,4.5)

A

B

β(3.75,2.875)

F

G

H

I

J

< A dA 0.5 < B dB 1.12 < C dC 0.5 < D dD 1.12

10

Example

cluster 1
E

C

D

P(1.6,4.8)

A

B

cente(rxi ,yj)
ij
M A,B,C,D ,E(1.6,4.8)
new center
NF,G ,H,I,J(4.8,1.6)

F
cluster 2 I

G

H

Q(4.8,1.6)

J

P , Q as the centre and K=2.

12
Disadvantages

one of the main

disadvantages to k-means is

dQA 4.49 dQB 3.69 dQC 5.10 d QD 4.4
dQE 5.22 dQF 0.89 dQG 0.45 dQH 1.26 dQI 1 dQJ 0.63

Step 2 again.

So,we classify A,B,C,D,E as a cluster and F,G,H,I,J as another cluster.
Step 3 again.

The new centers of

the two clusters are

equal to the original

P(1.6,4.8)

and

Q(4.8,1.6)

11
Final

E CD

A

B

cluster 1

cluster 2

F

G

H

I

J

Clustering finished !

4

Example

E

C

D

A

B

F

G

H

I

J

How to cluster A,B...H,J into two clusters?

5

Example

E

CD

d AC

d BC

A(1,4) B(2,4)

F

G

H

I

J

Randomly choose A,B as the centre and K=2.
Step 1 and 2.

>

dBG 3.61 dBH 4.47
dBI 3.61 dBJ 4.24

d AB means distance A→B

So,we classify A,C as a cluster and B,E,D,F,G,H,I and J as another cluster.

6

Example

E CD A(1,4) B(2,4)
cluster 1

cluster 2

F

G

H

I

J

cente(rxi ,yj)
ij
A,C(1 21,4 25)(1,4.5)
new center
B,D ,E,F,G ,H ,I,J(3.7,2 5.87 )

Randomly choose A,B as the centre and K=2.
Swk.baidu.comep 3.
< E dE 1.8 > F dF 3.91
> G dG 4.72 > H dH 5.59
> I dI 4.61 > J dJ 5.32

d A 2.97 d B 2.08 dC 3.48 dD 2.75
d E 3.58 d F 0.91
dG 1.53 d H 2.41
d I 1.89 d J 2.25

A dAA 0

< dBA 1

B

dAB 1

>

dBB 0

C dAC 1

< dBC 1.41

> D dAD 1.41

dBD 1

> E dAE 2.24

dBE 2

> F dAF 3.61

dBF 2.83

> G dAG 4.47 > H dAH 5.39

> I dAI 4.24

J d AJ 5