The document contains data from a k-means clustering algorithm with 5 clusters. It shows the cluster assignments of 50 data points to the 5 clusters over 10 iterations. The data points are numbered 0-49 on the x-axis and assigned to clusters 0-4 on the y-axis. The cluster assignments change over the 10 iterations as the k-means algorithm converges.

2. 4.1 4
•
• 1
10 20 30
0.74 0.76 1.34
40
1.75
10 2 2.01 2.62 30 0.87
20 40
0.69
3
0.74 0.87 0.60 1.34
0.76 1.83 1.90
1.75
4 1.73 1.83 0.96 0.93
2.01 2.62 0.87 0.69
4.1 10 20 30
40
0.87
4
0.60 1.83 0 1.90
1.73 1.83 0.96 0.93
2

3. •
•
•
•
•
•

4. (2)
•
•
•
•
4

5. (3)
• 2
•
•
•
•
•
• (
•
•
•
5

6. x2 x2
x x
dx2 + dx2
1 2
|dx1 | + |dx2 |
dx2 dx2
y y
dx1 dx1
x1 x1
(A) (B)
6

7. n
i=1 (xi − x)(yi − y )
¯ ¯
r= n n
i=1 (xi − x)2
¯ i=1 (yi − y )2
¯
y y y
x x x
r≈1 r≈0 r ≈ −1
7

8. •
•
•
• (Top-down
Clustering, Divisive Clustering)
(Bottom-up Clustering, Agglomerative Clustering)
C
B
A
F
G E
D
A B C D E F G
(A) (B)
8

10. k-
• k
• d S
S k S1 , S 2 , . . . , S k
k-
• S S = S1 ∪ S2 ∪ · · · ∪ Sk
• Si ∩ Sj = φ (i = j)
• 3-
C C
B B
A
A
G
E
F F
G E
D D
(A) 3- (B) 3- 10

11. k- (2)
• k-
• (A)
• v(Si)
• (B)
• q(V)
ci = (1/|Si |) x
(A) x∈Si
(A)
1 n
v(Si ) = (d(x, ci ))
|Si |
x∈Si
(B) diameter(Si ) = max {d(x1 , x2 )|x1 , x2 ∈ Si }
q(V ) = max {diameter(Si ) | i = 1, . . . , k}
(B) 11

12. k- (3)
• 2
• n, d O(n^(O(dn)))
•
• k-Means
•
• NP-
• 2
12

13. (Hard) K-means(K- )
• k-means
•
• K
•
1.
• K
• K
• K
2.
3.
4. 2, 3

14. 7
2 .
2-means 2
(0)
m(1)
7 2
m(2) m(1), m(2)
2
(1) k m
14

15. m(1)
x x
k = arg min{d(m(k) , x)}
m(2) k
k
x x m (k)
(2)
x m (k)
d(m(1) , x) > d(m(2) , x)
+ x m (2)
□
d(x,y)
□ □ □
15

16. +m(1)
+
□
m(2)
□
□ □ □ m(k)
(3) (n) (n)
n rk x
m(k) =
R(k)
(n)
rk x(n) k
R(k) k
16

17. m(1)
x
m(2)
x
(4) m (2) m (1)
+ +
+
□ (2),(3)
□ □ □
17

18. K-means
• 5000
•
• 0 1 2 3 4 5 6 7 8 9
0 21 3 1 7
1 7 14 1 1 3 4
2 21 1 1 19 1
3 6 7 2 3 21 1 14
Cluster #
4 1 24 21 1 1
5 37 1 1 17 9 4 6 27 13
6 8 8 1 9
7 15 6 10
8 29 22 2 12 23 1
9 4 5 1 12 3 7 18

19. K-means
•
•
• k
•
Copyright Cambridge University Press 2003. On-screen viewing permitted. Printing not permitted. http://www.cambridge
You can buy this book for 30 pounds or $50. See http://www.inference.phy.cam.ac.uk/mackay/itila/ for links.
288 20 — An Example Inf
10 10 Figure 2
for a cas
8 8 clusters.
data. (b
6 6 assignm
(a) (b) four poi
4 4 cluster h
assigned
2 2 (Points
cluster a
0 0
0 2 4 6 8 10 0 2 4 6 8 10
19
Figure 2

20. (1)
•
112 4
(1) V C
C {}
(2) V 1 c1 ∈ V C c1 V
(3) j = 2, . . . , k C (a),(b) C
(a) B neighbor(x) B
x(∈ V − C) C
x neighbor(x)
A A
E E
(b) cj F C F
G
d(cj , neighbor(cj )) = max {d(x, neighbor(x)) | x ∈ V − C}
G
D x∈V −C D
(A) 7 (B) G
cj
20

21. (1) V C
C {}
(2) V 1 c1 ∈ V C c1 (2) V
(3) j = 2, . . . , k (a),(b)
(a) neighbor(x) x(∈ V − C) C
x neighbor(x)
(b) cj C
d(cj , neighbor(cj )) = max {d(x, neighbor(x)) | x ∈ V − C}
x∈V −C
cj
C C
C
B B
B 4.38
A A
A
E
E F E
4.10 F F
G G
G D
k- D NP D
(C) (D) (E)
C D k- 21

22. (2)
C C
B B
A A
E F E F
G G
D D
(E) (F)
D
2
22

23. (Self Organizing Map)
•
•
•
•
•
23