MACHINE LEARNING TECHNIQUES - LASA

89
J
j
( µ
1,....,
µ
K) = ∑∑ φ( x ) −φ ( µ
i)
=
K
i= 1 x ∈C
K
∑∑
j
j
( x ) φ( x )
( )
2
l j
j l
( x ) φ( x ) ∑ φ( x ) φ( x )
2 φ
l i
∈
− +
m
x , x ∈C
i j
j l
( ) ∑ k( x , x )
( m )
( m )
i= 1 x ∈C i i
⎛⎛
K
⎜⎜
= ∑ ∑ ⎜⎜k x , x
j i
⎜⎜
⎝⎝
i
i
⎛⎛
⎜⎜
⎜⎜φ
⎜⎜
⎝⎝
j j x C
∑
2 k x , x
j i
∈
− +
m
i i x C
∑
j l i
x , x ∈C
i= 1 x ∈C i i
j l i
2
⎞⎞
⎟⎟
⎟⎟
⎟⎟
⎠⎠
2
⎞⎞
⎟⎟
⎟⎟
⎟⎟
⎠⎠
(5.26)
In kernel K-Means, the iteration stops when the change in J is sufficiently small.
As for all kernel methods, a clear bottleneck of kernel K-Means is that each iteration steps
2
requires O( M)
computation step. Smilarly to classical K-means, kernel K-Means is also very
sensitive to the initialization of the centers and may lead to poor partiotioning with a poor
initialization, as shown in Figure 5-4.
Figure 5-4: A difficult clustering problem. Standard K-Means (left) is unable to correctly separate the three
clusters. Using a Gaussian kernel (gamma = 0.01) Kernel K-Means (right) successfully separates the three
clusters. [DEMOS\CLUSTERING\KERNEL-KMEANS.ML]
© A.G.Billard 2004 – Last Update March 2011