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GMM-EM算法讲义PPT slides
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上传时间: 2019-03-01
详细说明：GMM-EM算法讲义PPT slides，讲解GMM算法和EM算法的理论K-Means Clustering
For each data point x we introduce a binary vector rn of length K(1-of-K
encoding), which indicates which of the K clusters the data point xn is
assigned to
Define objective(distortion measure)
N K
rnkllxn- ph
7=1k=1
It represents the sum of squares of the distances of each data point to its
assigned prototype pk
Our goal it find the values of rnk and the
cluster centers pk so as to minimize the
0
objective J
0
terative Algorithm
Define iterative procedure to minimize
N K
J
∠ rnk:llXn-k
7=1k=1
Hard assignments of
Given uK, minimize J with respect to nk(E-step): points to clusters
1 ifk= arg min
jXn- p
0 otherwise
which simply says assign nth data point xn to its closest cluster center
Given rnk, minimize J with respect to uk (M-step
Inks
Pk
Number of points
72k
assigned to cluster k
Set Pp equal to the mean of all the data points assigned to cluster k
Guaranteed convergence to local minimum(not global minimum
EXample
EXample of using K-means(K=2)on Old Faithful dataset
a
2(b)
0
0
0
0
(e)
0
C
×
響”」
onvergence
Plot of the cost function after each E-step(blue points)and M-step(red
points)
The algorithm has converged
1000
after 3 iterations
500
3
K-means can be generalized by introducing a more general dissimilarity
measure
N K
=∑∑T(xn,k)
=1k=1
Image Segmentation
Another application of K-means algorithm
Partition an image into regions corresponding, for example, to object parts
Each pixel in an image is a point in 3-D space, corresponding to R, G, B
channels
Original image
K=3
K=10
For a given value of K, the algorithm represent an image using K colors
Another application is image compression
Image Compression
For each data point, we store only the identity k of the assigned cluster
We also store the values of the cluster centers
k
Provided
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