(a) (b)

. (a) A mixture of three Gaussians. (b) A mixture of three Gamma densities.

The result of the K-means model and the model constructed by the mixture

rithm for the data shown in Figure 2.35(a).

K-means

Mixture model

1

2

3

1

2

3

1

764

236

0

857

140

3

2

7

978

15

45

923

32

3

0

87

913

0

65

935

88.5%

90.5%

Th results of the K-means model and the model constructed by the mixture

rithm for the data shown in Figure 2.35(b).

K-means

Mixture model

1

2

3

1

2

3

1

997

3

0

987

13

0

2

26

955

19

7

957

36

3

0

45

955

0

27

973

96.9%

97.2%

easure the goodness of a cluster model, the mixture model

m employs the Bayesian Information Criterion (BIC) [Schwarz,

optimise a model structure. The BIC is defined as below, where

e residual sum of squares, N is the number of data points and C

ant,

BIC ൌെ^ܰ

2 ^{log ൬RSS}

ܰ^൰൅ܥ

(2.28)

R package for modelling a Gamma mixture model is mixtools.

ackage mclust used for using the Gaussian mixture algorithm

IC measurement embedded. The following code can be used to