es of three clusters from two models are different.

(a) (b)

A further comparison of cluster models for data shown in Figure 2.32 using the

tra package for two models (a) The K-means model. (b) The fuzzy C-means

e mixture model cluster analysis algorithm

ure model algorithm is also a partitioning clustering algorithm

1984; Day, 1969; McLachlam and Basford, 1988; Bishop, 2006].

principle is similar to the semi-parametric density estimation

, i.e., it is a mixture of a few components such as the Gaussian

nts or the Gamma components. A final density is a linear

ion of a finite of component densities.

ose the k^th cluster is centred at ࢛௞ with a covariance matrix Σ௞.

mbership function is defined as a probability ݌ሺܠ௡|࢛௞, Σ௞ሻ, while

tive function is defined as the likelihood function shown below,

ܠ௡|࢛௞, Σ௞ሻ is the probability that ܠ௡∈࣬^ௗ is a member of the k^th

ݓ௞∈ሾ0,1ሿ is the mixing coefficient of the k^th cluster,

ܱൌෑ෍ݓ௞݌ሺܠ௡|࢛௞, Σ௞ሻൌෑ݌ሺܠ௡ሻ

ே

௡ୀଵ

௄

௞ୀଵ

ே

௡ୀଵ

(2.26)

mixing coefficients must satisfy the conditions, i.e., 0 ൏ݓ௞൏1

ݓ௞

ଵ

ൌ1. The most widely researched mixture model is the