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CLUSTERING ALGORITHMS VIA
CLUSTERING ALGORITHMS VIA
FUNCTION OPTIMIZATION
FUNCTION OPTIMIZATION
In this context the clusters are assumed to be described by a
parametric specic model whose parameters are unknown (all
parameters are included in a vector denoted by θ).
Examples:
Compact clusters. Each cluster C
i
is represented by a point
m
i
in the l-dimensional space. Thus θ=[m
1
T
, m
2
T
, …, m
m
T
]
T
.
Ring-shaped clusters. Each cluster C
i
is modeled by a
hypersphere C(c
i
,r
i
), where c
i
and r
i
are its center and its
radius, respectively. Thus
θ=[c
1
T
, r
1
, c
2
T
, r
2
, …, c
m
T
, r
m
]
T
.
A cost J(θ) is dened as a function of the data vectors in X and θ.
Optimization of J(θ) with respect to θ results in θ that
characterizes optimally the clusters underlying X.
The number of clusters m is a priori known in most of the cases.
