Fuzzy Hyperplane Clustering Algorithm and Applications ... - DIMACS

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Fuzzy
H
yperplane
C
lustering
A
lgorithm and
A
pplications to
S
parse
R
epresentations


Pando Georgiev
and

Anca Ralescu

ECECS Department

University of Cincinnati

E
-
mail:
f
pgeorgie,aralescu
g
@ececs.uc.edu

We develop a fuzzy hyperplane clustering algorithm based o
n finding a skeleton (a union
of hyper
-
planes) of a given set of data points. The resulting algorithm has a direct
application to the following sparse representation problem: represent a given data matrix
X




m

N

in the form

X = AS
, where

A


m

N
,
S



m

N
, as a priori is known that
such a representation exists and the matrix

S

is sparse in the sense that each column of
it has at least
n
-
m
+1 zeros. Applications to fMRI data analysis are considered.


Neuroscience 2006








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