Clustering algorithms based on volume criteria

Author

Krishnapuram, Raghu ; Kim, Jongwoo

Author_Institution

Dept. of Math. & Comput. Sci., Colorado Sch. of Mines, Golden, CO, USA

Volume

8

Issue

2

fYear

2000

fDate

4/1/2000 12:00:00 AM

Firstpage

228

Lastpage

236

Abstract

Clustering algorithms such as the K-means algorithm and the fuzzy C-means algorithm are based on the minimization of the trace of the (fuzzy) within-fluster scatter matrix. In this paper, we explore the use of determinant (volume) criteria for clustering. We derive an algorithm called the minimum scatter volume (MSV) algorithm, that minimizes the scatter volume, and another algorithm called the minimum cluster volume (MCV) that minimizes the sum of the volumes of the individual clusters. The behavior of MSV is shown to be similar to that of K-means, whereas MCV is more versatile

Keywords

fuzzy set theory; matrix algebra; minimisation; pattern clustering; K-means algorithm; MCV algorithm; MSV algorithm; clustering; clustering algorithms; determinant criteria; fuzzy C-means algorithm; fuzzy within-fluster scatter matrix; minimum cluster volume algorithm; minimum scatter volume algorithm; trace minimization; volume criteria; Clustering algorithms; Image segmentation; Iterative algorithms; Matrix decomposition; Maximum likelihood estimation; Minimization methods; Rough surfaces; Scattering; Shape; Surface roughness;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.842156

Filename

842156