ACPSO: A Novel Swarm Automatic Clustering Algorithm Based Image Segmentation

ACPSO: A Novel Swarm Automatic Clustering Algorithm Based Image Segmentation

Salima Ouadfel (University Mentouri – Constantine, Algeria), Mohamed Batouche (University Mentouri – Constantine, Algeria) and Abdlemalik Ahmed-Taleb (Universite Valenciennes, France)
DOI: 10.4018/978-1-4666-1830-5.ch014
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Abstract

In order to implement clustering under the condition that the number of clusters is not known a priori, the authors propose a novel automatic clustering algorithm in this chapter, based on particle swarm optimization algorithm. ACPSO can partition images into compact and well separated clusters without any knowledge on the real number of clusters. ACPSO used a novel representation scheme for the search variables in order to determine the optimal number of clusters. The partition of each particle of the swarm evolves using evolving operators which aim to reduce dynamically the number of naturally occurring clusters in the image as well as to refine the cluster centers. Experimental results on real images demonstrate the effectiveness of the proposed approach.
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Background

Problem Definition

The clustering problem can be formally defined as follows. Given a data set where is a data item and n is the number of data items in Z. The clustering aims to partitioning Z into K compacts and well separated clusters.

Compactness means that members of a cluster are all similar and close together. One measure of compactness of a cluster is the average distance of the cluster instances compared to the cluster center.

(1) where mj is the center of the jth cluster and nj is its cardinal. Lower value of compactness (cj) is better.

Thus, the overall compactness of a particular grouping of K clusters is just the sum of the compactness of the individual clusters

(2)

Separability means that members of one cluster are sufficiently different from members of another cluster (cluster dissimilarity). One measure of the separability of two clusters is their squared distance.

(3) where mi and mj are the center of the ith and jth cluster respectively.

The separability of the partition of K clusters could be defined as following:

(4)

The bigger the distance, the better the separability, so we would like to find groupings where separability is maximized.

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