This paper proposes a clustering algorithm, Fuzzy CLARA, which combines Fuzzy C-Medoids algorithm (FCMDD) with Clustering LARge Applications (CLARA) algorithm with an application of the proposed algorithm for fast image segmentation. CLARA finds wide applications in different areas of data mining and is known to reduce time complexity while dealing with large datasets. The performance of the fuzzy CLARA algorithm is compared with fuzzy c-medoids algorithm and its linearized low complexity version. The efficiency of the clustering algorithms is measured using the clustering validity index Xie-Beni. The findings of the study show that the fuzzy CLARA algorithm gives better results with respect to both time complexity and Xie-Beni index compared to Fuzzy c-medoids algorithm and its linearized low complexity version.

Image analysis is an important branch of study because of its ability to perform fast and non-invasive low-cost analysis on products and processes. Image segmentation is a critical and essential component of image analysis system. It is one of the most important steps in image processing because it determines the quality of the final result of the analysis. Image segmentation finds its application in the analysis of satellite images, MRI images, mammograms, etc. The process of image segmentation makes use of clustering algorithms. Some popular clustering algorithms are k-means algorithm due to MacQueen (1967) and k-medoids algorithm due to Kaufman and Rousseeuw (1987). These algorithms are mainly used for crisp partitioning of datasets. To create fuzzy partitions using k-means algorithm, Bezdek (1981) proposed the Fuzzy c-means clustering algorithm.

As a fuzzy relative of the k-medoids algorithm, Krishnapuram et al. (1999) proposed the fuzzy c-medoids algorithm with an application to web document and snippet clustering. A survey of the available literature leads us to believe that a majority of the work done in the direction of image segmentation used different versions of k-means and fuzzy c-means algorithms only. Some related works in this direction are Ramze et al. (1995), Ng et al. (2006) and Shasidhar et al. (2011).

A thorough literature review shows dearth of application of k-medoids clustering in image segmentation. However, recently, Pakhira (2008) proposed a modified version of CLARA for the purpose of image segmentation. In this paper, a new clustering algorithm that inherits the characteristics of both fuzzy c-medoids algorithm of Krishnapuram et al. (1999) and CLARA of Kaufman and Rousseeuw (1990) has been proposed with an application in image segmentation. The qualities of the clustering outputs produced by these two algorithms are measured using the clustering validity index proposed by Xie and Beni (1991).

The rest of the paper is organized as follows. In Section II, the fuzzy c-medoids algorithm of Krishnapuram et al. (1999) is explained in detail along with its low complexity linearized version accompanied by a discussion on the procedure for selecting initial medoids. Section III reviews the CLARA algorithm and also proposes the new Fuzzy CLARA algorithm. Xie-Beni index for measuring the quality of clustered output is explained in Section IV. Section V compares the performance of fuzzy c-medoids algorithm and its linearized version with the fuzzy CLARA algorithm for image segmentation applications.

Computer Sciences Journal, Business Intelligence, Enterprise Systems, Enterprise Resource Planning, Customer Relationship Management, CRM, Business Operations Management, Business Process Mining, Finite State Machine, Transactional Information System, Genetic Algorithms, Decision Making Process, Data Mining Tools, Online Analysis Processing, OLAP, Artificial Intelligence.