Incorporating Local Data and KL Membership Divergence into Hard C-Means Clustering for Fuzzy and Noise-Robust Data Segmentation

Abstract

Hard C-means (HCM) and fuzzy C-means (FCM) algorithms are among the most popular ones for data clustering including image data. The HCM algorithm offers each data entity with a cluster membership of 0 or 1. This implies that the entity will be assigned to only one cluster. On the contrary, the FCM algorithm provides an entity with a membership value between 0 and 1, which means that the entity may belong to all clusters but with different membership values. The main disadvantage of both HCM and FCM algorithms is that they cluster an entity based on only its self-features and do not incorporate the influence of the entity ’ s neighborhoods, which makes clustering prone to additive noise. In this chapter, Kullback-Leibler (KL) membership divergence is incorporated into the HCM for image data clustering. This HCM-KL-based clustering algorithm provides twofold advantage. The first one is that it offers a fuzzification approach to the HCM cluster- ing algorithm. The second one is that by incorporating a local spatial membership function into the HCM objective function, additive noise can be tolerated. Also spatial data is incorporated for more noise-robust clustering. pixels. Results of segmentation of synthetic, simulated medical and real-world images have shown that the proposed local membership KL divergence-based FCM (LMKLFCM) and the local data and membership KL divergence-based entropy FCM (LDMKLFCM) algorithms outperform several widely used FCM related algorithms. Moreover, the average runtimes of all algorithms have been measured via simulation. In all runs, all algorithms start from the same randomly generated initial conditions, as mentioned in the simulation section, and stopped at the same fixed point. The LDMKLFCM, LMKLFCM, standard FCM, MEFCM, and SFCM algorithms have provided average runtime of 1.5, 1.75, 1, 0.9 and 1 sec respectively. The simulation results have been done using Matlab R2013b under windows on a processor of Intel (R) core (TM) i3, CPU M370 2.4 GHZ, 4 GB RAM.