Ant Colony Optimization of Interval Type-2 Fuzzy C-Means with Subtractive Clustering and Multi-Round Sampling for Large Data

Abstract

Fuzzy C-Means (FCM) is widely accepted as a clustering technique. However, it cannot often manage different uncertainties associated with data. Interval Type-2 Fuzzy C-Means (IT2FCM) is an improvement over FCM since it can model and minimize the effect of uncertainty efficiently. However, IT2FCM for large data often gets trapped in local optima and fails to find optimal cluster centers. To overcome this challenge an Ant Colony-based Optimization (ACO) is proposed. Another challenge encountered is determining the number of clusters to perform clustering. Subtractive clustering (SC) is an efficient technique to estimate appropriate number of clusters. Though for large datasets the convergence rate of ACO and SC becomes high and thus, it becomes challenging to cluster data and evaluate correct number of clusters. To encounter the challenges of large dataset, Multi-Round Sampling (MRS) technique is proposed. IT2FCM-ACO with SC and MRS technique performs clustering on subsets of data and determines suitable cluster centers and cluster number. The obtained clusters are then extended to the entire dataset. This eliminates the need for IT2FCM to work on the complete dataset. Thus, the objective of this paper is to optimize IT2FCM using ACO algorithm and to estimate the optimal number of clusters using SC while employing MRS to handle the challenges of voluminous data. Results obtained from several clustering evaluation measures shows the improved performance of IT2FCM-ACO-MRS compared to ITFCM-ACO and IT2FCM. Speed up for different sample size of dataset is computed and is found that IT2FCM-ACO-MRS is ≈1–5 times faster than IT2FCM and IT2FCM-ACO for medium datasets whereas for large datasets it is reported to be ≈ 30–150 times faster.