On Expansion of Fuzzified Even-Sized Clustering Based on Optimization for Data with Tolerance

Abstract

Even-sized clustering based on optimization (ECBO) is a clustering algorithm that classifies the cluster size to be the same. It has been applied to problems such as K-anonymization in information security and transportation area segmentation in package delivery planning. However, ECBO may not provide the best classification when the cluster size does not need to be exactly equal and when some margin is allowed. Fuzzified Even-Sized Clustering Based on Optimization (FECBO) is a clustering algorithm that considered to be one of the solutions to this problem. By the way, data in the real world includes uncertainties such as having errors, widths, missing some of the attributes, etc., so we should think in terms of ranges, not points. However, FECBO is not able to handle data with tolerance. In this paper, we propose a new clustering method that extends the objective function in FECBO to the case where the objective function is a more general nonlinear function, such as entropy regularized one, and introduce the concept of tolerance to FECBO to handle those.