An Interval-Based Framework for Fuzzy Clustering Applications

Abstract

The main goal of using data with interval nature is to represent numeric information endowed with impreciseness, which are normally captured from measures of real world. However, in order to do this, it is necessary to adapt real-valued techniques to be applied on interval-based data. For interval-based clustering applications, for instance, it is necessary to propose an interval-based distance and also to adapt clustering algorithms to be used in this context. Therefore, in this paper, we aim to provide a platform for performing clustering applications using interval-based data, including distance measure, clustering algorithms, and validation indexes. In this case, we adapt an interval-based distance called $d_{km}$ , and we propose two interval-based fuzzy clustering algorithms: Interval-based FcM and interval-based ckMeans, and three interval-based validation indexes. In order to validate the proposed interval-based framework, an empirical analysis was conducted using seven clustering datasets, three real and four synthetic interval datasets. The empirical analysis is based on an external cluster validity index, corrected rand, and six internal-based validation indexes, in which three of them can be used in their original proposal and three are proposed in this paper. The obtained results show the usefulness of the proposed interval-based framework for interval-based clustering problems.