Clustering in the presence of side information: a non-linear approach

Abstract

Purpose Constrained clustering is an important recent development in clustering literature. The goal of an algorithm in constrained clustering research is to improve the quality of clustering by making use of background knowledge. The purpose of this paper is to suggest a new perspective for constrained clustering, by finding an effective transformation of data into target space on the reference of background knowledge given in the form of pairwise must- and cannot-link constraints. Design/methodology/approach Most of existing methods in constrained clustering are limited to learn a distance metric or kernel matrix from the background knowledge while looking for transformation of data in target space. Unlike previous efforts, the author presents a non-linear method for constraint clustering, whose basic idea is to use different non-linear functions for each dimension in target space. Findings The outcome of the paper is a novel non-linear method for constrained clustering which uses different non-linear functions for each dimension in target space. The proposed method for a particular case is formulated and explained for quadratic functions. To reduce the number of optimization parameters, the proposed method is modified to relax the quadratic function and approximate it by a factorized version that is easier to solve. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed method. Originality/value This study proposes a new direction to the problem of constrained clustering by learning a non-linear transformation of data into target space without using kernel functions. This work will assist researchers to start development of new methods based on the proposed framework which will potentially provide them with new research topics.