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.

On mathematical optimization for clustering categories in contingency tables

“…Clustering categories in rows and/or columns of a contingency table is also desirable to enhance interpretability and transparency (Baesens et al 2003;Carrizosa et al 2017bCarrizosa et al , 2022Goodman and Flaxman 2017;Ustun and Rudin 2016), by easing the presentation of the table as well as the conclusions of the analysis from a statistical perspective. Furthermore, constrained clustering allows the analyst to incorporate knowledge about the problem under study and support meaningful decision making (Abin 2019;Śmieja and Wiercioch 2017). However, it is known that the conclusions on independence depend, in general, on the granularity chosen for each of the categorical variables.…”

“…Our approach is flexible enough to include constraints on the desirable structure of the clusters, such as must-link or cannot-link constraints on the categories that can, or cannot, be merged together, and ensure reasonable sample sizes in the cells of the clustered table from which trustful statistical conclusions can be derived. This constrained clustering approach allows us to incorporate background knowledge to support the analysis and extract meaningful conclusions (Abin 2019;Śmieja and Wiercioch 2017).…”

CDEC: a constrained deep embedded clustering

“…In contrast to some previous efforts that implicitly encode ML and CL constraints by modifying the graph Laplacian or constraining the underlying Eigenspace, they present a more natural and principled formulation, which explicitly encodes the constraints as part of a constrained optimization problem. Abin (2019) suggests a new perspective for constrained clustering by finding an effective transformation of data into target space on the reference of background knowledge. Most of the 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.…”