Lexicographically Ordered Multi-Objective Clustering

TL;DR

This paper presents a novel multi-objective clustering model with lexicographic ordering and slack, along with an algorithm called Zeus that optimizes cluster quality across multiple objectives, demonstrated on real-world data.

Contribution

Introduces a new lexicographically ordered multi-objective clustering model with slack and proposes the Zeus algorithm to solve it with theoretical guarantees.

Findings

Zeus effectively balances multiple objectives in clustering.

The model accommodates deviations from optimality via slack.

Empirical results show improved clustering performance on real data.

Abstract

We introduce a rich model for multi-objective clustering with lexicographic ordering over objectives and a slack. The slack denotes the allowed multiplicative deviation from the optimal objective value of the higher priority objective to facilitate improvement in lower-priority objectives. We then propose an algorithm called Zeus to solve this class of problems, which is characterized by a makeshift function. The makeshift fine tunes the clusters formed by the processed objectives so as to improve the clustering with respect to the unprocessed objectives, given the slack. We present makeshift for solving three different classes of objectives and analyze their solution guarantees. Finally, we empirically demonstrate the effectiveness of our approach on three applications using real-world data.