Lexicographically Ordered Multi-Objective Clustering
This work addresses clustering challenges where multiple objectives must be prioritized, offering a method for applications like data analysis, but it appears incremental as it builds on existing multi-objective clustering concepts.
The paper tackles the problem of multi-objective clustering with lexicographic ordering and a slack, proposing the Zeus algorithm with a makeshift function to fine-tune clusters, and empirically demonstrates its effectiveness on real-world data.
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.