2019/10/28 by Wasim Huleihel, Arya Mazumdar, Huleihel, Wasim +5 · 4 citations
Computer Science · #Advanced Clustering Algorithms Research #Bayesian Methods and Mixture Models #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.1910.12490
openalex publication_date 2019/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given n elements to be clustered into k possibly overlapping clusters, and an oracle that can interactively answer queries of the form "do elements u and v belong to the same cluster?" The goal is to recover the clusters with minimum number of such queries. This problem has been of recent interest for the case of disjoint clusters. In this paper, we look at the more practical scenario of overlapping clusters, and provide upper bounds (with algorithms) on the sufficient number of queries. We provide algorithmic results under both arbitrary (worst-case) and statistical modeling assumptions. Our algorithms are parameter free, efficient, and work in the presence of random noise. We also derive information-theoretic lower bounds on the number of queries needed, proving that our algorithms are order optimal. Finally, we test our algorithms over both synthetic and real-world data, showing their practicality and effectiveness.