Year: 2019
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: CCF-BSF: CIF: Small: Collaborative Research: Coding and Information - Theoretic Aspects of Local Data Recovery, CIF: Small: New Directions in Clustering: Interactive Algorithms and Statistical Models, CAREER: Reliability in Large-Scale Storage, CIF: Small: Collaborative Research: Ordinal Data Compression
OpenAlex ID: W2970243649