Overlapping correlation clustering

Abstract

Abstract-We introduce a new approach to the problem of overlapping clustering. The main idea is to formulate overlapping clustering as an optimization problem in which each data point is mapped to a small set of labels, representing membership to different clusters. The objective is to find a mapping so that the distances between data points agree as much as possible with distances taken over their label sets. To define distances between label sets, we consider two measures: a set-intersection indicator function and the Jaccard coefficient.To solve the main optimization problem we propose a localsearch algorithm. The iterative step of our algorithm requires solving non-trivial optimization subproblems, which, for the measures of set-intersection and Jaccard, we solve using a greedy method and non-negative least squares, respectively.Since our frameworks uses pairwise similarities of objects as the input, it lends itself naturally to the task of clustering structured objects for which feature vectors can be difficult to obtain. As a proof of concept we show how easily our framework can be applied in two different complex application domains. Firstly, we develop overlapping clustering of animal trajectories, obtaining zoologically meaningful results. Secondly, we apply our framework for overlapping clustering of proteins based on pairwise similarities of aminoacid sequences, outperforming the of state-of-the-art method in matching a ground truth taxonomy.

Cost-optimal constrained correlation clustering via weighted partial Maximum Satisfiability

“…In [12] the authors experiment with correlation clustering allowing overlapping clusters. The proposed solution to overlapping correlation clustering is a local search algorithm that locally adjusts the solution clustering as long as the cost function decreases.…”

“…v N } be a set of data points, W ∈ R N×N a symmetric similarity matrix, and K an upper bound on the available clusters. Note that we allow K = N, so the proofs presented here cover the problem definition of [4,12] and [9] as well as [8]. …”

“…As a concrete example, consider the problem of clustering documents by topic without any prior knowledge on what those topics might be, based only on similarity information (edges) between pairs of different documents [4,10]. Indeed, correlation clustering has various applications in biosciences [11], social network analysis and information retrieval [12][13][14]. Furthermore, the related problem of consensus clustering [15], with recent applications in bioinformatics and in particular microarray data analysis [16][17][18][19], can also be naturally cast as correlation clustering.…”

Provably Fast Inference of Latent Features from Networks

“…To the best of our knowledge, this is the first rapidly mixing chain for learning latent features from network data. Furthermore, our method sheds light on the performance of the local heuristic due to Bonchi et al [14].…”

“…We show that maximizing the log-likelihood function is NP-hard by proving that it subsumes as a special instance the overlapping correlation clustering problem [14]. We provide combinatorial insights by connecting the machine learning problem with specific graph sub-structures.…”