LP-based pivoting algorithm for higher-order correlation clustering

Correlation clustering is an approach for clustering a set of objects from given pairwise information. In this approach, the given pairwise information is usually represented by an undirected graph with nodes corresponding to the objects, where each edge in the graph is assigned a nonnegative weight...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 37; no. 4; pp. 1312 - 1326
Main Author: Fukunaga, Takuro
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
Algorithms
Approximation
Clustering
Combinatorics
Convex and Discrete Geometry
Correlation
Graph theory
Graphical representations
Graphs
Linear programming
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nodes
Operations Research/Decision Theory
Optimization
Theory of Computation
Coclustering
Correlation clustering
LP-rounding algorithm
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:Correlation clustering is an approach for clustering a set of objects from given pairwise information. In this approach, the given pairwise information is usually represented by an undirected graph with nodes corresponding to the objects, where each edge in the graph is assigned a nonnegative weight, and either the positive or negative label. Then, a clustering is obtained by solving an optimization problem of finding a partition of the node set that minimizes the disagreement or maximizes the agreement with the pairwise information. In this paper, we extend correlation clustering with disagreement minimization to deal with higher-order relationships represented by hypergraphs. We give two pivoting algorithms based on a linear programming relaxation of the problem. One achieves an O ( k log n ) -approximation, where n is the number of nodes and k is the maximum size of hyperedges with the negative labels. This algorithm can be applied to any hyperedges with arbitrary weights. The other is an O ( r )-approximation for complete r -partite hypergraphs with uniform weights. This type of hypergraphs arise from the coclustering setting of correlation clustering.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-018-0354-y