Multi-way clustering on relation graphs

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Multi-way clustering on relation graphs (2006)

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by Arindam Banerjee , Sugato Basu , Srujana Merugu

Venue:	In Proc. of the 7th SIAM Intl. Conf. on Data Mining
Citations:	36 - 3 self

BibTeX

@TECHREPORT{Banerjee06multi-wayclustering,
    author = {Arindam Banerjee and Sugato Basu and Srujana Merugu},
    title = {Multi-way clustering on relation graphs},
    institution = {In Proc. of the 7th SIAM Intl. Conf. on Data Mining},
    year = {2006}
}

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Abstract

A number of real-world domains such as social networks and e-commerce involve heterogeneous data that describes relations between multiple classes of entities. Understanding the natural structure of this type of heterogeneous relational data is essential both for exploratory analysis and for performing various predictive modeling tasks. In this paper, we propose a principled multi-way clustering framework for relational data, wherein different types of entities are simultaneously clustered based not only on their intrinsic attribute values, but also on the multiple relations between the entities. To achieve this, we introduce a relation graph model that describes all the known relations between the different entity classes, in which each relation between a given set of entity classes is represented in the form of multi-modal tensor over an appropriate domain. Our multi-way clustering formulation is driven by the objective of capturing the maximal “information ” in the original relation graph, i.e., accurately approximating the set of tensors corresponding to the various relations. This formulation is applicable to all Bregman divergences (a broad family of loss functions that includes squared Euclidean distance, KL-divergence), and also permits analysis of mixed data types using convex combinations of appropriate Bregman loss functions. Furthermore, we present a large family of structurally different multi-way clustering schemes that preserve various linear summary statistics of the original data. We accomplish the above generalizations by extending a recently proposed key theoretical result, namely the minimum Bregman information principle [1], to the relation graph setting. We also describe an efficient multi-way clustering algorithm based on alternate minimization that generalizes a number of other recently proposed clustering methods. Empirical results on datasets obtained from real-world domains (e.g., movie recommendations, newsgroup articles) demonstrate the generality and efficacy of our framework. 1

Keyphrases

relation graph real-world domain broad family natural structure exploratory analysis loss function heterogeneous relational data efficient multi-way social network different multi-way clustering scheme newsgroup article mixed data type convex combination intrinsic attribute value relation graph model principled multi-way clustering framework alternate minimization multiple class minimum bregman information principle original relation graph wherein different type clustering method heterogeneous data various relation different entity class key theoretical result movie recommendation appropriate bregman loss function various linear summary statistic entity class various predictive modeling task bregman divergence large family multi-way clustering formulation relational data multiple relation maximal information euclidean distance multi-modal tensor appropriate domain empirical result original data

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