Hypergraph Models and Algorithms for Data-Pattern-Based Clustering

Abstract

In traditional approaches for clustering market basket type data, relations among transactions are modeled according to the items occurring in these transactions. However, an individual item might induce different relations in different contexts. Since such contexts might be captured by interesting patterns in the overall data, we represent each transaction as a set of patterns through modifying the conventional pattern semantics. By clustering the patterns in the dataset, we infer a clustering of the transactions represented this way. For this, we propose a novel hypergraph model to represent the relations among the patterns. Instead of a local measure that depends only on common items among patterns, we propose a global measure that is based on the cooccurences of these patterns in the overall data. The success of existing hypergraph partitioning based algorithms in other domains depends on sparsity of the hypergraph and explicit objective metrics. For this, we propose a two-phase clustering approach for the above hypergraph, which is expected to be dense. In the first phase, the vertices of the hypergraph are merged in a multilevel algorithm to obtain large number of high quality clusters. Here, we propose new quality metrics for merging decisions in hypergraph clustering specifically for this domain. In order to enable the use of existing metrics in the second phase, we introduce a vertex-to-cluster affinity concept to devise a method for constructing a sparse hypergraph based on the obtained clustering. The experiments we have performed show the effectiveness of the proposed framework.