PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Multi-way set enumeration in weight tensors
Elisabeth Georgii, Koji Tsuda and Bernhard Schölkopf
Machine Learning Volume 82, Number 2, pp. 123-155, 2011. ISSN 0885-6125

Abstract

The analysis of n-ary relations receives attention in many different fields, for instance biology, web mining, and social studies. In the basic setting, there are n sets of instances, and each observation associates n instances, one from each set. A common approach to explore these n-way data is the search for n-set patterns, the n-way equivalent of itemsets. More precisely, an n-set pattern consists of specific subsets of the n instance sets such that all possible associations between the corresponding instances are observed in the data. In contrast, traditional itemset mining approaches consider only two-way data, namely items versus transactions. The n-set patterns provide a higher-level view of the data, revealing associative relationships between groups of instances. Here, we generalize this approach in two respects. First, we tolerate missing observations to a certain degree, that means we are also interested in n-sets where most (although not all) of the possible associations have been recorded in the data. Second, we take association weights into account. In fact, we propose a method to enumerate all n-sets that satisfy a minimum threshold with respect to the average association weight. Technically, we solve the enumeration task using a reverse search strategy, which allows for effective pruning of the search space. In addition, our algorithm provides a ranking of the solutions and can consider further constraints. We show experimental results on artificial and real-world datasets from different domains.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:7819
Deposited By:Elisabeth Georgii
Deposited On:17 March 2011