Widening for MDL-Based Retail Signature Discovery

Abstract

Signature patterns have been introduced to model repetitive behavior, e.g., of customers repeatedly buying the same set of products in consecutive time periods. A disadvantage of existing approaches to signature discovery, however, is that the required number of occurrences of a signature needs to be manually chosen. To address this limitation, we formalize the problem of selecting the best signature using the minimum description length (MDL) principle. To this end, we propose an encoding for signature models and for any data stream given such a signature model. As finding the MDL-optimal solution is unfeasible, we propose a novel algorithm that is an instance of widening, i.e., a diversified beam search that heuristically explores promising parts of the search space. Finally, we demonstrate the effectiveness of the problem formalization and the algorithm on a real-world retail dataset, and show that our approach yields relevant signatures.

The minimum description length principle for pattern mining: a survey

“…Chen et al (2018) adopt a generic point of view on sequence segmentation, considering that the input data can be either univariate or multivariate, consist of categorical or real-valued variables, with no assumption on the underlying distribution. Gautrais et al (2020) aim to segment a sequence in such a way that each segment contains a collection of recurrent "signature" events. In particular, they consider retail data and apply the approach to the sequences of transactions of individual customers, in order to analyse their shopping behaviour.…”