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Valle, M. A., Ruz, G. A., & Morras, R. (2018). Market basket analysis: Complementing association rules with minimum spanning trees. Expert Syst. Appl., 97, 146–162.
Abstract: This study proposes a methodology for market basket analysis based on minimum spanning trees, which complements the search for significant association rules among the vast set of rules that usually characterize such an analysis. Thanks to the hierarchical tree structure of the subdominant ultrametric distances of the MST, the association network allows us to find strong interdependencies between products in the same category, and to find products that serve as accesses or bridges to a set of other products with a high correlation among themselves. One relevant aspect of this graph-based methodology is the ease with which pairs and groups of products susceptible to carrying out marketing actions can be identified. The application of our methodology to a real transactional database succeeded in: 1. revealing product interdependencies with the greatest strengths, 2. revealing products of high importance with access to another product set, 3. determining high quality association rules, and 4. detect clusters and taxonomic relations among supermarket subcategories. This is highly beneficial for a retail manager or for a retail analyst who must propose different promotion and offer activities in order to maximize the sales volume and increase the effectiveness of promotion campaigns. (C) 2017 Elsevier Ltd. All rights reserved.
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Valle, M. A., Ruz, G. A., & Rica, S. (2019). Market basket analysis by solving the inverse Ising problem: Discovering pairwise interaction strengths among products. Physica A, 524, 36–44.
Abstract: Large datasets containing the purchasing information of thousands of consumers are difficult to analyze because the possible number of different combinations of products is huge. Thus, market baskets analysis to obtain useful information and find interesting pattern of buying behavior could be a daunting task. Based on the maximum entropy principle, we build a probabilistic model that explains the probability of occurrence of market baskets which is equivalent to Ising models. This type of model allows us to understand and to explore the functional interactions among products that make up the market offer. Additionally, the parameters of the model inferred using Boltzmann learning, allow us to suggest that the buying behavior is very similar to the spin-glass physical system. Moreover, we show that the resulting parameters of the model could be useful to describe the hierarchical structure of the system which leads to interesting information about the different market baskets. (C) 2019 Elsevier B.V. All rights reserved.
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