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Valle, M. A., & Ruz, G. A. (2021). Finding Hierarchical Structures of Disordered Systems: An Application for Market Basket Analysis. IEEE Access, 9, 1626–1641.
Abstract: Complex systems can be characterized by their level of order or disorder. An ordered system is related to the presence of system properties that are correlated with each other. For example, it has been found in crisis periods that the financial systems tend to be synchronized, and symmetry appears in financial assets' behavior. In retail, the collective purchasing behavior tends to be highly disorderly, with a diversity of correlation patterns appearing between the available market supply. In those cases, it is essential to understand the hierarchical structures underlying these systems. For the latter, community detection techniques have been developed to find similar behavior clusters according to some similarity measure. However, these techniques do not consider the inherent interactions between the multitude of system elements. This paper proposes and tests an approach that incorporates a hierarchical grouping process capable of dealing with complete weighted networks. Experiments show that the proposal is superior in terms of the ability to find minimal energy clusters. These minimum energy clusters are equivalent to system states (market baskets) with a higher probability of occurrence; therefore, they are interesting for marketing and promotion activities in retail environments.
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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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