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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., & 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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