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Market basket analysis by solving the inverse Ising problem: Discovering pairwise interaction strengths among products

Author

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  • Valle, Mauricio A.
  • Ruz, Gonzalo A.
  • Rica, Sergio

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.

Suggested Citation

  • Valle, Mauricio A. & Ruz, Gonzalo A. & Rica, Sergio, 2019. "Market basket analysis by solving the inverse Ising problem: Discovering pairwise interaction strengths among products," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 36-44.
    • Handle: RePEc:eee:phsmap:v:524:y:2019:i:c:p:36-44
    DOI: 10.1016/j.physa.2019.03.001
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    References listed on IDEAS

    as
    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    2. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    3. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
    4. Gašper Tkačik & Olivier Marre & Dario Amodei & Elad Schneidman & William Bialek & Michael J Berry II, 2014. "Searching for Collective Behavior in a Large Network of Sensory Neurons," PLOS Computational Biology, Public Library of Science, vol. 10(1), pages 1-23, January.
    5. Elad Schneidman & Michael J. Berry & Ronen Segev & William Bialek, 2006. "Weak pairwise correlations imply strongly correlated network states in a neural population," Nature, Nature, vol. 440(7087), pages 1007-1012, April.
    6. Giovanni Bonanno & Nicolas Vandewalle & Rosario N. Mantegna, 2000. "Taxonomy of Stock Market Indices," Papers cond-mat/0001268, arXiv.org, revised Aug 2000.
    7. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    8. Ilija Zovko & J Doyne Farmer, 2002. "The power of patience: a behavioural regularity in limit-order placement," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 387-392.
    9. Maslov, Sergei & Mills, Mark, 2001. "Price fluctuations from the order book perspective—empirical facts and a simple model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 234-246.
    10. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    11. Gilmore, Claire G. & Lucey, Brian M. & Boscia, Marian, 2008. "An ever-closer union? Examining the evolution of linkages of European equity markets via minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6319-6329.
    12. Bury, Thomas, 2013. "Market structure explained by pairwise interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1375-1385.
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