TY - JOUR

T1 - Market basket analysis by solving the inverse Ising problem

T2 - Discovering pairwise interaction strengths among products

AU - Valle, Mauricio A.

AU - Ruz, Gonzalo A.

AU - Rica, Sergio

N1 - Funding Information:
The authors would like to thank CONICYT-Chile under grant Fondecyt 11160072 (M.A.V.) and Basal(CONICYT)-CMM, Fondecyt 1180706 (G.A.R.) for financially supporting this research.
Funding Information:
The authors would like to thank CONICYT-Chile under grant Fondecyt 11160072 (M.A.V.) and Basal(CONICYT)-CMM , Fondecyt 1180706 (G.A.R.) for financially supporting this research.
Publisher Copyright:
© 2019

PY - 2019/6/15

Y1 - 2019/6/15

N2 - 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.

AB - 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.

KW - Boltzmann machine

KW - Inverse Ising problem

KW - Minimum spanning tree

KW - Pairwise interaction

KW - Purchase pattern

KW - Transactional data base

UR - http://www.scopus.com/inward/record.url?scp=85063036513&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2019.03.001

DO - 10.1016/j.physa.2019.03.001

M3 - Article

AN - SCOPUS:85063036513

SN - 0378-4371

VL - 524

SP - 36

EP - 44

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -