Cardinality-stratified method clarifies item associations in baskets
Cardinality-Stratified Interaction Decomposition for Interpretable Pairwise and Higher-Order Structure in Transactional Basket Data
Machine Learning
Summary
When people buy items together, it's hard to tell if the connections are due to actual item relationships or just the size of the shopping basket. The authors introduce a new method, CSID, that breaks down these connections by considering basket size and specific item groups without needing a full complicated model. Their approach helps spot real pair and triple item connections more clearly and avoids false signals that happen with other methods. They tested CSID on fake and real grocery data, finding it to be a more interpretable and reliable way to explore how items relate in shopping baskets.
What this means in practice
- •For retail data analysts: Improve understanding of product relationships by separating true item interactions from basket size effects in sales data analysis.
- •For marketing analysts: Identify meaningful item combinations for targeted promotions by decomposing pairwise and triple associations in customer purchase baskets.
Authors
Hidetoshi Kawase, Toshihiro Ota
Abstract
Transactional basket data can reveal associations among items, but observed co-occurrence conflates item-specific relations with basket-size structure and unmodeled higher-order dependence. We introduce Cardinality-Stratified Interaction Decomposition (CSID), an interpretable framework that decomposes log-odds contrasts stratified by the number of remaining items into item-set-specific and cardinality-common components, without fitting a global joint distribution. CSID uses an information-weighted, gauge-constrained ridge projection to estimate pair and triple components and to diagnose higher-order contributions to pairwise structure. CSID is designed primarily for interpretable decomposition of association structure rather than for full-distribution prediction. In a simulation with zero pair effects, increasingly strong small-basket cardinality potentials drive ordinary Ising couplings spuriously negative, whereas CSID pair estimates remain centered near zero. Detection power rises with the magnitude of planted triple effects, and local deprojection reduces pair-coefficient RMSE from 0.244 to 0.073. Across three grocery datasets, high-information triple components are reproducible over time. In the matched cross-period partial-transfer evaluation, transferred CSID triple components show closer agreement with later-period stratified contrasts than the nodewise-symmetrized cardinality-aware higher-order pseudolikelihood comparator, with gains in weighted Lin's concordance correlation of 0.038--0.122. These results support CSID as an exploratory and interpretable decomposition framework for pairwise and higher-order association structure in transactional data.