Zero-Inflated Poisson Tensor Factorization for Sparse Purchase Data in E-Commerce Markets

Nonnegative tensor factorization (NTF) plays a crucial role in extracting latent factors and predicting future sales from purchase data consisting of user and item attributes. However, the increase in these attributes leads to tensor data becoming sparse, causing a reduction in decomposition accuracy. For example, when there are numerous combinations of unavailable item genres and prices, the purchase history data becomes sparse and follows a distribution where all its elements are zero. To address this issue, we propose a novel NTF method assuming zero-inflated Poisson (ZIP) distribution based on Expectation-Maximization (EM) algorithm. This enables us to effectively handle sparsity in high-dimensional multiway data and identify combinations of user and item attributes that are potentially not likely to be purchased. We verified the effectiveness of the proposed approach through numerical experiments using real-world e-commerce data. The results showed our proposed ZIP model outperforms existing methods in both in-sample and out-of-sample experiments. Moreover, the proposed method qualitatively demonstrated the effectiveness of handling sparsity.