Accurate PARAFAC2 Decomposition for Temporal Irregular Tensors with Missing Values

Abstract

Given a temporal irregular tensor with missing values, how can we perform accurate decomposition for the tensor? Many real-world data can be represented as a temporal irregular tensor which is a collection of matrices whose rows corresponding to the time dimension have different sizes, but columns have the same size. PARAFAC2 decomposition is a powerful tool for analyzing an irregular tensor in many interesting applications such as phenotype discovery and fault detection. However, existing PARAFAC2 decomposition methods fail to handle irregular tensors with missing values since they treat the missing values as zeros. Furthermore, few methods that utilize temporal regularization focus only on a specific type of temporal irregular tensors.In this paper, we propose ATOM, an accurate PARAFAC2 decomposition method which carefully handles missing values in a temporal irregular tensor. ATOM provides a reformulated loss function that fully excludes missing values and accurately updates factor matrices by considering sparsity patterns of each row. ATOM also captures temporal patterns by exploiting smoothing regularization with time dependency. Extensive experiments show that ATOM provides up to 7.9× lower error rate than existing PARAFAC2 decomposition methods.