Auto-Encoding Neural Tucker Factorization

Abstract

Low-rank latent factorization of tensors is a powerful method for analyzing high-dimensional and incomplete (HDI) data derived from cyber-physical systems, particularly when computational resources are limited. However, traditional tensor factorization models are inherently linear and struggle to capture the complex nonlinear spatiotemporal dependencies embedded in the data. This paper introduces a novel latent factorization model, namely Auto-encoding Neural Tucker Factorization (ANTucF) for accurate spatiotemporal representation learning on the HDI tensor. It constructs a low-rank Tucker factorization-based neural network to capture a potential latent manifold in space and time, built upon three core ideas: a) applying density-oriented modeling principles with neural networks to facilitate latent feature learning via positional and temporal encoding of mode indices; b) constructing a Tucker interaction tensor to represent all possible spatiotemporal interactions among distinct spatial and temporal modes; and c) enhancing the uniqueness of the core tensor in Tucker factorization by incorporating nonlinear spatiotemporal representation learning via auto-encoding latent interaction learning. The ANTucF model outperforms several state-of-the-art LFT models in estimating missing observations on real-world datasets. Additionally, visualizations demonstrate its ability to capture finer spatiotemporal dynamics by nonlinearly exploiting an optimal Tucker core tensor using a data-driven approach.