A Multilayer Latent Factorization of Nonstandard Tensors Model for Accurately Representing Higher-Order Graphs

Higher-order graphs characterize complex interaction systems involving multiple types of entities and relations, and can be naturally modeled as nonstandard tensors with extreme sparsity and high dimensionality. Tensor decomposition models have been widely used to learn low-dimensional representations of such tensors for higher-order graph inference. Existing tensor decomposition methods typically employ single-layer architectures, limiting their ability to learn expressive representations. To address this limitation, we propose a Multilayer Latent Factorization of Nonstandard tensors (MLFN) model, which enables progressive nonlinear representation learning through multiple latent factorization layers. Specifically, MLFN incorporates three key innovations: 1) a multilayer learning framework that progressively learns low-dimensional representations through layer-by-layer feature learning, 2) a nonlinear activation-based sampling strategy that generates informative training samples to alleviate the extreme sparsity of nonstandard tensor data, and 3) an efficient parallel training scheme using an alternating stochastic gradient descent for scalable model optimization. Experimental results on four types of higher-order graphs demonstrate that MLFN improves the average prediction accuracy by 22.81% over state-of-the-art methods for unobserved-link prediction.