Fanghui Bi

In this article, we present the dynamic graph mixer (DGM), a novel model for learning spatiotemporal-individual coupled features from high-dimensional and incomplete (HDI) tensors, which frequently represent dynamic interactions among real-world data samples. In contrast to existing methods, the proposed DGM possesses the following three advantages when learning representations from HDI tensors. First, it performs light graph message passing based on the conjoint attentions learned by jointly modeling latent features and implicit structures to extract the high-order connectivity. Second, a multilayer nonlinear tensor neural network (TNN) is adopted to learn the intricate attribute features of node–node–time from different views. Third, it follows the Tucker decomposition paradigm in a data density-oriented modeling mechanism to integrate node representations, preserving the overall multidimensional interaction patterns. In addition, we provide theoretical evidence that the key components in DGM can significantly improve expressiveness. Extensive experiments conducted on eight testing datasets of HDI tensors demonstrate that DGM outperforms state-of-the-art methods in both learning accuracy and efficiency.

High-dimensional and incomplete (HDI) data are frequently encountered in diverse real-world applications involving complex interactions among numerous nodes. Approaches based on latent feature analysis (LFA) have proven effective in performing representation learning in HDI data. Nevertheless, they cannot handle the high-order connectivity among nodes in HDI data well, resulting in severe accuracy loss. To address the previously mentioned issue, we present a novel model in this paper, namely Graph Linear Convolution Pooling Network (GLCPN). The proposed GLCPN adopts the three-fold ideas. First, it leverages simplified graph convolutions to efficiently capture high-order connectivity among nodes for learning representations of matrix factorization. Second, a simple yet effective priori convolution operator is adopted by each graph neural layer to capture node-node collaboration for aggregation. Third, a locality-enhanced pooling scheme is designed to holistically utilize multi-layer representations of the neighborhood. Therefore, GLCPN can effectively acquire the hidden information in HDI data with high efficiency. In addition, we have conducted a theoretical analysis demonstrating that the proposed GLCPN is more expressive compared with existing graph neural networks for HDI data. Extensive experiments have been further conducted on ten well-established HDI datasets from various applications. The experimental results demonstrate that the proposed GLCPN significantly outperforms state-of-the-art models for learning representations in HDI data evaluated by accuracy and efficiency metrics.

High-Dimensional and Incomplete (HDI) data are frequently encountered in various Big Data-related applications. Despite its incompleteness, an HDI data repository contains rich knowledge and patterns concerning the complex interactions among numerous nodes. Recently, a Neural Network (NN)-based approach to Latent Feature Analysis (LFA) model becomes popular owing to its strong representation learning ability to HDI data. Nevertheless, existing NN-based LFA models neglect the inherent nonnegativity in most HDI data, resulting in representation accuracy loss. Motivated by this discovery, this study innovatively proposes a Fast Nonnegative AutoEncoder (FNAE)-based approach to LFA on HDI data, whose ideas are three-fold: a) constructing a multilayered autoencoder subject to nonnegativity constraints for high representation learning ability; b) incorporating the data density-oriented modeling mechanism into FNAE's input and output layers for high computational and storage efficiency; and c) implementing an Adam-based single latent factor-dependent, nonnegative and multiplicative update algorithm for efficient model training as well as fulfilling the nonnegativity constraints. Experimental results on eight commonly-adopted HDI matrices from industrial applications demonstrate that the proposed FNAE significantly outperforms several state-of-the-art NN-based LFA models in both estimation accuracy for missing links of an HDI matrix and computational efficiency.