Graph Linear Convolution Pooling for Learning in Incomplete High-Dimensional Data

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.