Generalized Temporal Tensor Decomposition with Rank-revealing Latent-ODE

• URL: http://arxiv.org/abs/2502.06164v1
• Date: Mon, 10 Feb 2025 05:27:11 GMT
• Title: Generalized Temporal Tensor Decomposition with Rank-revealing Latent-ODE
• Authors: Panqi Chen, Lei Cheng, Jianlong Li, Weichang Li, Weiqing Liu, Jiang Bian, Shikai Fang,
• Abstract summary: We propose underlineGeneralized temporal tensor decomposition with underlineRank-runderlineEvealing latenunderlineT-ODE (GRET) Our approach encodes continuous spatial indexes as learnable features and employs neural ODEs in latent space to learn the temporal trajectories of factors. GRET significantly outperforms existing methods in prediction performance and robustness against noise.
• Score: 17.61798738261815
• License:
• Abstract: Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Additionally, the problem of determining the tensor rank remains largely unexplored in temporal tensor models. To address these limitations, we propose \underline{G}eneralized temporal tensor decomposition with \underline{R}ank-r\underline{E}vealing laten\underline{T}-ODE (GRET). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To automatically reveal the rank of temporal tensors, we introduce a rank-revealing Gaussian-Gamma prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that GRET not only reveals the underlying ranks of temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.

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