Ting-Wei Zhou | Searcharxiv

arXiv2026

Tensor Decomposition Structure Search Framework from an Interaction Perspective

Recently, tensor decompositions have attracted increasing attention. Fundamentally, different interactions among factors induce distinct tensor decomposition structures (i.e., tensor decomposition). Identifying an appropriate interaction-induced tensor decomposition structure for given data is a fundamental yet challenging problem in tensor modeling, and remains largely under-explored. Existing tensor decomposition structure search methods are typically restricted to a predefined interaction family, such as tensor contraction. To address this problem, we suggest a tensor decomposition structure search framework (I-TSS) from an interaction perspective that can identify either a single structure beyond a predefined interaction family or a mixture of structures involving heterogeneous interaction families. Specifically, we first systematically review existing tensor decomposition structures from an interaction perspective and construct a heterogeneous interaction-induced candidate structure set. Based on it, we propose a unified energy-based rank estimation scheme for heterogeneous interaction-induced candidate structure set. We then introduce the top-$k$ gating mechanism with learnable gating scores to dynamically select a suitable single-candidate structure or combine suitable multi-candidate structures, thereby identifying the tensor decomposition structure in a data-adaptive manner. Theoretically, we derive an approximation error bound for I-TSS, thereby establishing its approximation capability. Extensive experiments on synthetic and real-world datasets demonstrate that I-TSS consistently outperforms state-of-the-art tensor decomposition methods.

cs.CV↗

arXiv2024

DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery

Recently, the transform-based tensor representation has attracted increasing attention in multimedia data (e.g., images and videos) recovery problems, which consists of two indispensable components, i.e., transform and characterization. Previously, the development of transform-based tensor representation mainly focuses on the transform aspect. Although several attempts consider using shallow matrix factorization (e.g., singular value decomposition and negative matrix factorization) to characterize the frontal slices of transformed tensor (termed as latent tensor), the faithful characterization aspect is underexplored. To address this issue, we propose a unified Deep Tensor Representation (termed as DTR) framework by synergistically combining the deep latent generative module and the deep transform module. Especially, the deep latent generative module can faithfully generate the latent tensor as compared with shallow matrix factorization. The new DTR framework not only allows us to better understand the classic shallow representations, but also leads us to explore new representation. To examine the representation ability of the proposed DTR, we consider the representative multi-dimensional data recovery task and suggest an unsupervised DTR-based multi-dimensional data recovery model. Extensive experiments demonstrate that DTR achieves superior performance compared to state-of-the-art methods in both quantitative and qualitative aspects, especially for fine details recovery.

cs.CV↗