提出新型张量核学习框架，提升多模态数据相似性度量的准确与可解释性。
Subspace Kernel Learning on Tensor Sequences
- 通过模式子空间对比构建表达性强的核函数
- 在多个动作识别数据集上达到顶尖性能，优于现有方法
- 适用于需要可解释性的大规模多模态张量分析场景
从结构化多维数据（高阶张量）中学习，需捕捉跨张量模式的复杂交互，同时保持计算高效。本文提出不确定性驱动的核张量学习（UKTL），一种针对M模张量的新核框架，通过比较张量展开得到的模式子空间，实现表达丰富且鲁棒的相似性度量。为处理大规模张量数据，提出可扩展的Nyström核线性化方法，利用软k均值聚类动态学习枢纽张量。UKTL的关键创新在于不确定性感知的子空间加权机制，根据置信度估计自适应降低不可靠模式分量权重，提升输入与枢纽张量比较时的鲁棒性与可解释性。本框架全端到端可训练，通过结构化核组合自然融合多维与多模式交互。在动作识别基准（NTU-60、NTU-120、Kinetics-Skeleton）上的大量实验表明，UKTL取得最先进性能，具备更强泛化能力，并提供有意义的模式级洞察。该工作建立了一个原理严谨、可扩展、可解释的核学习范式，适用于结构化多维与多模态张量序列。
原文摘要 · Abstract (English)
Learning from structured multi-way data, represented as higher-order tensors, requires capturing complex interactions across tensor modes while remaining computationally efficient. We introduce Uncertainty-driven Kernel Tensor Learning (UKTL), a novel kernel framework for $M$-mode tensors that compares mode-wise subspaces derived from tensor unfoldings, enabling expressive and robust similarity measure. To handle large-scale tensor data, we propose a scalable Nyström kernel linearization with dynamically learned pivot tensors obtained via soft $k$-means clustering. A key innovation of UKTL is its uncertainty-aware subspace weighting, which adaptively down-weights unreliable mode components based on estimated confidence, improving robustness and interpretability in comparisons between input and pivot tensors. Our framework is fully end-to-end trainable and naturally incorporates both multi-way and multi-mode interactions through structured kernel compositions. Extensive evaluations on action recognition benchmarks (NTU-60, NTU-120, Kinetics-Skeleton) show that UKTL achieves state-of-the-art performance, superior generalization, and meaningful mode-wise insights. This work establishes a principled, scalable, and interpretable kernel learning paradigm for structured multi-way and multi-modal tensor sequences.
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