发表机构
Graduate School of Science and Technology, University of Tsukuba（筑波大学 理工学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究张量逼近中结构损失度量问题，利用交叉模式方向损失和交互损失表征退化，证明平方相对重建误差分解关系并推导稳定性界，实验表明相同重建误差会有不同结构损失轮廓，高光谱补丁方向损失差异与视觉模糊相关。
AI 中文摘要
通过奇异值分解（SVD）进行矩阵化低秩逼近是张量分解的标准替代方法，但逐元素重建误差无法捕捉多路几何退化。在正交塔克模型下，我们使用两个度量来表征这种退化：交叉模式方向损失，测量从秩截断和噪声旋转的几何子空间偏差；交互损失，量化核心张量中的多线性交互失真。我们证明平方相对重建误差正交分解为交互损失和子空间外能量，并推导了一个韦丁型界，建立了插件方向损失估计器的稳定性。在合成和高光谱数据集上的实验表明，几乎相同的重建误差可以产生明显不同的结构损失轮廓；具有可比重建误差的高光谱补丁在方向损失上表现出高达4.6倍的差异，与严重的视觉模糊相关。
英文摘要
Matricized low-rank approximation via SVD is a standard surrogate for tensor decompositions, but entry-wise reconstruction error fails to capture multiway geometric degradation. Under an orthogonal Tucker model, we characterize this degradation using two metrics: cross-mode Direction Loss, measuring geometric subspace deviation from rank truncation and noise rotation, and Interaction Loss, quantifying multilinear interaction distortion in the core tensor. We prove that squared relative reconstruction error orthogonally decomposes into interaction loss and out-of-subspace energy, and derive a Wedin-type bound establishing the stability of a plug-in Direction Loss estimator. Experiments on synthetic and hyperspectral datasets demonstrate that nearly identical reconstruction errors can yield markedly different structural-loss profiles; hyperspectral patches with comparable reconstruction errors exhibit up to a 4.6-fold difference in Direction Loss, correlating with severe visual blurring.
Comments10 pages, 4 figures
