通过形状张量分解实现无需标签的可解释二分类，精度超越肉眼观察。
Explainable Binary Classification of Separable Shape Ensembles
- 用积分算子特征空间近似生成曲线双表示，分离线性缩放与非线性波动。
- 在数千条曲线数据上实现秒级可解释特征构建，检测到人眼难以察觉的差异。
- 适合无标注数据场景，适用于生物、工程等需可视化推理的领域。
科学家、工程师、生物学家和技术专家普遍利用图像分割提取包含数千条曲线的形状集合，以分析观测和测量中的模式变化。本文提出新型模式识别框架与大规模曲线集合的推断方法。通过精确逼近复合积分算子的特征空间，构建在求积节点对齐的离散双表示。近似结果投影至基底矩阵流形，生成可分形状张量，将曲线分解为广义（线性）尺度变化与互补（非线性）波动。基于成对图像分割出的数千条曲线，我们展示如何利用可分形状张量的数据驱动特征，通过乘积最大均值差异实现可解释的二分类；无需标签数据，在秒级内完成可解释特征空间构建，且能检测低于肉眼可见阈值的差异。
原文摘要 · Abstract (English)
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve ensembles facilitate inferences about important changes when comparing and contrasting images. We introduce novel pattern recognition formalisms combined with inference methods over large ensembles of segmented curves. Our formalism involves accurately approximating eigenspaces of composite integral operators to motivate discrete, dual representations of curves collocated at quadrature nodes. Approximations are projected onto underlying matrix manifolds and the resulting separable shape tensors constitute rigid-invariant decompositions of curves into generalized (linear) scale variations and complementary (nonlinear) undulations. With thousands of curves segmented from pairs of images, we demonstrate how data-driven features of separable shape tensors inform explainable binary classification utilizing a product maximum mean discrepancy; absent labeled data, building interpretable feature spaces in seconds without high performance computation, and detecting discrepancies below cursory visual inspections.
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