A Robust Distance Measure for Similarity-Based Classification on the SPD Manifold
A Robust Distance Measure for Similarity-Based Classification on the SPD Manifold
复制标题
SPD流形上基于相似性分类的鲁棒距离测量
DOI：
10.1109/tnnls.2019.2939177
复制
发表时间：
2020-09-01
影响因子：
10.4
通讯作者：
Jia, Yunde
中科院分区：
文献类型：
--
作者：
Gao, Zhi;Wu, Yuwei;Jia, Yunde
对称正定（SPD）矩阵，形成一个黎曼流形，通常被用作视觉表示。流形的非欧几里德几何通常使得开发学习算法（例如，分类器）困难和复杂。基于相似性的学习的概念已被证明是有效的，以解决各种问题的SPD流形。这主要是因为基于相似性的算法对几何形状是不可知的，并且纯粹基于相似性/距离的概念工作。然而，现有的基于相似性的SPD流形模型选择整体表示，忽略了SPD矩阵捕获的信息的特性。为了克服这一限制，我们为基于相似性的算法提出了一种新的SPD距离度量。具体来说，我们引入了点到集变换的概念，这使我们能够从高维流形学习多个低维和判别性SPD流形。对于由点到集变换得到的低维SPD流形，我们利用α-β发散族提出了一个定制的集到集距离测度。我们进一步建议联合学习点到集合的变换和集合到集合的距离测度，从而在SPD流形上产生一个强大的基于相似性的算法。我们对几个视觉识别任务的全面评估（例如，动作分类和面部识别）表明我们的算法舒适地优于各种最先进的算法。
The symmetric positive definite (SPD) matrices, forming a Riemannian manifold, are commonly used as visual representations. The non-Euclidean geometry of the manifold often makes developing learning algorithms (e.g., classifiers) difficult and complicated. The concept of similarity-based learning has been shown to be effective to address various problems on SPD manifolds. This is mainly because the similarity-based algorithms are agnostic to the geometry and purely work based on the notion of similarities/distances. However, existing similarity-based models on SPD manifolds opt for holistic representations, ignoring characteristics of information captured by SPD matrices. To circumvent this limitation, we propose a novel SPD distance measure for the similarity-based algorithm. Specifically, we introduce the concept of point-to-set transformation, which enables us to learn multiple lower dimensional and discriminative SPD manifolds from a higher dimensional one. For lower dimensional SPD manifolds obtained by the point-to-set transformation, we propose a tailored set-to-set distance measure by making use of the family of alpha–beta divergences. We further propose to learn the point-to-set transformation and the set-to-set distance measure jointly, yielding a powerful similarity-based algorithm on SPD manifolds. Our thorough evaluations on several visual recognition tasks (e.g., action classification and face recognition) suggest that our algorithm comfortably outperforms various state-of-the-art algorithms.