Geometry-Aware Similarity Learning on SPD Manifolds for Visual Recognition
Geometry-Aware Similarity Learning on SPD Manifolds for Visual Recognition
复制标题
用于视觉识别的 SPD 流形上的几何感知相似性学习
DOI：
10.1109/tcsvt.2017.2729660
复制
发表时间：
2018-10-01
影响因子：
8.4
通讯作者：
Chen, Xilin
中科院分区：
文献类型：
--
作者：
Huang, Zhiwu;Wang, Ruiping;Chen, Xilin
对称正定（SPD）矩阵已被用于许多视觉识别任务中的数据表示。成功主要归功于学习判别SPD矩阵编码的黎曼几何的基础SPD流形。在本文中，我们提出了一个几何感知的SPD相似性学习（SPDSL）框架，通过直接追求满列秩的流形-流形变换矩阵来学习区分SPD特征。具体地说，通过利用黎曼几何的固定秩半正定（PSD）矩阵的流形，我们提出了一个新的解决方案，以减少优化列满秩变换矩阵的空间上的PSD流形上的优化，它具有良好的黎曼结构。在这种解决方案下，我们利用一种新的监督SPDSL技术，通过将选定SPD数据对的相似性回归到目标SPD流形上的地面真实相似性来学习流形-流形变换。为了优化提出的目标函数，我们进一步推导出PSD流形上的优化算法。三个视觉分类任务的评价表明，所提出的方法比现有的基于SPD的判别学习方法的优势。
Symmetric positive definite (SPD) matrices have been employed for data representation in many visual recognition tasks. The success is mainly attributed to learning discriminative SPD matrices encoding the Riemannian geometry of the underlying SPD manifolds. In this paper, we propose a geometry-aware SPD similarity learning (SPDSL) framework to learn discriminative SPD features by directly pursuing a manifold-manifold transformation matrix of full column rank. Specifically, by exploiting the Riemannian geometry of the manifolds of fixed-rank positive semidefinite (PSD) matrices, we present a new solution to reduce optimization over the space of column full-rank transformation matrices to optimization on the PSD manifold, which has a well-established Riemannian structure. Under this solution, we exploit a new supervised SPDSL technique to learn the manifold-manifold transformation by regressing the similarities of selected SPD data pairs to their ground-truth similarities on the target SPD manifold. To optimize the proposed objective function, we further derive an optimization algorithm on the PSD manifold. Evaluations on three visual classification tasks show the advantages of the proposed approach over the existing SPD-based discriminant learning methods.