Online Dictionary Learning on Symmetric Positive Definite Manifolds with Vision Applications
Online Dictionary Learning on Symmetric Positive Definite Manifolds with Vision Applications
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DOI：
10.1609/aaai.v29i1.9595
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Shengping Zhang;S. Kasiviswanathan;P. Yuen;Mehrtash Harandi
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文献类型：
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作者：
Shengping Zhang;S. Kasiviswanathan;P. Yuen;Mehrtash Harandi
区域协方差形式的对称正定（SPD）矩阵被认为是图像和视频的丰富描述符。最近的研究表明，利用黎曼几何的SPD流形可能会导致视觉应用的性能改善。对于涉及处理计算机视觉中大规模和动态数据的任务，底层模型需要逐步有效地适应新的和不可见的观察结果。基于这些需求，本文研究了SPD流形上的在线词典学习问题。我们利用Stein散度将流形上的在线字典学习问题转化为再生核Hilbert空间中的问题，为此，我们通过考虑SPD流形的几何结构来开发有效的算法。据我们所知，我们的工作是第一个研究，提供了一个解决方案，在线字典学习的SPD流形。大规模图像分类任务和动态视频处理任务的实验结果验证了我们的方法相比，几个国家的最先进的算法的上级性能。
Symmetric Positive Definite (SPD) matrices in the form of region covariances are considered rich descriptors for images and videos. Recent studies suggest that exploiting the Riemannian geometry of the SPD manifolds could lead to improved performances for vision applications. For tasks involving processing large-scale and dynamic data in computer vision, the underlying model is required to progressively and efficiently adapt itself to the new and unseen observations. Motivated by these requirements, this paper studies the problem of online dictionary learning on the SPD manifolds. We make use of the Stein divergence to recast the problem of online dictionary learning on the manifolds to a problem in Reproducing Kernel Hilbert Spaces, for which, we develop efficient algorithms by taking into account the geometric structure of the SPD manifolds. To our best knowledge, our work is the first study that provides a solution for online dictionary learning on the SPD manifolds. Empirical results on both large-scale image classification task and dynamic video processing tasks validate the superior performance of our approach as compared to several state-of-the-art algorithms.