Metric Learning with A-based Scalar Product for Image-set Recognition
Metric Learning with A-based Scalar Product for Image-set Recognition
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DOI：
10.1109/cvprw50498.2020.00433
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Naoya Sogi;L. S. Souza;B. Gatto;K. Fukui
中科院分区：
文献类型：
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作者：
Naoya Sogi;L. S. Souza;B. Gatto;K. Fukui
在本文中，我们提出了一个度量学习方法的图像集识别使用子空间表示。子空间表示对于图像集识别是有效的，其中每个图像集由高维向量空间中的子空间可压缩地表示。在这个框架中，两个给定的图像集之间的相似性是衡量的两个相应的子空间之间的正则角。利用正则角概念的许多类型的方法已经被广泛地开发和研究。然而，在提高测量正则角的能力方面仍然有很大的潜力。我们的关键思想是学习一个一般的标量积空间（度量空间），它在两个子空间之间产生更有效的标准角。为了实现这一思想，我们首先引入一个基于A的标量积来代替标准的标量积，其中A是一个对称正定矩阵，两个子空间之间的标准角通过基于A的标量积来度量.我们学习一个判别度量空间，通过优化度量A的Fisher比率从局部Fisher判别分析。此外，我们引入了一种机制，通过对度量A施加低秩约束来自动降低度量空间的维数。通过在三个真实数据集上的大量分类实验，验证了所提方法的有效性。
In this paper, we propose a metric learning method for image set recognition using subspace representation. The subspace representation is effective for image set recognition where each image set is compactly represented by a subspace in a high dimensional vector space. In this framework, the similarity between two given image sets is measured by the canonical angles between the two corresponding subspaces. Many types of methods utilizing the concept of canonical angles have been developed and studied extensively. However, there still remains large potential in improving the ability to measure canonical angles. Our key idea is to learn a general scalar product space (metric space) that produces more valid canonical angles between two subspaces. To realize this idea, we first introduce an A-based scalar product instead of the standard scalar product, where A is a symmetric positive definite matrix and the canonical angles between two subspaces are measured through the A-based scalar product. We learn a discriminative metric space by optimizing metric A in terms of the Fisher ratio from local Fisher discriminant analysis. Besides, we introduce a mechanism to automatically reduce the dimension of the metric space by imposing a low-rank constraint on metric A. The effectiveness of the proposed methods is validated through extensive classification experiments on three real-world datasets.