Abstract. In the field of pattern recognition and computer vision, applying the symmetric positive definite (SPD) matrix to represent an image set is widely studied, and the remarkable performance that it yields demonstrates its effectiveness. However, the computational burden of the original SPD matrices is usually high, which may restrict the applicability of existing methods. To address this problem, we proposed an SPD manifold dimensionality reduction (DR) algorithm. Specifically, we map the original SPD manifold into a more discriminative lower-dimensional one via a learned mapping. We first construct a graph model using the mechanism of collaborative representation to characterize the local structure of the original manifold data. Then, we formulate the SPD manifold DR problem into an elaborately designed objective function introduced by the graph-embedding framework, aiming to learn the mapping. Finally, the trace optimization method is chosen to solve this optimization problem. The experimental results on some benchmark datasets demonstrate the superiority of our method over the state-of-the-art image set classification methods.

中文翻译：

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对称正定流形降维在图像集分类中的应用

摘要。在模式识别和计算机视觉领域，应用对称正定（SPD）矩阵来表示图像集被广泛研究，其产生的显着性能证明了其有效性。然而，原始SPD矩阵的计算负担通常很高，这可能会限制现有方法的适用性。为了解决这个问题，我们提出了一种 SPD 流形降维 (DR) 算法。具体来说，我们通过学习映射将原始 SPD 流形映射到更具辨别力的低维流形。我们首先使用协同表示的机制构建一个图模型来表征原始流形数据的局部结构。然后，我们将 SPD 流形 DR 问题表述为由图嵌入框架引入的精心设计的目标函数，旨在学习映射。最后，选择迹优化方法来解决这个优化问题。一些基准数据集的实验结果证明了我们的方法优于最先进的图像集分类方法。