论文标题
SPD矩阵的协作表示与图像集分类的应用
Collaborative Representation for SPD Matrices with Application to Image-Set Classification
论文作者
论文摘要
基于协作表示的分类（CRC）在过去几年中表现出了显着的进展，因为其封闭形式的分析解决方案。但是，现有的CRC方法无法直接处理非线性变分信息。最近的进步表明，如何有效地对这些非线性变分信息进行建模并学习不变表示是计算机视觉和模式识别社区的一个开放挑战，我们试图设计一种新算法来解决这个问题。首先，将二阶统计量，即将协方差矩阵应用于对原始图像集建模。由于由一组非挥发性矩阵形成的空间是众所周知的对称正定（SPD）歧管，因此将Euclidean协作表示为SPD歧管并不是一件容易的任务。然后，我们制定了两种策略来应对这个问题。一种尝试通过矩阵对数映射将SPD歧管值数据表示嵌入到关联的切线空间中。另一个是通过利用Riemannian内核函数将它们嵌入复制的内核Hilbert Space（RKHS）中。在这两种处理后，CRC适用于SPD歧管值的特征。对四个Banchmark数据集的评估证明了其有效性。
Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear variational information directly. Recent advances illustrate that how to effectively model these nonlinear variational information and learn invariant representations is an open challenge in the community of computer vision and pattern recognition To this end, we try to design a new algorithm to handle this problem. Firstly, the second-order statistic, i.e., covariance matrix is applied to model the original image sets. Due to the space formed by a set of nonsingular covariance matrices is a well-known Symmetric Positive Definite (SPD) manifold, generalising the Euclidean collaborative representation to the SPD manifold is not an easy task. Then, we devise two strategies to cope with this issue. One attempts to embed the SPD manifold-valued data representations into an associated tangent space via the matrix logarithm map. Another is to embed them into a Reproducing Kernel Hilbert Space (RKHS) by utilizing the Riemannian kernel function. After these two treatments, CRC is applicable to the SPD manifold-valued features. The evaluations on four banchmarking datasets justify its effectiveness.
