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首页> 外文会议>IEEE International Conference on Big Data Security on Cloud;IEEE International Conference on High Performance and Smart Computing;IEEE International Conference on Intelligent Data and Security >Kernel Learning Method on Riemannian Manifold with Geodesic Distance Preservation
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Kernel Learning Method on Riemannian Manifold with Geodesic Distance Preservation

机译：测地距离保持的黎曼流形上的核学习方法

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摘要

Riemannian manifold recently has widely exploited in pattern recognition, data analysis, and machine learning. In this paper, a novel kernel learning method, based on preserving geodesic distance on Riemannian manifold, is proposed. In our approach, the features of data first are extracted by an covariance descriptor, and represented as covariance matrices (SPD matrices). Then an logarithm operation is used to transfer them to column vectors. Different from general doing, we introduce a parameterized Mahalanobis distance to define the distance between two column vectors, aiming to make it equal to the geodetic distance between two corresponding data on Riemannian manifold. Furthermore, an initialization kernel matrix is obtained from the learned Mahalanobis distance matrix by a linear transformation, and with it the Bregman optimization algorithm is applied to find the optimal kernel matrix, in which the distance in kernel space is equal to the geodetic distance on Riemannian manifold. We implement experiments on texture data sets to demonstrate the benefits of the proposed method.
机译：黎曼流形最近在模式识别，数据分析和机器学习中得到了广泛的利用。提出了一种基于在黎曼流形上保持测地距离的核学习方法。在我们的方法中，首先通过协方差描述符提取数据的特征，并将其表示为协方差矩阵（SPD矩阵）。然后，使用对数运算将其转换为列向量。与一般做法不同，我们引入了参数化的Mahalanobis距离来定义两个列向量之间的距离，旨在使其等于黎曼流形上两个相应数据之间的大地测量距离。此外，通过线性变换从学习到的马哈拉诺比斯距离矩阵中获得一个初始化核矩阵，并利用Bregman优化算法找到最优核矩阵，其中核空间中的距离等于黎曼方程上的大地测量距离流形。我们对纹理数据集进行实验，以证明该方法的好处。

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