用于高维数据分类的简约马氏核
Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data
AI总结：
利用高维空间的空性，基于马氏距离提出一种简约核，通过高维判别分析模型估计信号和噪声子空间，实现稳定逆协方差矩阵，并在SVM框架下优化半径-间隔界，实验表明该核优于高斯核。
摘要：
本文考虑使用核方法对高维数据进行分类。利用高维空间的空性，提出了一种基于马氏距离的核。计算马氏距离需要协方差矩阵的逆。在高维空间中，估计的协方差矩阵是病态的，其逆不稳定或不可能。使用简约统计模型，即高维判别分析模型，为每个考虑的类别估计特定的信号和噪声子空间，使得类别特定协方差矩阵的逆显式且稳定，从而定义了简约马氏核。采用基于SVM的框架，通过优化所谓的半径-间隔界来选择简约马氏核的超参数。在三个高维数据集上的实验结果表明，所提出的核适用于高维数据分类，比传统高斯核提供更好的分类精度。
英文摘要：
The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
