A Corrector for the Sample Mahalanobis Distance Free from Estimating the Population Eigenvalues of Covariance Matrix
A Corrector for the Sample Mahalanobis Distance Free from Estimating the Population Eigenvalues of Covariance Matrix
复制标题
免估计协方差矩阵总体特征值的样本马氏距离修正器
DOI：
10.1007/978-3-319-46672-9_26
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Yasuyuki Kobayashi
中科院分区：
文献类型：
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作者：
Takashi Kawamura;Katsuyuki Furihata;白鳥浩（編著）;Yasuyuki Kobayashi
为了纠正少量学习样本对样本马氏距离识别性能的影响，提出了一种新的样本马氏距离向相应总体马氏距离的校正方法，而不需要由定义样本马氏距离的样本协方差矩阵估计的总体特征值.为了避免计算难以估计的总体特征值，校正器使用协方差矩阵的Stein估计。校正器还利用统计学中的delta方法对样本马氏距离的主成分进行精确的期望。数值实验表明，与样本马氏距离相比，该方法改善了概率分布，提高了识别性能。
To correct the effect deteriorating the recognition performance of the sample Mahalanobis distance by a small number of learning sample, a new corrector for the sample Mahalanobis distance toward the corresponding population Mahalanobis distance is proposed without the population eigenvalues estimated from the sample covariance matrix defining the sample Mahalanobis distance. To omit computing the population eigenvalues difficult to estimate, the corrector uses the Stein’s estimator of covariance matrix. And the corrector also uses accurate expectation of the principal component of the sample Mahalanobis distance by the delta method in statistics. Numerical experiments show that the proposed corrector improves the probability distribution and the recognition performance in comparison with the sample Mahalanobis distance.