A Method to Estimate the True Mahalanobis Distance from Eigenvectors of Sample Covariance Matrix
A Method to Estimate the True Mahalanobis Distance from Eigenvectors of Sample Covariance Matrix
复制标题
一种从样本协方差矩阵特征向量估计真马氏距离的方法
DOI：
10.1007/3-540-70659-3_52
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
H. Aso
中科院分区：
文献类型：
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作者：
M. Iwamura;S. Omachi;H. Aso
在统计模式识别中，分布参数通常是根据训练样本向量估计的。然而，估计的参数存在估计误差，当样本量不足时，这些误差会对识别性能造成不良影响。有些方法可以更好地估计真实协方差矩阵的特征值，并且可以避免特征值估计误差带来的不良影响。然而，协方差矩阵特征向量的估计误差尚未得到充分考虑。在本文中，我们考虑特征向量的估计误差，并表明该误差可以被视为特征值的估计误差。然后，我们提出了一种根据样本协方差矩阵的特征向量估计真实马氏距离的方法。识别实验表明，应用该方法，即使样本量较小，也能估计出真实的马氏距离，并取得了较好的识别精度。该方法对于模式识别的实际应用很有用，因为该方法无需任何超参数即可有效。
In statistical pattern recognition, the parameters of distributions are usually estimated from training sample vectors. However, estimated parameters contain estimation errors, and the errors cause bad influence on recognition performance when the sample size is not sufficient. Some methods can obtain better estimates of the eigenvalues of the true covariance matrix and can avoid bad influences caused by estimation errors of eigenvalues. However, estimation errors of eigenvectors of covariance matrix have not been considered enough. In this paper, we consider estimation errors of eigenvectors and show the errors can be regarded as estimation errors of eigenvalues. Then, we present a method to estimate the true Mahalanobis distance from eigenvectors of the sample covariance matrix. Recognition experiments show that by applying the proposed method, the true Mahalanobis distance can be estimated even if the sample size is small, and better recognition accuracy is achieved. The proposed method is useful for the practical applications of pattern recognition since the proposed method is effective without any hyper-parameters.