A linear classifier for Gaussian class conditional distributions with unequal covariance matrices

In this paper we present a linear pattern classification algorithm, Principal Component Null Space Analysis (PCNSA) which uses only the first and second order statistics of data for classification and compare its performance with existing linear algorithms. PCNSA first projects data into the PCA space in order to maximize between class variance and then finds separate directions for each class in the PCA space along which the class has the least variance (in an ideal situation the null space of the within class covariance matrix) which we define as the "approximate null space" (ANS) of the class. To obtain the ANS, we calculate the covariance matrix of the class data in PCA space and find its eigenvectors with least eigenvalues. The method works on the assumption that an ANS of the within-class covariance matrix exists, which is true for many classification problems. A query is classified as belonging to the class for which its distance from the class mean projected along the ANS of the class is a minimum. Results for PCNSA's superior performance over LDA and PCA are shown for object recognition.

在本文中，我们提出了一种线性模式分类算法，主组件空空间分析（PCNSA），该算法仅使用数据的第一阶和二阶统计来进行分类，并将其性能与现有线性算法进行比较。 PCNSA首先将数据投射到PCA空间中，以最大化类别之间的差异，然后在PCA空间中的每个类别的单独说明中，该类别沿着该类别的差异最小（在理想情况下，类别协方差矩阵的空空间）我们将其定义为类的“近似空空间”（ANS）。为了获得ANS，我们计算PCA空间中类数据的协方差矩阵，并以最少特征值找到其特征向量。该方法的作用是假设存在类内部协方差矩阵的ANS，这对于许多分类问题是正确的。查询被归类为属于该类的距离，其距离沿类的均值的距离是最小的。为对象识别显示了PCNSA优于LDA和PCA的出色性能的结果。