The Fukunaga-Koontz transform (FKT) is a powerful supervised feature extraction method used in two-class recognition problems, particularly when the classes have equal mean vectors but different covariance matrices. The present work proves that it is also possible to perform the FKT in an unsupervised manner, sparing the need for labeled data, by using a variant of L1-norm Principal Component Analysis (L1-PCA) that minimizes the L1-norm in the feature space. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A working iterative algorithm based on gradient-descent in the Stiefel manifold is put forward to perform L1-norm minimization with orthogonal constraints. A number of numerical experiments on synthetic and real data confirm the theoretical findings and the good convergence characteristics of the proposed algorithm.

Fukunaga-Koontz变换（FKT）是一种强大的有监督的特征提取方法，用于两类识别问题，尤其是当两类的均值向量相等而协方差矩阵不同时。本工作证明，通过使用L1规范主成分分析（L1-PCA）的变体，该FKT还可以以无监督的方式执行FKT，从而节省了标记数据的需求，该变体使特征中的L1规范最小化空间。从混合高斯数据中给出严格的证明。提出了Stiefel流形中基于梯度下降的迭代算法，以正交约束执行L1范数最小化。在合成和真实数据上进行的大量数值实验证实了该算法的理论发现和良好的收敛性。