L1-norm unsupervised Fukunaga-Koontz transform

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. present work proves that it also possible to perform FKT an unsupervised manner, sparing need for labeled data, by using variant of L1-norm Principal Component Analysis (L1-PCA) minimizes space. Rigorous proof given case data drawn from mixture Gaussians. A working iterative algorithm based on gradient-descent Stiefel manifold put forward minimization with orthogonal constraints. number numerical experiments synthetic and real confirm theoretical findings good convergence characteristics proposed algorithm.