Article
L1-norm unsupervised Fukunaga-Koontz transform
Author/s | Camargo Olivares, José Luis
Martín Clemente, Rubén Hornillo Mellado, Susana Antonio Zarzoso, Vicente |
Department | Universidad de Sevilla. Departamento de Teoría de la Señal y Comunicaciones |
Publication Date | 2021 |
Deposit Date | 2022-07-04 |
Published in |
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Abstract | The Fukunaga-Koontz transform (FKT) is a powerful supervised feature extraction method used in twoclass recognition problems, particularly when the classes have equal mean vectors but different covariance matrices. The ... The Fukunaga-Koontz transform (FKT) is a powerful supervised feature extraction method used in twoclass 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. |
Citation | Camargo Olivares, J.L., Martín Clemente, R., Hornillo Mellado, S. y Antonio Zarzoso, V. (2021). L1-norm unsupervised Fukunaga-Koontz transform. Signal Processing, 182, 107942. |
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