Regularization in Relevance Learning Vector Quantization Using l one Norms

Martin Riedel (1) , Marika Kästner (1) , Fabrice Rossi (2) , Thomas Villmann (1)

1 Department of Mathematics, Natural and Computer Sciences
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those spectral bands which are not necessary for classification. In particular, we consider the sparsity in the relevance profile enforced by LASSO optimization. The latter one is obtained by a gradient learning scheme using a differentiable parametrized approximation of the $l_{1}$-norm, which has an upper error bound. We extend this regularization idea also to the matrix learning variant of LVQ as the natural generalization of relevance learning.

Mots clés: LVQ; sparse; l one; relevence learning

Domaines: Machine Learning [stat.ML]; Réseau de neurones [cs.NE]

Martin Riedel, Marika Kästner, Fabrice Rossi, Thomas Villmann. Regularization in Relevance Learning Vector Quantization Using l one Norms. 21-th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2013), Apr 2013, Bruges, Belgium. pp.17-22. ⟨hal-00874854⟩