Regularization in Relevance Learning Vector Quantization Using l one Norms

TL;DR

This paper introduces an L1 regularization method for relevance learning vector quantization (LVQ) that promotes sparse relevance profiles, aiding in hyperspectral data analysis by reducing unnecessary spectral bands.

Contribution

It presents a novel gradient-based L1 regularization approach for LVQ, including its extension to matrix learning variants, enhancing sparsity in relevance profiles.

Findings

Effective sparsity in relevance profiles achieved

Improved classification focus on necessary spectral bands

Extension to matrix LVQ demonstrated success

Abstract

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.