An extension of neural gas to local PCA

We suggest an extension of the neural gas vector quantization method to local principal component analysis. The distance measure for the competition between local units combines a normalized Mahalanobis distance in the principal subspace and the squared reconstruction error, with the weighting of both measures depending on the residual variance in the minor subspace. A recursive least-squares method performs the local principal component analysis. The method is tested on synthetic two- and three-dimensional data and on the recognition of handwritten digits. (C) 2004 Elsevier B.V. All rights reserved.