On the Basis Updating Rule of Adaptive-Subspace Self-Organizing Map (ASSOM)

Huicheng Zheng (1) , Christophe Laurent (1) , Grégoire Lefebvre (1)

1 FRANCE TELECOM R&D - France Telecom R&D

This paper gives other views on the basis updating rule of the ASSOM proposed by Kohonen. We first show that the traditional basis vector rotation rule can be expressed as a correction to the basis vector which is proportional to component vectors in the episode. With the latter form, some intermediate computations can be reused, leading to a computational load only linear to the input dimension and the subspace dimension, whereas naive implementation of the traditional rotation rule has a computational load quadratic to the input dimension. We then proceed to propose a batch-mode updating of the basis vectors. We show that the correction made to each basis vector is a linear combination of component vectors in the input episode. Computations can be further saved. Experiments show that the proposed methods preserve the ability to generate topologically ordered invariant-feature filters and that the learning procedure is largely boosted.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Réseau de neurones [cs.NE]

Huicheng Zheng, Christophe Laurent, Grégoire Lefebvre. On the Basis Updating Rule of Adaptive-Subspace Self-Organizing Map (ASSOM). Artificial Neural Networks - ICANN 2006, 16th International Conference,, Sep 2006, Athens, Greece. ⟨10.1007/11840817_46⟩. ⟨hal-01224793⟩