On the Basis Updating Rule of Adaptive-Subspace Self-Organizing Map (ASSOM)
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 a scaling of 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 a 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.
KeywordsBasis Vector Component Vector Computational Load Learning Procedure Input Dimension
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