Order statistics learning vector quantizer

Abstract

We propose a novel class of learning vector quantizers (LVQs) based on multivariate data ordering principles. A special case of the novel LVQ class is the median LVQ, which uses either the marginal median or the vector median as a multivariate estimator of location. The performance of the proposed marginal median LVQ in color image quantization is demonstrated by experiments.

On the Variants of the Self-Organizing Map That Are Based on Order Statistics

“…The MMSOM updates the weight vectors using the marginal median, while the VMSOM applies the vector median [8,9]. In contrast, the SOM calculates the weighted mean value of the input patterns, as can be seen in (2).…”

“…The standard SOM has some disadvantages, such as lack of robustness against outliers and against erroneous choices for the winner vector due to the linear estimators [8]. In order to face these problems, the variants of the standard SOM that employ multivariate order statistics can be used.…”

“…Let us explain the use of the Kuhn-Munkres algorithm in the calculation of the SOM clustering accuracy. The accuracy of the assignment performed by the SOM is defined by (8). Let us consider that the patterns must be clustered into K clusters.…”

“…T , is performed by ordering the winner neuron's vector components independently along each of the D dimensions [8,9]:…”

“…We are interested in the class of SOM training algorithms that employ multivariate order statistics, such as the marginal median and the vector median [8]. These SOM variants as well as the standard SOM, that is trained with the batch algorithm (to be referred to as SOM hereafter), are applied to pattern clustering.…”