Properties of creation and reduction according to the equinumber principle for adaptive vector quantisation

Abstract

For adaptive vector quantisation, properties of creation and reduction according to the equinumber principle are presented. The equinumber principle is that, partition errors are mutually equivalent when the number of inputs in a partition space is mutually equal, and average distortion is asymptotically minimised. Then creation and reduction of adaptive vector quantisation have been introduced to avoid the initial dependence of reference vectors. In creation, output units are sequentially created according to the equinumber principle in the learning process to reach a predetermined number of units. In reduction, output units are sequentially deleted according to the equinumber principle to reach the prespecified number. A novel algorithm is unified by creation and reduction, in which reduction is carried out after creation is conducted. Experimental results show the properties of our approach. Furthermore our approach is applied to image data and the practicability is confirmed for image coding.