Vector Quantization with γ-Observable Neighbors

Abstract

We define a new neighborhood called “γ-Observable” and investigate its use in Vector Quantization tasks. Considering a datum v and a set of n units W _i in a Euclidean space, let V _i be a point of the segment [VW _i] whose position depends on γ a real number between 0 and 1, the γ-Observable neighbors (γ-ON) of v are the units W _i for which V _i is in the Voronoï region of Wi. i.e. W _i is the closest unit to V _i. For γ=1, V _i merges with W _i, all the units are y-ON of v, while for γ=O, V _i merges with v, only the closest unit to v is γ-ON of v. The size of the neighborhood decreases from n to 1 While γ goes from 1 to O. For γ lower or equal to 0.5, the γ-ON of v are also its natural neighbors, i.e. their Voronoï regions share a common edge with that of v. We experimentally show that this neighborhood used in VQ gives faster convergence and similar final distortion than the “Neural-Gas” onto synthetic data distributions.