γ-Observable neighbours for vector quantization

We define the γ-observable neighbourhood and use it in soft-competitive learning for vector quantization. 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 neighbours (γ-ON) of v are the units w_i for which v_i is in the Voronoï of w_i, i.e. w_i is the closest unit to v_i. For γ=1, v_i merges with w_i, all the units are γ-ON of v, while for γ=0, v_i merges with v, only the closest unit to v is its γ-ON. The size of the neighbourhood decreases from n to 1 while γ goes from 1 to 0. For γ lower or equal to 0.5, the γ-ON of v are also its natural neighbours, i.e. their Voronoï regions share a common boundary with that of v. We show that this neighbourhood used in Vector Quantization gives faster convergence in terms of number of epochs and similar distortion than the Neural-Gas on several benchmark databases, and we propose the fact that it does not have the dimension selection property could explain these results. We show it also presents a new self-organization property we call 'self-distribution'.