Gamma-observable neighbours for vector quantization.

We define the gamma-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 gamma a real number between 0 and 1, the gamma-observable neighbours (gamma-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 gamma = 1, v(i) merges with w(i), all the units are gamma-ON of v, while for gamma = 0, v(i) merges with v, only the closest unit to v is its gamma-ON. The size of the neighbourhood decreases from n to 1 while gamma goes from 1 to 0. For gamma lower or equal to 0.5, the gamma-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'.