?-Observable neighbours for vector quantization
We define the ?-observable neighbourhood and use it in soft-competitive learning for vector quantization. Considering a datum v and a set of n units wi in a Euclidean space, let vi be a point of the segment [vwi] whose position depends on ? a real number between 0 and 1, the ?-observable neighbours (?-ON) of v are the units wi for which vi is in the Vorono?? of wi, i.e. wi is the closest unit to vi. For ?=1, vi merges with wi, all the units are ?-ON of v, while for ?=0, vi merges with v, only the closest unit to v is its ?-ON. The size of the neighbourhood decreases from n to 1 while ? goes from 1 to 0. For ? lower or equal to 0.5, the ?-ON of v are also its natural neighbours, i.e. their Vorono?? 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.
?-observable neighbours vector quantization natural neighbours neural-gas dimension selection self-organizing maps self-distribution