In vector quantization, an energy function or distortion measure is minimized. However, the iterative minimizing process frequently gets stuck in a local minima of the energy function. To overcome this shortcoming, a neighboring structure is defined, such that all the neighboring units of the winning unit are adapted at each iteration. Different quantization algorithms have different adaptation rules. In self-organizing maps, unit position is used to determine the adaptation strength: the higher the distance between the winner and a unit, the lower the adapting step. In neural-gas, units are ranked in the increasing order of their distance to the input datum: the lower their rank, the higher their move toward the input datum.

In this paper, the r-observable neighborhood is proposed. Ther-observable neighborhood is defined using the Voronoi of the units: the r-observable neighbors (r-ON) of datum v are the units wi for which vi is in the Voronoi of wi. The size of the neighborhood is determined by r, which ranges from 1 to 0. There are two extremes: for r=0, vi merges with v, whose r-ON is the closest unit to it, while for r=1, merges with wi, all the units are r-ON of v. An optimized algorithm is recommended to compute the r-ON, although it has the same worst-case complexity as a brute force algorithm. The experimental results show that under similar distortion, using r-ON in vector quantization results in a faster convergence rate than the neural-gas on several benchmark databases. Also, a new self-organization property, called self-distribution, is presented in the iteration process.