Code vector density in topographic mappings: Scalar case

摘要: The author derives some new results that build on his earlier work (1989) of combining vector quantization (VQ) theory and topographic mapping (TM) theory. A VQ model (with a noisy transmission medium) is used to the processes occur in TMs, which leads standard TM training algorithm, albeit with slight modification encoding process. To emphasize this difference, called quantizer (TVQ). In continuum limit one-dimensional (scalar) TVQ. It found density code vectors proportional P(x)/sup a/ ( alpha =1/3) assuming medium introduces additive noise zero-mean, symmetric, monotically decreasing probability density. This result dramatically different from predicted when algorithm uniform symmetric neighborhood (-n, +n), it noted difference arises entirely using minimum distortion rather than nearest neighbor encoding. >