TY - JOUR

T1 - Controlling the Magnification Factor of Self-Organizing Feature Maps

AU - Bauer, H.-U.

AU - Der, R.

AU - Herrmann, Michael

N1 - doi: 10.1162/neco.1996.8.4.757

PY - 1996/5/15

Y1 - 1996/5/15

N2 - The magnification exponents μ occurring in adaptive map formation algorithms like Kohonen's self-organizing feature map deviate for the information theoretically optimal value μ = 1 as well as from the values that optimize, e.g., the mean square distortion error (μ = 1/3 for one-dimensional maps). At the same time, models for categorical perception such as the "perceptual magnet" effect, which are based on topographic maps, require negative magnification exponents μ < 0. We present an extension of the self-organizing feature map algorithm, which utilizes adaptive local learning step sizes to actually control the magnification properties of the map. By change of a single parameter, maps with optimal information transfer, with various minimal reconstruction errors, or with an inverted magnification can be generated. Analytic results on this new algorithm are complemented by numerical simulations.

AB - The magnification exponents μ occurring in adaptive map formation algorithms like Kohonen's self-organizing feature map deviate for the information theoretically optimal value μ = 1 as well as from the values that optimize, e.g., the mean square distortion error (μ = 1/3 for one-dimensional maps). At the same time, models for categorical perception such as the "perceptual magnet" effect, which are based on topographic maps, require negative magnification exponents μ < 0. We present an extension of the self-organizing feature map algorithm, which utilizes adaptive local learning step sizes to actually control the magnification properties of the map. By change of a single parameter, maps with optimal information transfer, with various minimal reconstruction errors, or with an inverted magnification can be generated. Analytic results on this new algorithm are complemented by numerical simulations.

U2 - 10.1162/neco.1996.8.4.757

DO - 10.1162/neco.1996.8.4.757

M3 - Article

VL - 8

SP - 757

EP - 771

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 4

ER -