PA: Approximate Geometry Representations and Sensory Fusion

[Csaba Szepesvari]

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Title: Approximate Geometry Representations and Sensory Fusion

Keywords: self-organizing networks, sensory fusion, geometry 
representation,
topographical mapping, Kohonen network

        Csaba Szepesvari^*
        Andras Lorincz

     Adaptive Systems Laboratory, Insitute of Isotopes, Hungarian
     Academny of Sciences 
    *Bolyai Institute of Mathematics, Jozsef Attila University of 
     Szeged

Knowledge of the geometry of the world external to a system is
essential in cases such as navigation when for predicting the
trajectories of moving objects. It may also play a role in
recognition tasks, particularly when the procedures used for image
segmentation and feature extraction utilize information on the
geometry. A more abstract example is function approximation, where
this information is used to create better interpolation.

This paper summarizes the recent advances in the theory of
self-organizing development of approximate geometry representations
based on the use of neural networks. Part of this work is based on
the theoretical approach of (Szepesvari, 1993), which is different
from that of (Martinetz, 1993) and also is somewhat more general. The
Martinetz approach treats signals provided by artificial neuron-like
entities whereas the present work uses the entities of the external
world as its starting point. The relationship between the present
work and the Martinetz approach will be detailed.

We approach the problem of approximate geometry representations by
first examining the problem of sensory fusion, i.e., the problem of
fusing information from different transductors. A straightforward
solution is the simultaneous discretization of the output of all
transductors, which means the discretization of a space defined as
the product of the individual transductor output spaces. However, the
geometry relations are defined for the **external world** only, so it
is still an open question how to define the metrics on the product of
output spaces. It will be shown that **simple Hebbian learning** can
result in the formation of a correct geometry representation. Some
mathematical considerations will be presented to help us clarify the
underlying concepts and assumptions. The mathematical framework gives
rise to a corollary on the "topographical mappings" realized by
Kohonen networks. In fact, the present work as well as (Martinetz,
1993) may be considered as a generalization of Kohonen's topographic
maps. We develop topographic maps with self-organizing interneural
connections.
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Csaba Szepesvari
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Bolyai Institute of Mathematics        |e-mail: szepes at math.u-szeged.hu
"Jozsef Attila" University of Szeged   |http://www.inf.u-szeged.hu/~szepes
Szeged 6720                            |
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HUNGARY                                |
Tel.: (36-62) 311-622/3706             |phone at home (tel/fax): 
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