paper available "Symbolic vs Vector Space Learning"

[Kamat]

FTP-host: jupiter.csd.unb.ca
FTP-filename: /pub/symbol/vector.ps.Z 

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Dear Connectionists,

The following paper has been accepted for publication in Pattern Recognition
Letters and is available through anonymous ftp.

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       CAN A VECTOR SPACE BASED LEARNING MODEL DISCOVER INDUCTIVE CLASS
		GENERALIZATION IN A SYMBOLIC ENVIRONMENT?


      Lev Goldfarb, John Abela, Virendra C. Bhavsar and Vithal N. Kamat

 		     Faculty of Computer Science
                     University of New Brunswick
                  Fredericton, N.B., Canada  E3B 5A3
              E-mail: goldfarb, x45i, bhavsar, u095 at unb.ca

                               Abstract

We outline a general framework for inductive learning based on the recently
proposed evolving transformation system model. Mathematical foundations of
this framework include two basic components: a set of operations (on objects)
and the corresponding geometry defined by means of these operations. 
According to the framework, to perform inductive learning in a symbolic 
environment, the set of operations (class features) may need to be
dynamically updated, and this requires that the geometric component allows
for an evolving topology. In symbolic systems, as defined in this paper,
the geometric component allows for a dynamic change in topology, whereas
finite-dimensional numeric systems (vector spaces) can essentially have only
one natural topology. This fact should form the basis of a complete formal
proof that, in a symbolic setting, the vector space based models, e.g. 
artificial neural networks, cannot capture inductive generalization. Since
the presented argument indicates that the symbolic learning process is more
powerful than the numeric process, it appears that only the former should
be properly called an inductive learning process. 


Keywords: Inductive learning, inductive generalization, vector space 
          learning models, artificial neural networks, symbolic models,
          evolving transformation system, learning topologies.

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FTP-host: jupiter.csd.unb.ca
FTP-filename: /pub/symbol/vector.ps.Z 
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ftp instructions: 

% ftp jupiter.csd.unb.ca
Name: anonymous
password: your full email address
ftp> cd pub/symbol
ftp> binary
ftp> get vector.ps.Z
ftp> bye
% uncompress vector.ps.Z
% lpr vector.ps

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  Vithal N. Kamat	             	Tel.  (506) 453-4566
  Faculty of Computer Science   	Fax.  (506) 453-3566
  University of New Brunswick      	E-mail: u095 at unb.ca     
  Fredericton, N.B., CANADA E3B 5A3
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