What is a structural represetation?

[Lev Goldfarb]

(Our apologies if you receive multiple copies of this announcement)

Dear colleagues,

The following paper, titled "What is a structural representation?",

                     ( http://www.cs.unb.ca/profs/goldfarb/struct.ps )

which we believe to be, in a sense, the first one formally addressing the
issue of structural representation and proposing the formal ETS model,
should be of particular interest to researchers in pattern
recognition and machine learning. 

It implies, in particular, that the properly understood (non-trivial)
"structural" representations cannot be "replaced" by the classical
numeric, e.g. vector-space-based, representations. Moreover, the concept
of "structural" representation emerging from the ETS model is not the one
familiar to all of you.
 
(The abstract of the paper is appended below; for a change, the default
paper size is A4. Unfortunately for some, the language of the paper is of
necessity quite formal, since the main concepts do not have any analogues
and therefore must be treated carefully.)

Although the proposed model was motivated by, and will be applied to, the
"real" problems coming from such areas as pattern recognition, machine
learning, data mining, cheminformatics, bioinformatics, and many others,
in view of the required radical rethinking that must now go into its
implementations, at this time, we can only offer a very preliminary
discussion, in the following companion paper, addressing the model's
potential applications in chemistry
 
                      http://www.cs.unb.ca/profs/goldfarb/cadd.ps

(please keep in mind that the last paper was written on the basis of an
earlier draft of the paper we are announcing now and it will be updated
accordingly next month). 

We intend to discuss the paper shortly on INDUCTIVE mailing list.

(To subscribe, send to INDUCTIVE-SERVER at UNB.CA the following text 
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We would greatly appreciate any comments regarding both of the above
papers.


Best regards,  

     Lev Goldfarb                                 Tel:      506-458-7271
     Faculty of Computer Science                  Tel(secret.): 453-4566
     University of New Brunswick                  Fax:      506-453-3566
     P.O. Box 4400                                E-mail:  goldfarb at unb.ca
     Fredericton, N.B., E3B 5A3                   Home tel: 506-455-4323
     Canada
 
 
     http://www.cs.unb.ca/profs/goldfarb/goldfarb.htm

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                     WHAT IS A STRUCTURAL REPRESENTATION?

                Lev Goldfarb, Oleg Golubitsky, Dmitry Korkin

                         Faculty of Computer Science 
                         University of New Brunswick 
                           Fredericton, NB, Canada 


  We outline a formal foundation for a "structural" (or "symbolic")
object/event representation, the necessity of which is acutely felt in
all sciences, including mathematics and computer science. The proposed
foundation incorporates two hypotheses:
    1) the object's formative history must be an integral part of the
       object representation and
    2) the process of object construction is irreversible, i.e. the
       "trajectory" of the object's formative evolution does not intersect
       itself.  
The last hypothesis is equivalent to the generalized axiom of (structural)
induction. Some of the main difficulties associated with the transition
from the classical numeric to the structural representations appear to be
related precisely to the development of a formal framework satisfying
these two hypotheses. The concept of (inductive) class--which has inspired
the development of this approach to structural representation--differs
fundamentally from the known concepts of class.
  In the proposed, evolving transformations system (ETS), model, the class
is defined by the transformation system---a finite set of weighted
transformations acting on the class progenitor--and the generation of the
class elements is associated with the corresponding generative process
which also induces the class typicality measure. 
  Moreover, in the ETS model, a fundamental role of the object's class in
the object's representation is clarified: the representation of an object
must include the class.
  From the point of view of ETS model, the classical discrete
representations,  e.g. strings and graphs, appear now as incomplete
special cases, the proper completion of which should incorporate the
corresponding formative histories, i.e. those of the corresponding strings
or graphs.