Dear subscribers to our mailing list,
After a longer than anticipated delay (see one of the earlier
announcements of our paper attached below), I'm opening the discussion on
a central scientific question: the nature, including a formal model,
of structural representation.
Since this question is of enormous scope and has been (and will be)
discussed very often and in many sciences, I propose to delineate our
discussion to the adequacy (both theoretical and applied) of the evolving
transformations system (ETS) model proposed in the paper indicated in the
announcement attached below.
In case some of you may wonder why this topic is being proposed for
discussion on our mailing list, i.e. on INDUCTIVE mailing list, I want to
emphasize a very direct relationship (as suggested by the ETS model)
between the topic of structural representation and that of inductive
learning.
--Lev Goldfarb
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Date: Sat, 28 Jul 2001 12:56:47 -0300 (ADT)
From: Lev Goldfarb <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Subject: What is a structural representation?
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COLT MAILING LIST ([EMAIL PROTECTED]) The following message was received
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(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 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 [EMAIL PROTECTED] the following text
SUBSCRIBE INDUCTIVE FIRSTNAME LASTNAME)
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: [EMAIL PROTECTED]
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.
