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Welcome !! |
Lev Goldfarb
Diploma Math/CS ( Ph.D. in Systems Design
Engineering ( Area: Pattern Recognition Retired prof., Faculty of Computer
Science, UNB ************ Inductive Information Systems tel:
(506) 455-4323 |
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Book
in progress: “Is There a Common
Structuring Law in the Universe: Integrating
Mind into Scientific View of the Universe”
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A general description of the
fundamentally new, event-based, representational formalism (ETS) proposed by us :
It is the first and so far the only general formal
framework for modeling evolving forms
of (object and class) representations.
While all of modern science is based on the formalism
that is precise elaboration of the ‘continuous’, ETS can be considered as a
proposal for a precise and general elaboration of the ‘discrete’. Moreover, and what is more, while in the
conventional scientific models syntax is not related to semantics—and hence, of
necessity, we have no choice but to
project onto reality their formal
structures, e.g. the vector space structure—ETS is the first formalism which
has been designed in such a way that syntax
and semantics are congruent, so that the proposed formal structures are
supposed to be the blueprints of the corresponding structures in nature.
Also, in contrast to the conventional scientific models—which
do not make any explicit assumptions about the structure of objects in nature and represent objects as ‘points’—in
ETS, objects are viewed and represented as irreversible
structural processes, i.e. as (non-linear, temporal) streams of interconnected structured
events.
On the philosophical side, the opposition between the ‘mind’
and ‘matter’ has been overcome, since now both ‘rely’ on the same form of
representation.
Is there a different mathematics,
of generatively structured entities,
which would clarify the nature of
the structural ‘measurement’ processes?
Natural numbers—think of them
as strings
of •'s—which have gradually emerged over many millennia, served as the
basis of the ubiquitous numeric forms for representing information about
objects or events. All our basic
scientific paradigms are built on the foundation of this representation. Measurement,
as conventionally understood, is the corresponding process for (numeric)
representation of objects, i.e. it is a procedure or device that realizes the
mapping from the set of objects to the set of numbers.
Accordingly, in science, there
has existed only one underlying (i.e.
numeric) representational model, and it has served as a universal blueprint
for building all known measurement devices.
Moreover, we, collectively, have had no experience with any other kind
of measurement device! Thus, when contemplating
the transition from the classical measurement processes to the structural ones,
we are faced with the situation absolutely unprecedented in the history of
science, with the ensuing benefits far outweighing the difficulties.
When considering structural
generalization of the classical measurement, or representation, theory, one has
to keep in mind that any ‘measurement device’ can be conceived (and
constructed) provided we have identified the underlying formal structure. This
formal structure—in contrast to the conventional mathematical, point-like, view of objects entrenched
in the concept of the set—is supposed to provide a fundamentally new,
structural, form of object representation, and the developments associated with
such formal structure will constitute a new, structural, mathematics.
A crucial feature of the ETS
representation that we have proposed is related to the observation that all objects in nature (including mental
objects) have a formative history. We have gradually realized that the concept
of formative object history and the concept of object representation are very
similar. Thus, a ‘true’ representational formalism must provide a unified formal structure
for capturing an object's formative ‘history’: both, complete history (as in Nature
itself) or subjective (as perceived by an agent). It is not difficult to see that the numeric
representation possesses this feature but only in a very rudimentary form: numeric representation records the process of
object formation relying on the extremely limited concatenation operation for strings over a single letter
alphabet {•} (because this is how a natural number is
built). Such trivially temporal
representation intrinsically cannot
capture any non-trivial structural formative history, in which the
corresponding events are of more complex structure (than the concatenation
operation).
Accordingly, all conventional discrete ‘representations’—such as strings over an
alphabet of size > 1, trees, and graphs—cannot
be viewed as true object representations, since they do not capture the
formative history. For example, the
formative history of a string is not part of the string representation. Hence a string is not a reliable form of
object representation, since it has an exponential number of formative
histories associated with its generation, creating a computationally
insurmountable problem for inductive learning process, which is supposed to
discover the (generative) class representation.
Returning to the measurement
process, one can say that all classical measurement processes ‘produce’ numbers
as their outputs, while the generalized measurement process is supposed to
output non-numeric entities, which we call structs. Thus, the generalized measurement process
captures the temporal, or informational,
structure of objects in an inductive manner, through a more dynamic
interaction with the environment.
I am convinced that gradually, as
the development of various applications of the ETS formalism progresses, the
new form of object representation should supersede such preliminary and
incomplete ones as the string, tree, graph, etc.
ETS
group
Muhammad
Al-Digeil
Lev Goldfarb
Ian Scrimger
Research areas of interest
Inductive
informatics :
·
structural
representations (equivalently: evolutionary-, or inductively-,
structured environments);
structural (inductive, intelligent) measurement processes
connections with: physics,
chemistry, biochemistry, biology,
neurobiology, neuroscience, cognitive science
·
fundamental limitations of the classical (numeric)
representations and measurement processes
·
inductive learning processes (natural and artificial)
·
ETS (theory and applications)
·
fundamental limitations of numeric learning models
·
pattern recognition/machine learning
·
protein representation & classification
·
inductive databases and data
(including image and web) mining
·
bioinformatics
& cheminformatics
·
information retrieval
·
inductive models of vision and their applications
·
speech recognition and understanding
·
cognitive models based on ETS formalism
Journal
editorial boards
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· Pattern Recognition (1991 – 2008) |
Selected
publications, talks, and workshops
My second (updated) FQXi essay “Nature is fundamentally
discrete but our basic formalism is not” and its discussion
My first FQXi essay and its discussion “What is possible in
physics depends on the chosen representational formalism”
A simplified visual
illustration of the process of spatial instantiation of the ETS
representation for the Bubble Man example from Part III of our main paper (produced by Reuben Peter-Paul)
Slightly modified talk at MPI ,
Tübingen, July 2007 (PowerPoint slides:
if you want to see the “hidden” slides and notes, save the file first; the
latter option is also faster)
IIT,
"Pattern
representation and the future of pattern recognition: a program for
action" ICPR 2004 satellite workshop,
Cornell Biophysics March 2003 talk "Can a formal model unify biology?"
Topic for "Birds of a Feather" discussion at ISMB 2002 (MSWord version)
· Four papers for the ETS book
·
Dmitry
Korkin and Lev Goldfarb, "Multiple genome rearrangement: A General
approach via the evolutionary genome graph" (PDF
version), ISMB 2002 (also to appear in a special issue of Bioinformatics).
·
Lev
Goldfarb and Oleg Golubitsky, "What is a structural measurement
process?" (PDF version), Faculty of Computer
Science, U.N.B., Technical Report TR01-147, October 2001.
·
Lev
Goldfarb, Oleg Golubitsky, and Dmitry Korkin, "What is a structural
representation?" (PDF version), Faculty of
Computer Science, U.N.B., Technical Report TR00-137, December 2000.
·
Lev
Goldfarb, Oleg Golubitsky, and Dmitry Korkin, "What is a structural
representation in chemistry: Towards a unified framework for CADD?" (PDF version), Faculty of Computer Science, U.N.B.,
Technical Report TR00-138, December 2000.
·
Lev
Goldfarb and Jaroslav Hook, "Why classical models for
pattern recognition are not pattern recognition models", in International
Conference on Advances in Pattern Recognition, ed. Sameer Singh, Springer,
pp.405-414, 1998.
·
Lev
Goldfarb, Sanjay S. Deshpande and Virendra C. Bhavsar, "
Inductive theory of vision", Faculty of Computer Science",
U.N.B., Technical Report TR96-108, April 1996.
·
Sanjay
·
Lev
Goldfarb, John Abela, Virendra C. Bhavsar and Vithal N. Kamat, "Can a vector space based learning model discover
inductive class generalization in a symbolic environment?",
Pattern Recognition Letters 16, pp. 719-726, 1995.
·
Lev
Goldfarb and Sandeep Nigam, "The unified learning
paradigm: A foundation for AI", in V. Honavar and L. Uhr, eds., Artificial
Intelligence and Neural Networks: Steps towards Principled Integration,
Academic Press, Boston, MA, 1994.
·
Lev
Goldfarb, "What is distance and why do we need the
metric model for pattern learning?", Pattern Recognition 25, pp.
431-438, 1992.
·
Tony Y.
T. Chan and Lev Goldfarb, "Primitive pattern
learning", Pattern Recognition 25, pp. 883-889, 1992.
·
Lev
Goldfarb, "On the foundations of intelligent
processes - I: An evolving model for pattern learning", Pattern
Recognition 23, pp. 595-616, 1990. (Received an annual Pattern Recognition
Society Award)
Graduate thesis supervised since 1990
· Ian Scrimger (2007) Structural Representation of the Game of Go, Master's Thesis
· Mohammad S. Al-Digeil (2005) Towards an ETS Representation of Proteins,
Master's Thesis
· David
Clement (2003) Information Retrieval via the ETS Model, Master's Thesis
· John M. Abela (2002) ETS Learning of Kernel
Languages, Ph.D. Thesis
· Jaroslav Hook (1998) Are
Artificial Neural Networks Learning Machines?, Master's Thesis
·
Sanjay S.
Deshpande (1996) On the Foundations of Vision, Master's Thesis
· Vithal N. Kamat (1995) Inductive
Learning with the Evolving Tree Transformation System, Ph.D. Thesis
· John M. Abela (1994) Topics in
Evolving Transformation Systems,
Master's Thesis
· Sandeep Nigam (1993) Metric
Model Based Generalization and Generalization Capabilities of Connectionist
Models, Master's Thesis
· Wiranto B. Santoso (1992) Learning
Algorithm for the Reconfigurable Learning Machine, Master's Thesis
· Tony Y. T. Chan (1992) Learning
as Optimization, Ph.D. Thesis
· Sonya Dewi (1991) Dynamic
Selection of Primitives in the Metric Model for Pattern Learning, Master's Thesis
· Ahmady Satriawan (1990) A Tree
Transformation System for Pattern Learning,
Master's Thesis
Advising external graduate
students
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