### Browsing by Author "Goldfarb, Lev"

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Item A working characterization of intelligence and a new model(1990) Goldfarb, LevA working description of "intelligence" is proposed: intelligence is characterized by autonomously evolving purposeful processing of meaningful signals (events). The purposefulness should be interpreted in terms of orientation in the environment (physical or abstract) from which the "signals" came, and the evolving nature of the process points to the dominant role of learning mechanisms in acquiring the relevant knowledge. A new model for intelligent machines - pattern learning machines, which can be viewed as far reaching symbolic generalizations of the artificial neural nets - is briefly outlined, A longer and more detailed exposition of the model is currently in press.Item Inductive theory of vision(1996) Goldfarb, Lev; Deshpande, Sanjay, S.; Bhavsar, Virendra, C.In spite of the fact that some of the outstanding physiologists and neurophysiologists (e.g. Hermann von Helmholtz and Horace Barlow) insisted on the central role of inductive learning processes in vision as well as in other sensory processes, there are absolutely no (computational) theories of vision that are guided by these processes. It appears that this is mainly due to the lack of understanding of what inductive learning processes are. We strongly believe in the central role of inductive learning processes, around which, we think, all other (intelligent) biological processes have evolved. In this paper we outline a (computational) theory of vision completely built around the inductive learning processes for all levels in vision. The development of such a theory became possible with the advent of the formal model of inductive learning--evolving transformation system (ETS). The proposed theory is based on the concept of structured measurement device, which is motivated by the formal model of inductive learning and is a far-reaching generalization of the concept of classical measurement device whose output measurements are not numbers but structured entities ("symbols") with an appropriate metric geometry. We propose that the triad of object structure, image structure and the appropriate mathematical structure (ETS)--to capture the latter two structures-is precisely what computational vision should be about. And it is the inductive learning process that relates the members of this triad. We suggest that since the structure of objects in the universe has evolved in a combinative (agglomerative) and hierarchical manner, it is quite natural to expect that biological processes have also evolved (to learn) to capture the latter combinative and hierarchical structure. In connection with this, the inadequacy of the classical mathematical structures as well as the role of mathematical structures in information processing are discussed. We propose the following postulates on which we base the theory. Postulate 1. The objects in the universe have emergent combinative hierarchical structure. Moreover, the term "object structure" cannot be properly understood and defined outside the inductive learning process. Postulate 2. The inductive learning process is an evolving process that tries to capture the emergent object (class) structure mentioned in Postulate 1. The mathematical structure on which the inductive learning model is based should have the intrinsic capability to capture the evolving object structure. (It turns out that the corresponding mathematical structure is fundamentally different from the classical mathematical structures.) Postulate 3. All basic representations in vision processes are constructed on the basis of the inductive image representation, which, in turn, is constructed by the inductive learning process (see Postulate 2). Thus, the inductive learning processes form the core around which all vision processes have evolved. We present simple examples to illustrate the proposed theory for the case of "low-level" vision.Item Non-numeric measurement devices(1996) Goldfarb, Lev; Deshpande, Sanjay, S.In this report we define a fundamentally new type of measurement device- structured measurement device. The readings of all existing measurement devices are numeric. We propose a measurement device whose readings are non-numeric, or symbolic, i.e. the readings are structured objects, e.g. string, graphs, etc., with the geometry defined by the corresponding transformation operations. Thus the set of numbers in the classical devices is replaced by a transformation system.Item On a General Concept of the Inductive Learning Process(1995) Deshpande, Sanjay, S.; Goldfarb, LevWe propose to modify the original definition of the inductive learning process proposed by one of us to include two modes of operation of the evolving transformation system (ETS), supervised and unsupervised, which we will call external and internal. Keywords: inductive learning, evolving transformation system, supervised and unsupervised pattern recognition.Item The design of efficient pattern recognition systemsGoldfarb, LevA new general methodology for design of pattern recognition systems is proposed. 'This methodology is based on the new approach to pattern recognition proposed by the author. The principles of the design considered here should also be of use in the design of some complex database systems and error-correcting systems. Keywords: Pattern recognition, distance function, abstract nearest neighbour, search algorithm in metric space, pseudoeuclidean spaceItem Transformation systems are more economical and informative class descriptions than formal grammars(1990) Goldfarb, LevThe concept of the transformation system was introduced earlier by the author as a basic part of a general model for pattern learning. In this paper, for several formal languages (of various types) the equivalent transformation systems are presented. From these examples one can draw the conclusion that the transformation systems give shorter and more informative structural class descriptions than the formal grammars. Keywords: Transformation systems, Formal grammars, Structural class description.Item Typed three automata(1999) Bhavsar, Virendra; Goldfarb, Lev; Mironov, AndrewItem Vision of Information Science Inspired by a New Representational FormalismGoldfarb, LevA recently developed formalism for structural representation—called Evolving Transformations System (ETS)—is discussed as suggesting a radically different direction for the development of computer/information science. One can gain an initial intuitive understanding of the ETS object representation by generalizing the temporal process of the (Peano) construction of natural numbers: replace the single ‘structureless’ unit out of which a number is built by one of several more general structural units. The new formalism points to the informational view of nature in which the basic object encoding is temporal, event-based, while the ubiquitous in science ‘spatial’ object instantiation can be constructed on the basis of the former. Thus, this far-reaching structural generalization of natural numbers emerges as a universal form of both temporal and structural representation that can be variously instantiated, depending on the desired target medium, e.g. 3D-space, biotic, network, etc. Moreover, the ETS representation satisfies a unique and very desirable property not possessed by any other known language, scientific or spoken: its syntax and semantics are congruent. Keywords: new representational formalism, structural representation, class-oriented representational formalism, congruence of syntax and semanticsItem What Is a Structural Measurement Process?(2001) Goldfarb, Lev; Golubitsky, OlegNumbers have emerged historically as by far the most popular form of representation. All our basic scientific paradigms are built on the foundation of these, numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects or events, i.e., it is a procedure or device that realizes the mapping from the set of objects to the set of numbers. Any (including a future) measurement device is constructed based on the underlying mathematical structure that is thought appropriate for the purpose. It has gradually become clear to us that the classical numeric mathematical structures, and hence the corresponding (including all present) measurement devices, impose on “real” events/objects a very rigid form of representation, which cannot be modified dynamically in order to capture their combinative, or compositional, structure. To remove this fundamental limitation, a new mathematical structure—evolving transformation system (ETS)—was proposed earlier. This mathematical structure specifies a radically new form of object representation that, in particular, allows one to capture (inductively) the compositional, or combinative, structure of objects or events. Thus, since the new structure also captures the concept of number, it offers one the possibility of capturing simultaneously both the qualitative (compositional) and the quantitative structure of events. In a broader scientific context, we briefly discuss the concept of a fundamentally new, biologically inspired, “measurement process”, the inductive measurement process, based on the ETS model. In simple terms, all existing measurement processes “produce” numbers as their outputs, while we are proposing a measurement process whose outputs capture the representation of the corresponding class of objects, which includes the class progenitor (a non-numeric entity) plus the class transformation system (the structural class operations). Such processes capture the structure of events/objects in an inductive manner, through a direct interaction with the environment.Item What Is a Structural Representation in Chemistry: Towards a Unified Framework for CADD?(2001) Goldfarb, Lev; Golubitsky, Oleg; Korkin, DmitryA fundamentally new formal framework for structural representation of organic compounds based on the first "true" (general) formalism for structural object representation recently proposed by us|evolving transformation system (ETS) model is outlined. The applied orientation of the paper is towards the molecular design in general and computer aided drug design (CADD) in particular. Inadequacies of the conventional models used in (CADD) for molecular representation and classification as well as the advantages of the proposed ETS model are discussed. Some advantages of the ETS model is its capability to represent naturally all important structural features of molecules, e.g. different atoms and their bonding types (including hydrogen bonding), basic 2D and 3D isometries, the molecular class structure. The model allows one not only to classify a new compound, but also to construct a chemically valid new compound from the class of compounds that was previously learned based on a small set of examples. The model also guarantees the inheritance of the chemical structural class information from the parent class to all its subclasses. In general, the ETS model offers a much more precise "language" for chemical structural formulas. The central role of the class learning problem in CADD is suggested. Moreover, we propose the ETS model as a unified framework for the class learning problem and therefore as a unified formal framework for CADD. This would allow considerable streamlining of the CADD by assigning to the chemist the role of an interactive user of the system rather that a role of a human weak link within the CADD process.Item What Is a Structural Representation?(2001) Goldfarb, Lev; Golubitsky, Oleg; Korkin, DmitryWe 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 representation—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.Item What is a structural representation? A proposal for an event-based representational formalism: Sixth Variation(2007) Goldfarb, Lev; Gay, David; Golubitsky, Oleg; Korkin, Dmitry; Scrimger, IanWe outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt not just in artificial intelligence and pattern recognition, but also in the natural sciences, particularly biology. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important (to society) and interesting (to science), but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural entities/processes that we aim to formally address here, in contrast to theubiquitous mathematical view of objects as points in some abstract space. In light of the above, the paper is addressed to a very broad group of scientists. One can gain an initial intuitive understanding of the proposed representation by generalizing the temporal process of the (Peano) construction of natural numbers: replace the single structureless unit out of which a number is built by multiple structural ones. An immediate and important consequence of the distinguishability (or multiplicity) of units in the construction process is that we can now see which unit was attached and when. Hence, the resulting (object) representation for the first time embodies temporal structural information in the form of a formative, or generative, object “history” recorded as a series of (structured) events. Each such event stands for a “standard” interaction of several objects/processes. We introduce the new concept of class representation via the concept of class generating system, which outputs structural entities belonging to that class. Hence, the concept of class is introduced as that of a class of similar structural entities, where the “similarity” of such entities is ensured by them being outputs of the same class generating system and hence having similar formative histories. In particular, such a concept of class representation implies that—in contrast to all existing formalisms—no two classes have elements in common. The evolving transformation system (ETS) formalism proposed here is the first one developed to support such a new vision of classes. Most important, since the operations that participated in the object’s construction are, for the first time, made explicit in the representation, it makes the inductive recovery of class representation (on the basis of object representation) much more reliable. As a result, ETS offers a formalism that outlines, for the first time, a tentative framework for understanding what a class is. Even this tentative framework makes it quite clear that the term “class” has been improperly understood, used, and applied: many, if not most, of the current “classes” should not be viewed as such. A detailed example of a class representation is included. In light of ETS, the classical discrete “representations” (strings, graphs) appear as incomplete special cases at best, the proper adaptation of which should incorporate corresponding formative histories, as is done here. The gradual emergence of ETS—including the concepts of structural object and class representations, the resulting radically different (temporal) view of “data”, as well as the associated inductive learning processes and the representational levels—points to the beginning of a new field, inductive informatics, which is intended as a class oriented rival to conventional information processing paradigms.Item What is a structural representation?: Second version(2004) Goldfarb, Lev; Gay, David; Golubitsky, Oleg; Korkin, DmitryWe outline a formalism for “structural”, or “symbolic”, representation, the necessity of which is acutely felt in all sciences. One can develop an initial intuitive understanding of the proposed representation by simply generalizing the process of construction of natural numbers: replace the identical structureless units out of which numbers are built by several structural ones, attached consecutively. Now, however, the resulting constructions embody the corresponding formative/generative histories, since we can see what was attached and when. The concept of class representation—which inspired and directed the development of this formalism—differs radically from the known concepts of class. Indeed, the evolving transformation system (ETS) formalism proposed here is the first one developed to support that concept; a class representation is a finite set of weighted and interrelated transformations (“structural segments”), out of which class elements are built. The formalism allows for a very natural introduction of representational levels: a next-level unit corresponds to a class representation at the previous level. We introduce the concept of “intelligent process”, which provides a suitable scientific environment for the investigation of structural representation. This process is responsible for the actual construction of levels and of representations at those levels; conventional “learning” and “recognition” processes are integrated into this process, which operates in an unsupervised mode. Together with the concept of structural representation, this leads to the delineation of a new field—inductive informatics—which is intended as a rival to conventional information processing paradigms. From the point of view of the ETS formalism, classical discrete “representations” (strings, graphs) now appear as incomplete special cases at best, the proper “completion” of which should incorporate corresponding generative histories (e.g. those of strings or graphs).Item Why do we need the auxiliary vector representation for the metric pattern recognition problem?(1990) Goldfarb, Lev"Direct" pattern recognition algorithms in metric spaces, i.e., those that do not use auxiliary vector space, are inferior to the pattern recognition algorithms that rely on the vector approximation of the original, metric, recognition problem. The critical issues associated with the role of the auxiliary vector space representation for the metric pattern recognition problem are considered. Keywords: Pattern recognition in Metric Spaces, Efficiency, Auxiliary Vector Representation.