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What is a structural representation
, 2001
"... 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 ..."
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Cited by 17 (9 self)
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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 diculties 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 representationwhich has inspired the development of this approach to structural representationdiers fundamentally from the known concepts of class. In the proposed, evolving transformations system (ETS), model, the class is dened by the transformation systema nite 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 claried: 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. 1 Concepts which have proved useful for ordinary things easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts. They then become labeled as \conceptual necessities", a priori situations, etc. The road of scientic progress is frequently blocked for long periods by such errors.
The Unified Learning Paradigm: A Foundation for AI
 In: Artificial Intelligence and Neural Networks: Steps Toward Principled
, 1994
"... Introduction As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive lea ..."
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Cited by 16 (3 self)
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Introduction As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive learning model (see also [5], [34], [43]). Unfortunately, this issue was not perceived to be the central issue by the three leading (and founding) schools of AI, which had a very negative effect on the development of AI up to now. In particular, due only to the difference between the formal models used originally in some areas of AI and pattern recognition, AI had severed practically all ties with pattern recognition, which was very counterproductive to the development of both areas and particularly to AI. 1 With the recent rise of connectionism, this situation has begun to change, which is reflected in the content of the recent AI textbooks ([39], [4
What Is a Structural Measurement Process?
, 2001
"... Numbers 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 ..."
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Cited by 9 (3 self)
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Numbers 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 structureevolving 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 o#ers 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 whos...
Towards Formal Structural Representation of Spoken Language: An Evolving Transformation System (ETS) Approach
, 2005
"... Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation ..."
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Cited by 5 (0 self)
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Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation behind the undertaken research is an observation that the notion of representation of objects and concepts that once was considered to be central in the early days of pattern recognition, has been largely marginalised by the advent of statistical approaches. As a consequence of a predominantly statistical approach to speech recognition problem, due to the numeric, feature vectorbased, nature of representation, the classes inductively discovered from real data using decisiontheoretic techniques have little meaning outside the statistical framework. This is because decision surfaces or probability distributions are difficult to analyse linguistically. Because of the later limitation it is doubtful that the gap between speech recognition and linguistic research can be bridged by the numeric representations. This thesis investigates an alternative, structural, approach to spoken language representation and categorisa
International Standards Organization  ISO. Information technology  open systems interconnection  common management information protocol  part 1: Speci cation. volume ISO/IEC 9596
, 1990
"... Statistical pattern recognition traditionally relies on a feature representation. This approach can be powerful, if sufficient knowledge is available to select a small set of welldiscriminating features. If there is a lack of such knowledge, a large set of possible features has to be collected and ..."
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Cited by 4 (1 self)
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Statistical pattern recognition traditionally relies on a feature representation. This approach can be powerful, if sufficient knowledge is available to select a small set of welldiscriminating features. If there is a lack of such knowledge, a large set of possible features has to be collected and a large training set, representative in distribution for the given problem, is needed to build a reliable classifier. This is partially caused by the inherent difficulties in the feature based representation, when a (large) set of suboptimal features is used, in may result in a class overlap and strong feature dependency. The dissimilarity representation aims at treating objects in their wholeness, avoiding the use of isolated features. If the dissimilarity measure is defined such that a zero value is only permitted for identical objects, class overlap may be avoided. Consequently, proper knowledge of class densities is not needed, which opens the possibility to a domain based classification in which the training set should be just representative for the domain of the classes. In this paper, first, the basic ideas and some results of the dissimilarity representation are summarized. It is followed by a discussion on how this may be worked out for the domain based pattern recognition. 1. Issues of pattern recognition In general, pattern recognition relies on the description of regularities in observations of classes of objects.
What is a Structural Representation? (Second Version)
, 2004
"... We 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 iden ..."
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Cited by 3 (1 self)
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We 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.
What is a structural representation? Fourth variation
, 2005
"... [W]e may again recall what Einstein stressed: that given a sufficiently powerful formal assumption, a fertile and comprehensive theory may... be constructed without prior attention to the detailed facts, or even before they are known. L. L. Whyte, Internal Factors in Evolution, 1965 We outline a for ..."
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Cited by 3 (2 self)
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[W]e may again recall what Einstein stressed: that given a sufficiently powerful formal assumption, a fertile and comprehensive theory may... be constructed without prior attention to the detailed facts, or even before they are known. L. L. Whyte, Internal Factors in Evolution, 1965 We outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt in all sciences, particularly biology, for quite some time now. 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—which is quite primitive as compared, for example, to that of physics. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important and interesting, 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 processes that we aim to address here, in contrast to the ubiquitous mathematical view of objects as points in some abstract space. One can gain an initial intuitive understanding of the proposed representation by generalizing the (Peano) process of construction of natural numbers: replace the single structureless unit out of which a number is built by multiple structural ones. An immediate but critical consequence of the distinguishability/multiplicity of units in the construction process is that we can now see which unit was attached and when. Hence, the resulting representation for the first time embodies temporal structural information in the form of a formative, or generative, history.
What is a Symbolic Measurement Process?
"... Numbers have emerged historically as the most popular/convenient form of representation, and our basic scientific paradigm is built on the foundation of numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects ..."
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Cited by 1 (0 self)
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Numbers have emerged historically as the most popular/convenient form of representation, and our basic scientific paradigm is built on the foundation of numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects or events. 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 structureevolving transformation system (ETS)was proposed earlier. This mathematical structure allows one to capture inductively the com...
Classification on Dissimilarity Data: A First Look
"... In a dissimilarity (distance) data each pair of objects is characterized by a value which expresses the magnitude of di#erence between them. This type of data can be now classified using various approaches, provided that a new object is represented by its distances to the training samples. ..."
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Cited by 1 (0 self)
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In a dissimilarity (distance) data each pair of objects is characterized by a value which expresses the magnitude of di#erence between them. This type of data can be now classified using various approaches, provided that a new object is represented by its distances to the training samples.
A proposal for a representational formalism Fifth variation ∗
, 2006
"... What is a structural representation? ..."