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Mathematical recognition theory has long history and the variety of its reality modeling methods is quite wide.

Every research group has its own traditions and usually works in specific area of mathematics. There are two basic approaches which are commonly said to be different. They are functional and algorithmic ones. For example, neural networks approximate output function but their parameters has no appropriate interpretation.

Algorithmic models as for example algorithms of estimates calculating provide interpretable parameters though may have high calculation difficulty. Integration of scientific schools and small groups of Уparticular specialistsФ in the framework of joint projects provide possibilities for revealing potentials of different methods and their combinations. Developing of one such integrated approach is connected to the execution of series of INTAS projects by research groups from Russia, Spain, Armenia and some other countries.

Algebraic theory of pattern recognition based upon discrete analysis and algebra [1] is the basic approach which has been being used for 35 years in the Computing Centre of RAS under the direction of academician Yu.I. Zhuravlev. Research activities of the Institute for Informatics and Automation Problems of NAS Armenia lie in the same area of discrete recognition models. Their specific is the use of optimization structures of discrete isoperimetric tasks, discrete topology and hierarchical>

Some hybrid methods and applications for pattern recognition have been developed by these groups in the framework of INTAS projects 96-952, 00-367, 00-636 and 03-55-1969. One of them is based on assembling of neural networks and logical correction schemes. The main cause of this research was the idea of creating such pattern recognition and forecasting application which requires minimal human intervention or no intervention at all. It should be possible for the operator with no specific knowledge in mathematics to use that software. Such NNLC (Neural Networks with Logical Correction) application has been developed in the framework of INTAS projects 03-56-182 inno and 03-55-1969 YSF. Now we are proud to say that it has justified our expectations in a great extent. The method has shown high and stable results in many practical tasks.

Knowledge Engineering Further we shall describe general training and recognition scheme for the l-classes task. The notation from [1] will be used. Let the training sample be S1, S2,..., Sm and the testing one S'1, S'2,..., S'q :

Sm +1, Sm +2,..., Sm Ki,i = 1,2,...,l,m0 = 1,ml = m, i-1 i-1 i S'q +1, S'q +2,..., S'q Ki,i =1,2,...,l,q0 =1,ql = q.

i-1 i-1 i For simplicity sake let us also suppose the task is solved without denials.

Finally, let us have N neural networks Aj (S) = (1j (S),2j (S),...,lj (S)) trained for this task. It will give us the following matrix of recognition results:

Aj (S't ) = (1j (S't ),2j (S't ),...,lj (S't )), ij (S't ) {0,1},i = 1,2,..., l, j = 1,2,..., N,t = 1,2,..., q.

Algorithm of recognition by the group of neural networks will be designed according to the principle of potential correction [4]. New object will be assigned to the>

q j i (S) =.

(S't, S),i =1,2,...,l i q - q t =q +j j-j-The variable i (S't,S) is called the potential between S't и S and is calculated as follows:

1, {ij (S) ij (S't ), j = 1,2,..., N,} / N, a) i (S't,S) = otherwise.

0, b) i (S't, S) = {the number of correct inequalities ij (S) ij (S't ), j = 1,2,..., N}.

A-type potential we will call monotonous, b-type one will be called weekly monotonous with monotony parameter, 0 < 1.

Thus, training phase consists of training of N neural networks (with no denials) and consequent calculation of binary matrix ij (S't ). New object S is>

Acknowledgements The authors are glad to acknowledge support of the following organizations for execution of the described research: INTAS (projects 03-56-182 inno, 04-77-7076, 03-55-1969 YSF), RFBR (projects 05-07-90333, 06-0100492, 05-01-00332). The work has been also supported by the program N 14 of RAS PresidiumТs.

Bibliography [1] Zhuravlev Yu.I., On algebraic approach for pattern recognition or>

[2] Aslanyan L., Zhuravlev Yu., Logic Separation Principle, Computer Science & Information Technologies Conference // Yerevan, 2001, pp. 151-156.

[3] Luis Mingo, Levon Aslanyan, Juan Castellanos, Miguel Diaz and Vladimir Riazanov // Fourier Neural Networks: An Approach with Sinusoidal Activation Functions. International Journal Information Theories and Applications. Vol. 11.

ISSN: 1310-0513. 2004. Pp. 52-53.

[4] Zuev Yu.A., Method for increasing of>

Fourth International Conference I.TECH 2006 AuthorsТ Information L.A. Aslanyan - Institute for Informatics and Automation Problems, NAS Armenia; P.Sevak St. 1, Yerevan-14, Armenia; e-mail: lasl@sci.am L.F. Mingo - Dpto. Organizacin y Estructura de la Informacin, Escuela Universitaria de Informtica, Universidad Politcnica de Madrid; Crta. de Valencia km. 7 - 28031 Madrid, Spain; e-mail: lfmingo@eui.upm.es J.B. Castellanos - Dpto. Inteligencia Artificial, Facultad de Informtica, Universidad Politcnica de Madrid;

Boadilla del Monte - 28660 Madrid, Spain; e-mail: jcastellanos@fi.upm.es V.V. Ryazanov - Department of Mathematical Pattern Recognition and Methods of Combinatorial Analysis, Computing Centre of the Russian Academy of Sciences; 40 Vavilova St., Moscow GSP-1, 119991, Russian Federation; e-mail: rvvccas@mail.ru F.B. Chelnokov - Department of Mathematical Pattern Recognition and Methods of Combinatorial Analysis, Computing Centre of the Russian Academy of Sciences; 40 Vavilova St., Moscow GSP-1, 119991, Russian Federation; e-mail: fchel@mail.ru A.A. Dokukin - Department of Mathematical Pattern Recognition and Methods of Combinatorial Analysis, Computing Centre of the Russian Academy of Sciences; 40 Vavilova St., Moscow GSP-1, 119991, Russian Federation; e-mail: dalex@ccas.ru LOGIC BASED PATTERN RECOGNITION - ONTOLOGY CONTENT (1) Levon Aslanyan, Juan Castellanos Abstract: Pattern recognition (classification) algorithmic models and related structures were considered and discussed since 70s: - one, which is formally related to the similarity treatment and so - to the discrete isoperimetric property, and the second, - logic based and introduced in terms of Reduced Disjunctive Normal Forms of Boolean Functions. A series of properties of structures appearing in Logical Models are listed and interpreted. This brings new knowledge on formalisms and ontology when a logic based hypothesis is the model base for Pattern Recognition (classification).

1. Introduction Pattern Recognition is in reasonable formalization (ontology) of informal relations between objects visible/measurable properties and of object>

Considering>

LSA is based on implementation of additional logical treatments on learning set elements, and above the AEA specific metric considerations. Some formalization of additional properties on>

K1 and K2. Let K1, and K2, and is an unknown object in the sense of>

After this assumption we get, that the reduced disjunctive normal forms of two complementary partially defined Boolean functions describe the structure of information enlargement of the learning set. This construction is extending the model of estimation of analogies. It was shown that the logical separators divide the object sets into three subsets, where only one of them needs the treatment by AEA. This set is large enough for almost all weakly defined Boolean functions, but for the functions with the property of compactness it is small. Let, for 0 k0 < k1 n Fn,k0,k1 is the set of all Boolean functions consisting of pair of k0 and n - k1 spheres centered at 0 and 1 respectively as the sets of zeros and ones of the function. On the remainder part of vertices of n cube the assignment/evaluation of the functions are arbitrary. This functions satisfy the compactness assumptions, and their quantity is not less than 2 ( n )2n for an appropriate ( n ) 0 with n 0. For these functions, also, it is enough learning set, consisting of any n2n- ( n ) n or more arbitrary points for recovering the full>

2. Logic Based Model Solving the main problem of pattern recognition or>

Above we already considered the general formalization models of hypothesis by metrics and by logic. More formalizations move to more restricted sets of allowable> Pages:     | 1 |   ...   | 11 | 12 | 13 | 14 | 15 |   ...   | 54 |    Книги по разным темам