The Search of Precedent-Based Logical Regularities
for Recognition and Data Analysis Problems¹

S. B. Larin and V. V. Ryazanov

Computer Center, Russian Academy of Sciences, ul. Vavilova 40, GSP-1, Moscow, 117967 Russia
Fax: 7(095)135 6159; e-mail: rvv@ccas.ru

Abstract—The paper describes an analysis of numerical precedent information (tables of feature descriptions
of objects, of situations, or phenomena) done to find logical relations in classes of objects; to set up logical
descriptions of the classes; to compute information characteristics of features, objects, and classes; and to solve
recognition problems. Logical relations are understood as special predicates defined on feature subspaces,
which take the value “true” on some template (learning) objects of a given class and the value “false” on the
template objects of the other classes, and satisfy the optimality criteria.

A new efficient approach is proposed to the search for logical class regularities, which is based on finding opti
mal parallelepipeds in feature subspaces centered at template objects. In solving the prime extremum problem,
we assume the independent variables to be those which define the feature subset and the parallelepiped dimen
sions. The prime optimization problem is reduced to the integer-valued linear programming problem whose
coefficients of the constraint matrix and of the objective functional have a special block structure with properties
of monotonicity. The connection is estimated between the quality of original information and the values of opti
mal decisions.

Adaptation of the proposed recognition model to new practical tasks is discussed. An attempt is made to identify
and formalize the steps of the recognition process, for which an important consideration is the possibility of
performing them in more than one way tailored to a particular applied task. A learning and recognition program
readily adaptable to new standards of information was developed on this basis. A solution of a medical diag
nostic task is examined.

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