A. P. Vinogradov

Approaches to construction of linear classifiers in the case of many classes

Some approaches to the problem of constructing linear classifiers, including embedded ones, are studied for the case of many classes. Sufficient conditions for linear separability of classes are formulated, and specifics of the problem statement when sets are not linearly separable are considered. Different approaches to construction of optimal linear classifiers are studied, and the results of numerical experiments are presented. The properties of embedded (convex piecewise linear) classifiers are studied. It is shown that, for an arbitrary family of finite nonintersecting sets, there is an embedded linear classifier that correctly separates the points of these sets.

Accurate reconstruction of 3D model of a human face using structured light

An automated system for the reconstruction of textured 3D models of human faces has been developed. 3D information is read using the structured lighting used in calibrated projector-camera system. The accuracy of 3D reconstruction is studied experimentally.

Stochastic filtering of approximate symmetries in dense packings of clusters

Certain questions concerning the arrangement of optimal dense packings of clusters are considered when simple routine long-term procedures are applied instead of a laborious method of direct solution. A unified approach to searching for hidden symmetries in such packings is proposed that represents a certain combination of the generalized Hough transform and the Purzen windows technique in nonparametric density estimation. All symmetries are sought via the Hough transforms adjusted to certain types of adjacent classes on the SON group manifold. Exact symmetries and separate solutions are filtered out by using the ergodic properties of the independent sequential choice procedure.

Methods for discrete analysis of medical data on the basis of recognition theory and some of their applications

Methods for the analysis of medical data and the results of their application to the treatment of a number of socially important diseases in important medical areas (cardiology, neurology, surgery, and oncology) are considered. The precedent approach is investigated. Practical methods of discrete analysis of training data, logical and statistical methods for searching logical regularities in data, combinatorial logic and logical statistical classification methods, and methods for estimating models and searching for “nonstandard” descriptions are presented. The results of experiments on real data are demonstrated.

A comparison of some approaches to classification problems, and possibilities to construct optimal solutions efficiently

We consider sequential linear (binary) classifiers for the case of many classes along with the linear classifiers based on determining the maximum discriminant function. It is shown that the capabilities of sequential binary classifiers are wider than those of linear classifiers. For the case of linearly non-separable training samples there are considered approaches based on minimizing the margin of misclassification and minimizing empirical risk. It is shown that problem of minimizing the margin of misclassification is polynomially solvable for a certain choice of the norm in the feature space. A refined model of the empirical risk minimization problem and its continuous relaxation are considered, a comparison with the mathematical model of SVM is done. The results of numerical experiments comparing different approaches are discussed.

Analysis of a 3D face-scanning system by active triangulation

An automated system for reconstructing textured, three-dimensional models of human faces has been developed. Three-dimensional information is read by structured highlighting used in a calibrated projector-camera system. The accuracy of 3D reconstruction has been experimentally investigated.

Discrete approach for automatic knowledge extraction and knowledge based classification algorithms

Abstract The new discrete universal approach for automatic knowledge extraction and knowledge based classification algorithms are proposed. The initial information is the sample of objects, situations or processes described in terms of numerical features. The sets of special predicates are calculated. They realise the relationships of the “if… then ...” type between feature values and classes affiliation. The practical example and applications are considered.

On Finding the Maximum Feasible Subsystem of a System of Linear Inequalities

Some methods for finding the maximum feasible subsystems of systems of linear inequalities are considered. The problem of finding the most accurate algorithm in a parametric family of linear classification algorithms is one of the most important problems in machine learning. In order to solve this discrete optimization problem, an exact (combinatorial) algorithm, its approximations (relaxation and greedy combinatorial descent algorithms), and the approximation algorithm are given. The latter consists in replacing the original discrete optimization problem with a nonlinear programming problem by changing from linear inequalities to their sigmoid functions. The initial results of their comparison are presented.

Linear classifiers and selection of informative features

In this work, to construct classifiers for two linearly inseparable sets, the problem of minimizing the margin of incorrect classification is formulated, approaches to achieving approximate solution, and calculation estimates of the optimal value for this problem, are considered. Results of computational experiments that compare proposed approaches with SVM are presented. The problem of identifying informative features for large-dimensional diagnostic applications is analyzed and algorithms for its solution are developed.

Using generalized precedents for big data sample compression at learning

The role of intrinsic and introduced data structures at constructing efficient recognition algorithms is analyzed. The concept of generalized precedent as representation of stable local regularity in data and based on its use methods of reduction of the dimension of tasks has been investigated. Two new approaches to the problem based on positional data representation and on cluster means for elementary logical regularities are proposed. The results of computational experiment with data compression in parametric spaces for several practical tasks are