Statistical testing of segment homogeneity in classification of piecewise-regular objects
The paper is focused on the problem of multi-class classification of composite (piecewise-regular) objects (e.g., speech signals, complex images, etc.). We propose a mathematical model of composite object representation as a sequence of independent segments. Each segment is represented as a random sample of independent identically distributed feature vectors. Based on this model and statistical approach we reduce the task to a problem of composite hypothesis testing of segment homogeneity. Several nearest-neighbor criteria are implemented, for some of them the well-known special cases (e.g., the Kullback-Leibler minimum information discrimination principle, the probabilistic neural network) are highlighted. It is experimentally shown that the proposed approach improves the accuracy when compared with contemporary classifiers.
Low-cost gaze tracking systems are in great demand due to their wide range of application. Commonly, extra devices are needed (for instance, head mounted cameras); however, in this investigation gaze tracking is performed in real-time based on the video stream from an infrared video camera. A comparative analysis of the existing analogues was executed and the main features of gaze tracking systems were highlighted and prioritized. These features are price, tracking accuracy, angle error, flexibility, and usability.
A methodology was developed which allows to calculate a gaze direction vector according to the relative position of eye center and corneal reflection from an infrared diode. The centers of an eye and reflection are estimated using the vector field of image gradients and additional weighting. CUDA technology is used to accelerate the developed algorithms.
The main advantage of the developed algorithm is the ability to detect and continuously track pupils’ centers, regardless of the head position, which significantly extends the scope of the gaze tracking system under consideration.
Diffculties concerning the choice of the invariants of the projective transformation groups used for the identification of the shapes of planar objects are illustrated and solutions allowing the derivation of robust identification criteria are discussed.
Problems of identification of plane unclosed curves are considered. Methods are proposed that allow one to classify graphic objects invariantly to affine transformations. An answer is given to the question on the types and the quantity of features that are needed to construct a mathematical description of curves for the recognition of an unclosed contour of an object. Metrics are introduced on the basis of which one can identify unclosed curves. The quality of identification on the basis of the metrics introduced is analyzed.
This paper addresses the problem of insufficient performance of statistical classification with the medium-sized database (thousands of classes). Each object is represented as a sequence of independent segments. Each segment is defined as a random sample of independent features with the distribution of multivariate exponential type. To increase the speed of the optimal Kullback-Leibler minimum information discrimination principle, we apply the clustering of the training set and an approximate nearest neighbor search of the input object in a set of cluster medoids. By using the asymptotic properties of the Kullback-Leibler divergence, we propose the maximal likelihood search procedure. In this method the medoid to check is selected from the cluster with the maximal joint density (likelihood) of the distances to the previously checked medoids. Experimental results in image recognition with artificially generated dataset and Essex facial database prove that the proposed approach is much more effective, than an exhaustive search and the known approximate nearest neighbor methods from FLANN and NonMetricSpace libraries.
The problem of management of the nonlinear object which is exposed to impact of uncontrollable indignations, is considered in a key of differential game. Synthesis of optimum managements is made with application of transformation of the nonlinear equation of initial object in the differential equation with the parameters depending on a condition. The square-law functional of quality allows to formulate synthesis conditions in the form of need of search of solutions of the equation of Rikkati. The solution of the equation of Rikkati with the parameters depending on a condition, is in a symbolical view with application of algebraic methods that allows to generalize a number of earlier published theoretical results, to receive rather constructive decisions in a number of statements of problems of management.
The article is based upon the fact that the growing demand for master data management systems has not yet produced a commonly accepted metodology for their design and development/ The article offers two mathematical models? that allow a master data management systems designer a way to formally describe their system before development and verify the system quality by measurements? unique to master data management systems.