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## Метод максимально правдоподобных рассогласований в задаче распознавания изображений на основе глубоких нейронных сетей

In this paper we focus on the image recognition problem in the case of small sample size based on the nearest neighbor rule and matching of high-dimensional feature vectors extracted with the deep convolutional neural network. We propose the novel recognition algorithm based on the maximum likelihood method for the joint density of dissimilarities between an observed image and available instances in the training set. This likelihood is estimated using the known asymptotically normally distribution of the Jensen-Shannon divergence between image features, if the latter can be treated as the probability density estimates. This asymptotic behavior is in agreement with the well-known experimental estimates of distributions of dissimilarity distances between high-dimensional vectors. The experimental study in unconstrained face recognition for the LFW (Labeled Faces in the Wild) and YTF (YouTube Faces) datasets demonstrated, that the proposed approach makes it possible to increase the recognition accuracy at 1-5% when compared with conventional classifiers.

The article is devoted to pattern recognition task with the database containing small number of samples per class. By mapping of local continuous feature vectors to a discrete range, this problem is reduced to statistical classification of a set of discrete finite patterns. It is demonstrated that Bayesian decision under the assumption that probability distributions can be estimated using the Parzen kernel and the Gaussian window with a fixed variance for all the classes, implemented in the PNN, is not optimal in the classification of a set of patterns. We presented here the novel modification of the PNN with homogeneity testing which gives an optimal solution of the latter task under the same assumption about probability densities. By exploiting the discrete nature of patterns our modification prevents the well-known drawbacks of the memory-based approach implemented in both the PNN and the PNN with homogeneity testing, namely, low classification speed and high requirements to the memory usage. Our modification only requires the storage and processing of the histograms of input and training samples. We present the results of an experimental study in two practically important tasks: 1) the problem of Russian text authorship attribution with character n-grams features; and 2) face recognition with well-known datasets (AT&T, FERET and JAFFE) and comparison of color- and gradient-orientation histograms. Our results support the statement that the proposed network provides better accuracy (1-7%) and is much more resistant to change of the smoothing parameter of Gaussian kernel function in comparison with the original PNN.

The usage of the probabilistic neural network with homogeneity testing is proposed in image recognition problem. This decision is shown to be optimal in Bayesian terms if the task is formulated as a statistical testing for homogeneity of query and model images' feature sets. The problem of the lack of computing efficiency with many classes and large dimensions of feature set is discovered. The possibility of its overcoming in the case of discrete features is explored by synthesizing the novel recognition criterion with the comparison of the histograms of query and model images. It is shown that a particular case of this criterion is the nearest neighbor rule with popular measures of similarity, namely, chi-square distance and Jensen-Shannon divergence. The results of experimental research in a problem of face recognition with widely used databases (AT&T, JAFFE) are presented. The proposed approach is demonstrated to achieve better recognition accuracy in comparison with conventional solution with reduction the recognition task to the statistical classification.

In the paper we present a new notion of stochastic monotone measure and its application to image processing. By definition, a stochastic monotone measure is a random value with values in the set of monotone measures and it can describe a choice of random features in image processing. In this case, a monotone measure describes uncertainty in the problem of choosing the set of features with the highest value of informativeness and its stochastic behavior is explained by a noise that can corrupt images.

This book constitutes the refereed proceedings of the 12th Industrial Conference on Data Mining, ICDM 2012, held in Berlin, Germany in July 2012. The 22 revised full papers presented were carefully reviewed and selected from 97 submissions. The papers are organized in topical sections on data mining in medicine and biology; data mining for energy industry; data mining in traffic and logistic; data mining in telecommunication; data mining in engineering; theory in data mining; theory in data mining: clustering; theory in data mining: association rule mining and decision rule mining.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXPNP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study this question in a more restricted setting: what is the computational complexity of sparse sets that are *selfreducible*? It follows from earlier work of Lozano and Torán (in: Mathematical systems theory, 1991) that EXPNP does not have sparse selfreducible hard sets. We define a natural version of selfreduction, tree-selfreducibility, and show that NEXP does not have sparse tree-selfreducible hard sets. We also construct an oracle relative to which all of EXP is reducible to a sparse tree-selfreducible set. These lower bounds are corollaries of more general results about the computational complexity of sparse sets that are selfreducible, and can be interpreted as super-polynomial circuit lower bounds for NEXP.