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## Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing

The paper is focused on an application of sequential three-way decisions and granular computing to the problem of multi-class statistical recognition of the objects, which can be represented as a sequence of independent homogeneous (regular) segments. As the segmentation algorithms usually make it possible to choose the degree of homogeneity of the features in a segment, we propose to associate each object with a set of such piecewise regular representations (granules). The coarse-grained granules stand for a low number of weakly homogeneous segments. On the contrary, a sequence with a large count of high-homogeneous small segments is considered as a fine-grained granule. During recognition, the sequential analysis of each granularity level is performed. The next level with the finer granularity is processed, only if the decision at the current level is unreliable. The conventional Chow’s rule is used for a non-commitment option. The decision on each granularity level is proposed to be also sequential. The probabilistic rough set of the distance of objects from different classes at each level is created. If the distance between the query object and the next checked reference object is included in the negative region (i.e., it is less than a fixed threshold), the search procedure is terminated. Experimental results in face recognition with the Essex dataset and the state-of-the-art HOG features are presented. It is demonstrated, that the proposed approach can increase the recognition performance in 2.5–6.5 times, in comparison with the conventional PHOG (pyramid HOG) method.

In this paper it is proposed to improve performance of the automatic speech recognition by using sequential three-way decisions. At first, the largest piecewise quasi-stationary segments are detected in the speech signal. Every segment is classified using the maximum a-posteriori (MAP) method implemented with the Kullback-Leibler minimum information discrimination principle. The three-way decisions are taken for each segment using the multiple comparisons and asymptotical properties of the Kullback-Leibler divergence. If the non-commitment option is chosen for any segment, it is divided into small subparts, and the decision-making is sequentially repeated by fusing the classification results for each subpart until accept or reject options are chosen or the size of each subpart becomes relatively low. Thus, each segment is associated with a hierarchy of variable-scale subparts (granules in rough set theory). In the experimental study the proposed procedure is used in speech recognition with Russian language. It was shown that our approach makes it possible to achieve high efficiency even in the presence of high level of noise in the observed utterance.

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.

Statistical pattern recognition was reduced to the hypothesis test for homogeneity. The probabilistic neural network (PNN) modification was proposed to achieve its optimal decision in terms of minimum Bayes-risk. The comparative analysis' results of the proposed modification with an original PNN were presented in a problem of automatic author identification

This volume contains papers presented at the 13th International Conference on Rough Sets, Fuzzy Sets and Granular Computing (RSFDGrC) held during June 25–27, 2011, at the National Research University Higher School of Economics (NRU HSE) in Moscow, Russia. RSFDGrC is a series of scientific events spanning the last 15 years. It investigates the meeting points among the four major disciplines outlined in its title, with respect to both foundations and applications. In 2011, RSFDGrC was co-organized with the 4th International Conference on Pattern Recognition and Machine Intelligence (PReMI), providing a great opportunity for multi-faceted interaction between scientists and practitioners. There were 83 paper submissions from over 20 countries. Each submission was reviewed by at least three Chairs or PC members.We accepted 34 regular papers (41%). In order to stimulate the exchange of research ideas, we also accepted 15 short papers. All 49 papers are distributed among 10 thematic sections of this volume. The conference program featured five invited talks given by Jiawei Han, Vladik Kreinovich, Guoyin Wang, Radim Belohlavek, and C.A. Murthy, as well as two tutorials given by Marcin Szczuka and Richard Jensen. Their corresponding papers and abstracts are gathered in the first two sections of this volume.

A unified methodology for categorizing various complex objects is presented in this book. Through probability theory, novel asymptotically minimax criteria suitable for practical applications in imaging and data analysis are examined including the special cases such as the Jensen-Shannon divergence and the probabilistic neural network. An optimal approximate nearest neighbor search algorithm, which allows faster classification of databases is featured. Rough set theory, sequential analysis and granular computing are used to improve performance of the hierarchical classifiers. Practical examples in face identification (including deep neural networks), isolated commands recognition in voice control system and classification of visemes captured by the Kinect depth camera are included. This approach creates fast and accurate search procedures by using exact probability densities of applied dissimilarity measures.

This book can be used as a guide for independent study and as supplementary material for a technically oriented graduate course in intelligent systems and data mining. Students and researchers interested in the theoretical and practical aspects of intelligent classification systems will find answers to:

- Why conventional implementation of the naive Bayesian approach does not work well in image classification?

- How to deal with insufficient performance of hierarchical classification systems?

- Is it possible to prevent an exhaustive search of the nearest neighbor in a database?

This paper comprises papers accepted for presentation at the 14th Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGRC) International Conference which was held as a major part of Joint Rough Set Symposium (JRS 2013) held at Halifax Canada during October 11-14, 2013.

Since the works by Specht, the probabilistic neural networks (PNNs) have attracted researchers due to their ability to increase training speed and their equivalence to the optimal Bayesian decision of classification task. However, it is known that the PNN's conventional implementation is not optimal in statistical recognition of a set of patterns. In this article we present the novel modification of the PNN and prove that it is optimal in this task with general assumptions of the Bayes classifier. The modification is based on a reduction of recognition task to homogeneity testing problem. In the experiment we examine a problem of authorship attribution of Russian texts. Our results support the statement that the proposed network provides better accuracy and is much more resistant to change the smoothing parameter of Gaussian kernel function in comparison with the original PNN.

This paper is focused on still-to-video face recog- nition with large number of subjects based on computation of distances between high-dimensional embeddings extracted using deep convolution neural networks. We propose to utilize granular structures and sequentially process granular representations of all frames of the input video. The coarse-grained granules include only low number of the first principal components of deep embeddings. The representation of each frame at finer granularity levels is matched with the representations of photos of only those individuals, for whom the decision at previous levels was reliable. The reliability is checked by thresholding the ratio of distance between reference instance and input frame to the minimal distance. As a result, the photos of all unreliable individuals are not examined anymore for a particular frame at the next levels with finer granularity. Decisions for all frames are united into a candidate set of identities, and the maximal a-posterior final decision is chosen. The experimental study with the LFW, YTF and IJB-A datasets and the state-of-the-art deep embeddings demonstrated that the proposed approach is 2-10 times faster than conventional methods

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.