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# Department of Mathematical Methods of Forecasting

Head of the department: Zhuravlev Yury, Academician of RAS, Professor, Dr.Sc.

The Department trains specialists in machine learning, data-mining, image processing algorithms and their applications in natural sciences, economics, finance, etc. The Department’s specialization includes mathematical methods for diagnosing complex systems (including technical and economic ones), analyzing these systems, constructing optimal or near optimal solutions that are based on an indirect, incomplete, or contradictory information.

During training, students receive a fundamental education in different areas of mathematics such as modern algebra and mathematical logic, theory of algorithms, discrete and combinatorial mathematics, mathematical models of artificial intelligence, including the mathematical methods of pattern recognition, machine learning, image processing, probability theory, applied statistics, graphical models.

Attending practical sessions, students acquire a skill of working with modern databases and software, learn modern programming languages and techniques, gain experience in solving applied problems. Students also have practice in research institutions of the Russian Academy of Sciences, innovative companies, financial organizations, etc. To the time of their masters many of them already have papers in scientific journals and top conferences’ proceedings.

The Department prepares professionals in the development and application of mathematical methods to solve various data processing problems such as scoring systems, fraud detection, retails prediction, bioinformatics, natural language processing, computer vision, expert systems, etc.

### Staff members:

- Rudakov Konstantin, Corresponding Member of RAS, Professor, Dr.Sc.
- Mestetsky Leonid, Corresponding Member of RAS, Professor, Dr.Sc.
- Dyakonov Alexander, Professor, Dr.Sc.
- Leontyev Vladimir, Professor, Dr.Sc.
- Vorontsov Konstantin, Associate Professor, Dr.Sc.
- Gurevich Igor, Associate Professor, PhD
- Gurov Sergey, Associate Professor, PhD
- Dyukova Elena, Associate Professor, Dr.Sc.
- Maisuradze Archil, Associate Professor, PhD
- Ryazanov Vladimir, Associate Professor, Dr.Sc.
- Senko Oleg, Associate Professor, Dr.Sc.
- Vetrov Dmitry, Associate Professor, PhD
- Kropotov Dmitry, Researcher, Scientific Secretary of the Department

### Regular courses:

- Algebraic methods in machine learning by Prof. Zhuravlev, 16 lecture hours and 16 seminar hours.
- Applied algebra by Prof. Dyakonov, Prof. Leontyev, Assoc. Prof. Gurov, 48 lecture hours and 48 seminar hours.
- Machine learning by Assoc. Prof. Voronstov, 32 lecture hours.
- Bayesian methods in machine learning by Assoc. Prof. Vetrov, 16 lecture hours and 16 seminar hours.
- Graphical models by Assoc. Prof. Vetrov, 16 lecture hours and 16 seminar hours.
- Mathematical methods of classification by Prof. Rudakov, 32 lecture hours.
- Computer workshop by Assoc. Prof. Maisuradze, 48 lecture hours.
- Image processing and analysis by Prof. Mestetsky, 16 lecture hours.
- Algorithms, models, algebras by Prof. Dyakonov, 16 lecture hours.
- Applied statistics by Assoc. Prof. Voronstov, 16 lecture hours and 16 seminar hours.
- Signal Processing by Ass. Prof. Krasotkina, 16 lecture hours.

### Special courses:

- Bayesian methods of machine learning by Dr. Vetrov, 16 lecture hours.
- Computational problems of bioinformatics by Assoc. Prof. Makhortyh and Assoc. Prof. Pankratov, 16 lecture hours.
- Image Mining by Assoc. Prof. Gurevich, 16 lecture hours.
- Propositional calculus of classical logic by Assoc. Prof. Gurov, 32 lecture hours.
- Combinatorial foundations of information theory by Assoc. Prof. Voronstov, 16 lecture hours.
- Logical methods in pattern recognition by Assoc. Prof. Dyukova, 16 lecture hours.
- Mathematical methods of biometrics by Prof. Rudakov, 16 lecture hours.
- Metric Methods of Data Mining by Assoc. Prof. Maisuradze, 16 lecture hours.
- Continuous morphological models and algorithms by Prof. Mestetsky, 16 lecture hours.
- Non-statistical methods of data mining and classification by Assoc. Prof. Ryazanov, 32 lecture hours.
- Generalized spectral-analytical method, 16 lecture hours.

## Special scientific seminars and directions of research:

### Algebraic approach to data mining, machine learning and pattern recognition

(Academician of RAS Yu. I. Zhuravlyov, Corresponding Member of RAS K.V. Rudakov, Dr.Sc. V.V. Ryazanov, Dr.Sc. A.G. Dyakonov).

In the framework of an algebraic approach new algorithms are constructed as formulas over initial algorithms (weak learners) or as Boolean functions (logic correctors). The main result is that every algorithm can be presented as a superposition of a recognition operator and a decision rule. It allows one to describe the algorithm results as special matrices – the estimate matrices (outputs of recognition operators) and the result matrices (outputs of decision rules). Operations over algorithms are induced by operations over the corresponding estimate matrices. The algebraic approach allows one to construct formulas over algorithms, the formulas that are correct on the test set (or have better performance than initial algorithms).

### Computational learning theory and machine learning applications

(Dr. K. Vorontsov)

One of the most challenging problems in machine learning research is analyzing the general performance of a learning machine. A combinatorial theory of overfitting which gives tight and in some cases exact generalization bounds is developed. These bounds are applied to designing learning algorithms in such machine learning subareas as the ensemble learning, rule induction, the distance learning, features selection, prototype selection. Another research direction is information retrieval, collaborative filtering, and probabilistic topic modeling with applications to the analysis of big collections of scientific documents.

### Continuous models in image shape analysis and classification

(Prof. L. Mestetsky)

Approaches and methods of objects shape representation in digital images by continuous models are investigated. Human eye does not see the discrete nature of digital images. Images look like continuous pictures, and it is more customary and simpler to operate “solid” continuous geometric models of the shape. Therefore the use of continuous models significantly simplifies the creation of algorithms for analyzing, classifying, and transforming image shapes. The concept of a figure as a universal continuous model of shape is used. A figure is defined as a closed domain whose boundary consists of the finite number of nonintersecting Jordan curves. Three interconnected methods of figure representation are investigated; these are boundary, medial and circular descriptions. The task of constructing the continuous model for the digital image is reduced to the approximation of this image by continuous figures. Then efficient computational geometry algorithms are applied for the shape analysis and related classification of discrete objects in digital images.

### Bayesian Methods in Machine Learning

(Dr. D. Vetrov and D. Kropotov)

The research work is focused on investigating the Bayesian approach in the probability theory and its application for solving different machine learning and computer vision problems. Bayesian methods have become a wide-spread technique in the last 15 years. Their main advantages include an automatic tuning of structural parameters in machine learning models, a correct way for reasoning in case of uncertainty, a possibility of considering structural and probabilistic interactions in data arrays (based on actively developing graphical models concept), and an approach for data and model parameter representation that allows an easy fusion of indirect observations and prior ideas.

The developed techniques are intensively used for solving different applied problems including gene expression analysis in animal brains during cognitive processes.

### Data Mining: New Challenges and Methods

(Dr. S. Gurov)

The related seminar is designed for 2nd-5th year students, graduate students and anyone interested. It takes place in the spring semester in the form of reports of the participants and invited experts. Topics are diverse. They include (but not limited to) the hypothesis of compactness in pattern recognition; the solution of Boolean equations and synthesis of control circuits; mathematical methods for the analysis of brain activity; characteristics of partially ordered sets; detection of the latent image-based processing of radiographs and photographs of paintings; analysis of formal concepts in applied problems.

### Clustering problems

(Academician of RAS Yu. Zhuravlev and Dr. V. Ryazanov)

There are many clustering algorithms based on different principles and leading to different partitions of a given sample. In the absence of statistical models of data, evaluation and comparison problems of clustering arise. Does the resulting clustering correspond to the objective reality, or just get a partition? Criteria for evaluating the quality of clustering and methods of their calculation are designed. These criteria allow us to construct ensembles of clustering algorithms.

### Intellectual data-mining: new problems and methods

(Dr. S. Gurov and Dr. A. Maisuradze)

### Data-mining in metric spaces

(Dr. A. Maisuradze)

### Analysis and estimation of information contained in images

(Dr. I. Gurevich)

### Logical methods of pattern recognition

(Dr. E. Dyukova)

### Combinatorial methods of information theory

(Dr. V. Leontyev)

### Problem-oriented methods of pattern recognition

(Corresponding Member of RAS Prof. K. Rudakov and Dr. Yu. Chekhovich)

### Recent papers

- V.V. Ryazanov and Y.I. Tkachev, Estimation of Dependences Based on Bayesian Correction of a Committee of Classification Algorithms // Computat. Mathem. and Math. Physics, vol. 50. no. 9, pp. 1605-1614, 2010.
- V.V. Ryazanov, Some Imputation Algorithms for Restoration of Missing Data // Lecture Notes in Computer Science (LNCS), vol. 7042, pp. 372-379, 2011.
- K. Vorontsov, Exact Combinatorial Bounds on the Probability of Overfitting for Empirical Risk Minimization // Pattern Recognition and Image Analysis, vol. 20, no. 3, pp. 269–285, PDF, 427Kb, 2010.
- K. Vorontsov and A. Ivakhnenko, Tight Combinatorial Generalization Bounds for Threshold Conjunction Rules // Lecture Notes on Computer Science. 4th International Conference on Pattern Recognition and Machine Intelligence (PReMI’11), Russia, Moscow, June 27–July 1, pp. 66–73, PDF, 153Kb, 2011.
- N. Spirin and K. Vorontsov, Learning to Rank with Nonlinear Monotonic Ensemble // Lecture Notes on Computer Science. 10th International Workshop on Multiple Classidier Systems (MCS-10). Naples, Italy, June 15–17, pp. 16–25, PDF, 490Kb, 2011.
- D. Vetrov and A. Osokin, Graph Preserving Label Decomposition in Discrete MRFs with Selfish Potentials // Proceedings of International Workshop on Discrete Optiization in Machine learning (DISSML NIPS 2011), 2011.
- Osokin, D. Vetrov and V. Kolmogorov, Submodular Decomposition Framework for Inference in Associative Markov Networks with Global Constraints // Proceedings of International Conference on Computer Vision and Pattern Recognition (CVPR2011), N.Y., USA, Springer, pp. 135-142, 2011.
- Yangel and D. Vetrov, Image Segmentation with a Shape Prior Based on Simplified Skeleton // Proceedings of International Workhop on Energy Minimization Methods (EMMCVPR2011), 2011.
- Dyakonov, Two Recommendation Algorithms Based on Deformed Linear Combinations // Proc. of ECML-PKDD, 2011, Discovery Challenge Workshop, pp. 21-28, 2011.
- Dyakonov, Theory of Equivalence Systems for Describing Algebraic Closures of a Generalized Estimation Model. II // Computational Mathematics and Mathematical Physics, vol. 51, no. 3, pp. 490-504, 2011.
- N. Dyshkant, L. Mestetskiy, B.H. Shekar and Sharmila Kumari, Face recognition using kernel component analysis // Neurocomputing, vol. 74, no. 6, pp. 1053-1057, 2011.
- B.H. Shekar, Sharmila Kumari, N. Dyshkant and L. Mestetskiy, FLD-SIFT: Class Based Scale Invariant Feature Transform for Accurate Classification of Faces // Comm. in Computer and Information Science, 1, Computer Networks and Information Technologies, vol. 142, part 1, pp. 15-21, 2011.
- Kurakin and L. Mestetskiy, Hand gesture recognition through on-line skeletonization – application of continuous skeleton to real-time shape analysis // Proceedings of the International conference on computer vision theory and applications (VISAPP 2011), Vilamoura, Portugal, 2011, March 5-7, pp. 555-560, 2011.
- Bakina, A. Kurakin and L. Mestetskiy, Hand geometry analysis by continuous skeletons // Lecture Notes in computer science, Image analysis and recognition, Springer, vol. 6753/2011, part 2, pp. 130-139, 2011.
- I.G. Bakina and L.M. Mestetskiy, Hand Shape Recognition from Natural Hand Position // Proceedings of the IEEE International Conference on Hand-Based Biometrics, Hong Kong Polytechnic University, Hong Kong, pp. 170-175, 2011.
- Bilateral Russian-Indian Scientific Workshop on Emerging Applications of Computer Vision: Workshop Proc. / Ed. by A. Maysuradze – Moscow, MAKS Press, 2011. – 224 p. ISBN 978-5-317-03937-0
- D.P.Vetrov, D.A.Kropotov, A.A.Osokin and D.A.Laptev, Variational segmentation algorithms with label frequency constraints // Pattern Recogn. and Image Anal., vol. 20, no. 3, pp. 324-334, 2010.
- D.P.Vetrov, D.A.Kropotov, A.A.Osokin, A.Lebedev, V.Galatenko and K.Anokhin, An interactive method of anatomical segmentation and gene expression estimation for an experimental mouse brain slice // Proc. of 7th Intern. Conf. on Computational Intelligence Methods for Biostatistics and Bioinformatics, Palermo, Italy: Springer, no. 1, pp. 23-34, 2010.
- D.P.Vetrov and V.Vishnevsky, The algorithm for detection of fuzzy behavioral patterns // Proc. of Measuring Behavior 2010, 7th Intern. Conf. on Methods and Techniques in Behavioral Research, Eindoven, Holland: Springer, no. 1, pp. 41-45, 2010.
- S.I.Gurov, New principle for specifying a priori distribution and consistency interval estimate // Scientific Computing. Proc. of the Intern. Eugene Lawler Ph.D. School. Waterford, Ireland: WIT press, pp. 8-20, 2010.
- S.I.Gurov, Probability estimation of 0-event // Scientific Computing. Proc. of the Intern. Eugene Lawler Ph.D. School. Waterford, Ireland: WIT press, pp. 198-209, 2010.
- A.I.Maysuradze, Domain-oriented bases in spaces of finite metrics of a given rank // Scientific Computing. Proc. of the Intern. Eugene Lawler Ph.D. School. Waterford, Ireland: WIT press, pp. 210-221, 2010.
- D.P.Vetrov, D.A.Kropotov and A.A.Osokin, 3-D mouse brain model reconstruction from a sequence of 2-d slices in application to allen brain atlas // Computational Intelligence Methods for Bioinformaticcs and Biostatistics. Lecture Notes in Computer Science, Berlin, Germany: Springer, no. 6160, pp. 291-303, 2010.
- E.V.Djukova, Yu.I.Zhuravlev and R.M.Sotnezov, Construction of an ensemble of logical correctors on the basis of elementary classifiers // Pattern Recogn. and Image Anal., vol. 21, no. 4, pp. 599-605, 2011.
- D.P.Vetrov and B.K.Yangel, Image segmentation with a shape prior based on simplifies skeleton // Proc. of Intern. Workshop on Energy Minimization Methods. Berlin, Germany: Springer, pp. 148-161, 2011.

• 2014

- Novikov Alexander, Rodomanov Anton, Osokin Anton, and Vetrov Dmitry. Putting mrfs on a tensor train. Journal of Machine Learning Research, 32(1):811–819, 2014.
- A. Osokin and D. Vetrov. Submodular relaxation for inference in markov random fields. IEEE Transactions on Pattern Analysis and Machine Intelligence, 99, 2014.
- Bartunov Sergey and Vetrov Dmitry. Variational inference for sequential distance dependent chinese restaurant process. Journal of Machine Learning Research, 32(1):1404–1412, 2014.
- L. Mestetskiy. Representation of linear segment voronoi diagram by bezier curves. In Труды 24 международной конф. ГРАФИКОН-2014, pages 83–87. Академия архитектуры и искусств ЮФУ Ростов-на-Дону, 2014.
- S.V. Ablameyko, A.S. Biryukov, A.A. Dokukin, A.G. D’yakonov, Yu I. Zhuravlev, V.V. Krasnoproshin, V.A. Obraztsov, M.Yu Romanov, and V.V. Ryazanov. Practical algorithms for algebraic and logical correction in precedent-based recognition problems. Computational Mathematics and Mathematical Physics, 54(12):1915–1928, 2014.
- Tsoumakas Grigorios, Papadopoulos Apostolos, Qian Weining, Vologiannidis Stavros, D'yakonov Alexander, Puurula Antti, Read Jesse, Svec Jan, and Semenov Stanislav. Wise 2014 challenge: Multi-label classification of print media articles to topics. Lecture Notes in Computer Science, 8787:541–548, 2014.
- Vorontsov K. V. Additive Regularization for Topic Models of Text Collections // Doklady Mathematics. 2014, Pleiades Publishing, Ltd. — Vol. 89, No. 3, pp. 301–304.
- Vorontsov K. V., Potapenko A. A. Tutorial on Probabilistic Topic Modeling: Additive Regularization for Stochastic Matrix Factorization // AIST’2014, Analysis of Images, Social networks and Texts. Springer International Publishing Switzerland, 2014. Communications in Computer and Information Science (CCIS). Vol. 436. pp. 29–46.
- Uspenskiy V. M., Vorontsov K. V., Tselykh V. R., Bunakov V. A. Information Function of the Heart: Discrete and Fuzzy Encoding of the ECG-Signal for Multidisease Diagnostic System // in Advances in Mathematical and Computational Tools in Metrology and Testing X (vol.10), Series on Advances in Mathematics for Applied Sciences, vol. 86, World Scientific, Singapore (2015) pp 375-382.
- Vorontsov K. V., Potapenko A. A. Additive Regularization of Topic Models // Machine Learning Journal. Special Issue “Data Analysis and Intelligent Optimization with Applications” (to appear).

• 2013

- Gurov S.I. Estimation of the reliability of a classification algorithm as based on a new information model // Comput. Mathematics and Math. Phys. 2013. 53. N 5. P. 640-656.
- Nekrasov K.V., Laptev D.A., Vetrov D.P. Automatic determination of cell division rate using microscope images // Pattern Recogn. and Image Anal. 2013. 23. N 1. P. 105-110.
- Osokin A.A., Amelchenko E.M., Zworikina S.V., Chekhov S.A., Lebedev A.E., Voronin P.A., Galatenko V.V., Vetrov D.P., Anokhin K.V. Statistic parametric mapping of changes in gene activity in animal brain during acoustic stimulation // Bulletin of Experimental Biology and Medicine. 2013. 154. N 5. P. 697-699.
- Voronin P.А., Vetrov D.P., Ismailov K. An approach to segmentation of mouse brain images via intermodal registration // Pattern Recogn. and Image Anal. 2013. 23. N 2. P. 335-339.
- Zhuravlev Y.I., Laptin Y., Vinogradov A., Likhovid A. A comparison of some approaches to the recognition problems in care of two classes // Information Models & Analyses. 2013. 2. N 2. P. 103-111.
- Chernyshov V.A., Mestetskiy L.M. Mobile machine vision system for palm-based recognition // Proc. of 11th Intern. Conf. Pattern Recogn. and Image Anal.: New Information Technologies. N 1. Самара: ИСОИ РАН, 2013. P. 398-401.
- Djukova E.V., Lyubimtseva М.М., Prokofjev P.A. Logical correctors in recognition problems // Proc. of 11th Intern. Conf. Pattern Recogn. and Image Anal.: New Information Technologies. N 1. Самара: ИСОИ РАН, 2013. P. 82-83.
- Dyshkant N.F. Comparison of point clouds acquired by 3d scanner // Discrete Geometry for Computer Imagery. 17th Intern. Conf. Lecture Notes in Computer Science. N 7749. Berlin, Germany: Springer, 2013. P. 47-58.
- Gurov S.I., Prokasheva O.V., Onishchenko A.A. Classification methods based on formal concept analysis // The 35th European FCAIR 2013-Formal Concept Analysis Meets Information Retrieval. N 1. М.: Издательский дом НИУ ВШЭ, 2013. P. 95-104.
- Mestetskiy L.M., Zimovnov A.V. Curve-skeleton extraction using silhouettes' medial axes // ГрафиКон'2013. 23-я Международная конференция по компьютерной графике и зрению. Труды конференции. Владивосток: Дальнаука, 2013. P. 91-94.
- Osokin А., Kohli P., Jegelka S. A principled deep random field model for image segmentation // 2013 IEEE Conf. on Computer Vision and Pattern Recogn. N.Y., USA: IEEE Computer Society Press, 2013. P. 1971-1978.
- Zhuravlev Y.I., Gurevich I., Trusova Yu., Vashina V. The challenge the problems and the tasks of the descriptive approaches to imaage analysis // Proc. of 11th Intern. Conf. Pattern Recogn. and Image Anal.: New Information Technologies. N 1. Самара: ИСОИ РАН, 2013. P. 30-35.
- Дьяконов А.Г. Деформация ответов алгоритмов анализа данных // Spectral and Evolution Problems. № 23. Симферополь, Украина: Taurida National V. Vernadsky University, 2013. C. 74-78.

• 2012

- Bondarenko N.N., Zhuravlev Yu.I. Algorithm for choosing conjunctions for logical recognition methods // Comput. Math. and Math. Phys. 2012. 52. N 4. P. 746-749.
- D'yakonov A.G. Criteria for the singularity of a pairwise L1-distance matrix and their generalizations // Izvestiya. Mathematics. 2012. 76. N 3. P. 517-534.
- Onishchenko A.A., Gurov S.I. Classification based on formal concept analysis and biclustering: possibilities of the approach // Computational Mathematics and Modeling. 2012. 23. N 3. P. 329-336.
- Voronin P.A., Adinetz A.V., Vetrov D.P. A new measure for distance-field based shape matching // ГрафиКон'2012. 22-я Международная конференция по компьютерной графике и зрению. Труды конференции. М.: МАКС Пресс, 2012. P. 101-106.
- D'yakonov A.G. A blending of simple algorithms for topical classification // Rough Sets and Current Trends in Computing. Lecture Notes in Computer Science. N 7413. Berlin, Germany: Springer, 2012. P. 432-438.
- Osokin A.A., Vetrov D.P. Submodular relaxation for MRFs with high-order potentials // Computer Vision - ECCV 2012. Workshops and Demonstrations. Lecture Notes in Computer Science. N 7585. Berlin, Germany: Springer, 2012. P. 305-314.
- Voronin P.A., Vetrov D.P. Robust distance fields for shape-based registration // Интеллектуализация обработки информации: 9-я международная конференция. М.: Торус Пресс, 2012. P. 382-385.
- Yangel B.K., Vetrov D.P. Globally optimal segmentation with a graph-based shape prior // Интеллектуализация обработки информации: 9-я международная конференция. М.: Торус Пресс, 2012. P. 456-459.