# Publications

We developed a new method for measuring the pitch frequency of speech signals with elevated noise immunity. The problem of protection against intense background noise is solved in this method by the frequency selection of vocalized segments of speech signals according to a scheme with comb filter of interperiodic accumulation. The efficiency of the method is analyzed both theoretically and experimentally with the help of a multichannel frequency meter intended for the acoustic speech analysis. It is shown that, for a signal-to-noise ratio of 10 dB and higher, the error of the method does not exceed 2%.

For a graph *G* and a positive integer *k*, a subset *C* of vertices of *G* is called a *k*-path vertex cover if *C* intersects all paths of *k* vertices in *G*. The cardinality of a minimum *k*-path vertex cover is denoted by *β_{**P_**k*}(*G*). For a graph *G* and a positive integer *k*, a subset *M* of pairwise vertex-disjoint paths of *k* vertices in *G* is called a *k*-path packing. The cardinality of a maximum *k*-path packing is denoted by *μ**_{P_**k*}(*G*). In this paper, we describe some graphs, having equal values of *β**_{P_**k}* and *μ**{P**_k}*, for *k*≥5, and present polynomial-time algorithms of finding a minimum *k*-path vertex cover and a maximum *k*-path packing in such graphs.

Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications. In this paper we consider several compression techniques for recurrent neural networks including Long–Short Term Memory models. We make particular attention to the high-dimensional output problem caused by the very large vocabulary size. We focus on effective compression methods in the context of their exploitation on devices: pruning, quantization, and matrix decomposition approaches (low-rank factorization and tensor train decomposition, in particular). For each model we investigate the trade-off between its size, suitability for fast inference and perplexity. We propose a general pipeline for applying the most suitable methods to compress recurrent neural networks for language modeling. It has been shown in the experimental study with the Penn Treebank (PTB) dataset that the most efficient results in terms of speed and compression–perplexity balance are obtained by matrix decomposition techniques.

It is researched a wide class of parametric estimations of power spectral density based on principle of entropy maximum and autoregression observation model. At that there is distinguished the key parameter which is used model order. It is considered a problem of a priori uncertainty when true value of order is a priori unknown. It is proposed a new criterion for definition of order using finite sampling volume with purpose of overcome of the drawbacks of existing algorithms in conditions of small sampling. The principle of guaranteed significance level in a problem of complex statistic hypothesis verification is a basic principle of this criterion. In contrast to criteria of AIC, BIC, etc. this criterion is not related to determination of measurements inaccuracy, since it uses a conception of “significance level” of formed solution only. The efficiency of proposed criterion is researched theoretically and experimentally. An example of its application in a problem of spectral analysis of voice signals is considered. Recommendations about its practical application in the systems of digital signal processing are given.

This paper is focused on the automatic extraction of persons and their attributes (gender, year of born) from album of photos and videos. A two-stage approach is proposed in which, firstly, the convolutional neural network simultaneously predicts age/gender from all photos and additionally extracts facial representations suitable for face identification. Here the MobileNet is modified and is preliminarily trained to perform face recognition in order to additionally recognize age and gender. The age is estimated as the expected value of top predictions in the neural network. In the second stage of the proposed approach, extracted faces are grouped using hierarchical agglomerative clustering techniques. The birth year and gender of a person in each cluster are estimated using aggregation of predictions for individual photos. The proposed approach is implemented in an Android mobile application. It is experimentally demonstrated that the quality of facial clustering for the developed network is competitive with the state-of-the-art results achieved by deep neural networks, though implementation of the proposed approach is much computationally cheaper. Moreover, this approach is characterized by more accurate age/gender recognition when compared to the publicly available models.

The problem of computing the width of simplices generated by the convex hull of their integer vertices is considered. An FPT algorithm, in which the parameter is the maximum absolute value of the rank minors of the matrix consisting from the simplex vertices, is presented.

In this paper, we studied the phonetic approach for voice processing. A method for automatic recognition of speech signals, in which each quasistationary segment is associated with a fuzzy set of phonemes, was developed. We proposed the operation of the probabilistic triangular norm for fuzzy sets corresponding to the input frame and the nearest reference phoneme. The developed method was experimentally shown to allow a 1.5–5% reduction in the probability of erroneous recognition in comparison with known analogues.

Let f:R^n→R be a conic function and x_0∈R^n. In this note, we show that the shallow separation oracle for the set K={x∈R^n:f(x)≤f(x_0)} can be polynomially reduced to the comparison oracle of the function *f*. Combining these results with known results of D. Dadush et al., we give an algorithm with (O(n))^n*logR calls to the comparison oracle for checking the non-emptiness of the set K∩Z^n, where *K* is included to the Euclidean ball of a radius *R*. Additionally, we give a randomized algorithm with the expected oracle complexity (O(n))^n*logR for the problem to find an integral vector that minimizes values of *f* on an Euclidean ball of a radius *R*. It is known that the classes of convex, strictly quasiconvex functions, and quasiconvex polynomials are included into the class of conic functions. Since any system of conic functions can be represented by a single conic function, the last facts give us an opportunity to check the feasibility of any system of convex, strictly quasiconvex functions, and quasiconvex polynomials by an algorithm with (O(n))^n*logR calls to the comparison oracle of the functions. It is also possible to solve a constraint minimization problem with the considered classes of functions by a randomized algorithm with (O(n))^n*logR expected oracle calls.Let f:R^n→R be a conic function and x_0∈R^n. In this note, we show that the shallow separation oracle for the set K={x∈R^n:f(x)≤f(x_0)} can be polynomially reduced to the comparison oracle of the function *f*. Combining these results with known results of D. Dadush et al., we give an algorithm with (O(n))^n*logR calls to the comparison oracle for checking the non-emptiness of the set K∩Z^n, where *K* is included to the Euclidean ball of a radius *R*. Additionally, we give a randomized algorithm with the expected oracle complexity (O(n))^n*logR for the problem to find an integral vector that minimizes values of *f* on an Euclidean ball of a radius *R*. It is known that the classes of convex, strictly quasiconvex functions, and quasiconvex polynomials are included into the class of conic functions. Since any system of conic functions can be represented by a single conic function, the last facts give us an opportunity to check the feasibility of any system of convex, strictly quasiconvex functions, and quasiconvex polynomials by an algorithm with (O(n))^n*logR calls to the comparison oracle of the functions. It is also possible to solve a constraint minimization problem with the considered classes of functions by a randomized algorithm with (O(n))^n*logR expected oracle calls.

We describe the class of graphs whose each subgraph has the next property: The maximal number of disjoint 4-paths is equal to the minimal cardinality of sets of vertices such that every 4-path in the subgraph contains at least one of these vertices. We completely describe the set of minimal forbidden subgraphs for this class. Moreover, we present an alternative description of the class based on the operations of edge subdivision applied to bipartite multigraphs and the addition of so-called pendant subgraphs, isomorphic to triangles and stars.

A Gaussian graphical model is a graphical representation of the dependence structure for

a Gaussian random vector. Gaussian graphical model selection is a statistical problem that

identifies the Gaussian graphical model from observations. There are several statistical

approaches for Gaussian graphical model identification. Their properties, such as unbiasedeness

and optimality, are not established. In this paper we study these properties.

We consider the graphical model selection problem in the framework of multiple decision

theory and suggest assessing these procedures using an additive loss function. Associated

risk function in this case is a linear combination of the expected numbers of the two types

of error (False Positive and False Negative). We combine the tests of a Neyman structure for

individual hypotheses with simultaneous inference and prove that the obtained multiple

decision procedure is optimal in the class of unbiased multiple decision procedures.

This survey paper attempts to cover a broad range of topics related to computational biomedicine. The field has been attracting great attention due to a number of benefits it can provide the society with. New technological and theoretical advances have made it possible to progress considerably. Traditionally, problems emerging in this field are challenging from many perspectives. In this paper,we considered the influence of big data on the field, problems associated with massive datasets in biomedicine and ways to address these problems. We analyzed the most commonly used machine learning and feature mining tools and several new trends and tendencies such as deep learning and biological networks for computational biomedicine.

We consider the class $G$ of gradient-like orientation preserving diffeomorphisms of the 2-sphere with saddles of negative orientation type. We show that the for every diffeomorphism $f\in G$ every saddle point is fixed. We show that there are exactly three equivalence classes (up to topological conjugacy) $G=G_1\cup G_2\cup G_3$ where a diffeomorphism $f_1\in G_1$ has exactly one saddle and three nodes (one fixed source and two periodic sinks); a diffeomorphism $f_2\in G_2$ has exactly two saddles and four nodes (two periodic sources and two periodic sinks) and a diffeomorphism $f_3\in G_3$ is topologically conjugate to a diffeomorphism $f_1^{-1}$. The main result is the proof that every diffeomorphism $f\in G$ can be connected to the ``source-sink'' diffeomorphism by a stable arc and this arc contains at most finitely many points of period-doubling bifurcations.

In this paper we find all possible periodic data for orientation preserving gradient-like diffeomorphisms of orientable surfaces with one saddle orbit. We also construct a system of this class for every admissible collection of periodic data.

In this paper, we consider the class of quasiconvex functions and its proper subclass of conic functions. The integer minimization problem of these functions is considered, assuming that the optimized function is defined by the comparison oracle. We will show that there is no a polynomial algorithm on log R to optimize quasiconvex functions in the ball of radius R using only the comparison oracle. On the other hand, if the optimized function is conic, then we show that there is a polynomial on log R algorithm (the dimension is fixed). We also present an exponential on the dimension lower bound for the oracle complexity of the conic function integer optimization problem. Additionally, we give examples of known problems that can be polynomially reduced to the minimization problem of functions in our classes.

Gaussian graphical model selection is a statistical problem

that identifies the Gaussian graphical model from observations. Existing

Gaussian graphical model selection methods focus on the error rate

for incorrect edge inclusion. However, when comparing statistical procedures,

it is also important to take into account the error rate for

incorrect edge exclusion. To handle this issue we consider the graphical

model selection problem in the framework of multiple decision theory.We

show that the statistical procedure based on simultaneous inference with

UMPU individual tests is optimal in the class of unbiased procedures.

We propose a novel algorithm portfolio model that incorporates time series forecasting techniques to predict online the performance of its constituent algorithms. The predictions are used to allocate computational resources to the algorithms, accordingly. The proposed model is demonstrated on parallel algorithm portfolios consisting of three popular metaheuristics, namely tabu search, variable neighbourhood search, and multistart local search. Moving average and exponential smoothing techniques are employed for forecasting purposes. A challenging combinatorial problem, namely the detection of circulant weighing matrices, is selected as the testbed for the analysis of the proposed approach. Experimental evidence and statistical analysis provide insight on the performance of the proposed algorithms and reveal the benefits of using forecasting techniques for resource allocation in algorithm portfolios.

In this paper we consider general scene recognition problem for analysis of user preferences based on his or her photos on mobile phone. Special attention is paid to out-of-class detections and efficient processing using MobileNet-based architectures. We propose the three stage procedure. At first, pre-trained convolutional neural network (CNN) is used extraction of input image embeddings at one of the last layers, which are used for training a classifier, e.g., support vector machine or random forest. Secondly, we fine-tune the pre-trained network on the given training set and compute the predictions (scores) at the output of the resulted CNN. Finally, we perform object detection in the input image, and the resulted sparse vector of detected objects is classified. The decision is made based on a computation of a weighted sum of the class posterior probabilities estimated by all three classifiers. Experimental results with a subset of ImageNet dataset demonstrate that the proposed approach is up to 5% more accurate when compared to conventional fine-tuned models.

The paper addresses the issue of insufficient speed of image recognition methods if the number of classes is rather large. We propose the novel algorithm based on sequential three-way decisions and a formal description of granular computing. Each image is associated with principal component scores of the high-dimensional features extracted by deep convolution neural network. Low number of principal components stand for the coarse-grained granules, while fine-grained granules include all components. Initially, first principal components of an observed image and all training instances are matched at the coarsest granularity level. Next, negative decisions are defined by using the multiple comparisons theory and asymptotic distribution of the Kullback-Leibler divergence. Namely, the distance factors (ratios of the minimum distance and all other distances) are evaluated. The set of negative decisions is populated by the instances, for which the distance factors exceed a certain threshold. The images from this set are not examined at the next levels with finer granularity. In the experiments unconstrained face recognition and image categorisation are considered using the state-of-the-art deep learning-based feature extractors. We demonstrate that the proposed approach decreases the running time in 1.5–10 times when compared to conventional classifiers and the known multi-class decision-theoretic rough sets.

The article describes an approach for extraction of user preferences based on the analysis of a gallery of photos and videos on mobile device. It is proposed to firstly use fast SSD-based methods in order to detect objects of interests in offline mode directly on mobile device. Next we perform facial analysis of all visual data: extract feature vectors from detected facial regions, cluster them and select public photos and videos which do not contain faces from the large clusters of an owner of mobile device and his or her friends and relatives. At the second stage, these public images are processed on the remote server using very accurate but rather slow object detectors. Experimental study of several contemporary detectors is presented with the specially designed subset of MS COCO, ImageNet and Open Images datasets.