### Article

## Fuzzy Analysis and Deep Convolution Neural Networks in Still-to-video Recognition

We discuss the video classification problem with the matching of feature vectors extracted using deep convolutional neural networks from each frame. We propose the novel recognition method based on representation of each frame as a sequence of fuzzy sets of reference classes whose degrees of membership are defined based on asymptotic distribution of the Kullback–Leibler information divergence and its relation with the maximum likelihood method. In order to increase the classification accuracy, we perform the fuzzy intersection (product triangular norms) of these sets. Experimental study with YTF (YouTube Faces) and IJB-A (IARPA Janus Benchmark A) video datasets and VGGFace, ResFace and LightCNN descriptors shows that the proposed approach allows us to increase the accuracy of recognition by 2–6% compering with the known classification methods.

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.

It has been shown that the activations invoked by an image within the top layers of a large convolutional neural network provide a high-level descriptor of the visual content of the image. In this paper, we investigate the use of such descriptors (neural codes) within the image retrieval application. In the experiments with several standard retrieval benchmarks, we establish that neural codes perform competitively even when the convolutional neural network has been trained for an unrelated classification task (e.g. Image-Net). We also evaluate the improvement in the retrieval performance of neural codes, when the network is retrained on a dataset of images that are similar to images encountered at test time. We further evaluate the performance of the compressed neural codes and show that a simple PCA compression provides very good short codes that give state-of-the-art accuracy on a number of datasets. In general, neural codes turn out to be much more resilient to such compression in comparison other state-of-the-art descriptors. Finally, we show that discriminative dimensionality reduction trained on a dataset of pairs of matched photographs improves the performance of PCA-compressed neural codes even further. Overall, our quantitative experiments demonstrate the promise of neural codes as visual descriptors for image retrieval.

On the informatics and the software sides the questions of practical security are linked to the unstructured information processing algorithms applicable for the video array frames obtained by cross platform registration systems. Compression solutions become crucially important when the temporal evolution of the video stream exceeds the traffic capacity of the communication network. The basic image processing approach we exploited is to maintain of the highest resolution degree for the main part of the object we survey (for example, a man’s face or figure) whilst minimizing the information traffic from the image background by its artificial substitution with a homogeneous color filling. This method allowed us to obtain a significant compression rate (up to 7000).

An ensemble of classifiers has been built to solve the problem of video image recognition. The paper offers a way to estimate the a posteriori probability of an image belonging to a particular class in the case of an arbitrary distance and nearest neighbor method. The estimation is shown to be equivalent to the optimal naive Bayesian estimate given Kullback-Leibler divergence being used as proximity measure. The block diagram of a video image recognition system is presented. The system features automatic adaptation of the list of images of identical objects which is fed to the committee machine input. The system is tested in face recognition task using popular data bases (FERET, AT&T, Yale) and the results are discussed.

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?

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.

The problem of automatic detection of the moving forklift truck in video data is explored. This task is formulated in terms of computer vision approach as a moving object detection in noisy environment. It is shown that the state-of-the-art local descriptors (SURF, SIFT, FAST, ORB) are not characterized with satisfactory detection quality if the camera resolution is low, the lighting is changed dramatically and shadows are observed. In this paper we propose to use a simple mathematical morphological algorithm to detect the presence of a cargo on the forklift truck. Its first step is the estimation of the movement direction and the front part of the truck by using the updating motion history image. The second step is the application of Canny contour detection and binary morphological operations in front of the moving object to estimate simple geometric features of empty forklift. The algorithm is implemented with the OpenCV library. Our experimental study shows that the best results are achieved if the difference of the width of bounding rectangles is used as a feature. Namely, the detection accuracy is 78.7% (compare with 40% achieved by the best local descriptor), while the average frame processing time is only 5 ms (compare with 35 ms for the fastest descriptor).

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.