Статистическое распознавание образов на основе вероятностной нейронной сети с проверкой однородности
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
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.
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?
In this paper we explore an application of the pyramid HOG (Histograms of Oriented Gradients) features in image recognition problem with small samples. A sequential analysis is used to improve the performance of hierarchical methods. We propose to process the next, more detailed level of pyramid only if the decision at the current level is unreliable. The Chow’s reject option of comparison of the posterior probability with a fixed threshold is used to verify recognition reliability. The posterior probability is estimated for the homogeneity-testing probabilistic neural network classifier on the basis of its relation with the Bayesian decision. Experimental results in face recognition are presented. It is shown that the proposed approach allows to increase the recognition performance in 2–4 times in comparison with conventional classification of pyramid HOGs.
Probabilistic neural network (PNN) is the well-known instance-based learning algorithm, which is widely used in various pattern classification and regression tasks, if rather small number of instances for each class is available. The known disadvantage of this network is its insufficient classification computational complexity. The common way to overcome this drawback is the reduction techniques with selection of the most typical instances. Such approach causes the shifting of the estimates of the class probability distribution, and, in turn, the decrease of the classification accuracy. In this paper we examine another possible solution by replacing the Gaussian window and the Parzen kernel to the orthogonal series Fejér kernel and using the naïve assumption about independence of features. It is shown, that our approach makes it possible to achieve much better runtime complexity in comparison with either original PNN or its modification with the preliminary clustering of the training set.
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.