An Optimal Greedy Approximate Nearest Neighbor Method in Statistical Pattern Recognition
The insufficient performance of statistical recognition of composite objects (images, speech signals) is explored in case of medium-sized database (thousands of classes). In contrast to heuristic approximate nearest-neighbor methods we propose a statistically optimal greedy algorithm. The decision is made based on the Kullback-Leibler minimum information discrimination principle. The model object to be checked at the next step is selected from the class with the maximal likelihood (joint density) of distances to previously checked models. Experimental study results in face recognition task with FERET dataset are presented. It is shown that the proposed method is much more effective than the brute force and fast approximate nearest neighbor algorithms, such as randomized kd-tree, perm-sort, directed enumeration method.
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.
The article is devoted to the problem of image recognition in real-time applications with a large database containing hundreds of classes. The directed enumeration method as an alternative to exhaustive search is examined. This method has two advantages. First, it could be applied with measures of similarity which do not satisfy metric properties (chi-square distance, Kullback-Leibler information discrimination, etc). Second, the directed enumeration method increases recognition speed even in the most difficult cases which seem to be very important in practical terms. In these cases many neighbors are located at very similar distances. In this paper we present the results of an experimental study of the directed enumeration method with comparison of color- and gradient-orientation histograms in solving the problem of face recognition with well-known datasets (Essex, FERET). It is shown that the proposed method is characterized by increased computing efficiency of automatic image recognition (3-12 times in comparison with a conventional nearest neighbor classifier).
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?
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.