Search results for "Order statistic"

On the First- and Second-Order Statistics of Selective Combining over Double Nakagami-m Fading Channels

2014

Ultimate Order Statistics-Based Prototype Reduction Schemes

2013

Published version of a chapter in the book: AI 2013: Advances in Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-319-03680-9_42 The objective of Prototype Reduction Schemes (PRSs) and Border Identification (BI) algorithms is to reduce the number of training vectors, while simultaneously attempting to guarantee that the classifier built on the reduced design set performs as well, or nearly as well, as the classifier built on the original design set. In this paper, we shall push the limit on the field of PRSs to see if we can obtain a classification accuracy comparable to the optimal, by condensing the information in the data set into a single tr…

On achieving near-optimal “Anti-Bayesian” Order Statistics-Based classification fora asymmetric exponential distributions

2013

Published version of a Chapter in the book: Computer Analysis of Images and Patterns. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-40261-6_44 This paper considers the use of Order Statistics (OS) in the theory of Pattern Recognition (PR). The pioneering work on using OS for classification was presented in [1] for the Uniform distribution, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean - which is distinct from the optimal Bayesian paradigm. In [2], we showed that the results could be extended for a few sym…

“Anti-Bayesian” parametric pattern classification using order statistics criteria for some members of the exponential family

2013

This paper submits a comprehensive report of the use of order statistics (OS) for parametric pattern recognition (PR) for various distributions within the exponential family. Although the field of parametric PR has been thoroughly studied for over five decades, the use of the OS of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented earlier for the uniform distribution and for some members of the exponential family, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. A…

An Exact Solution for the Level-Crossing Rate of Shadow Fading Processes Modelled by Using the Sum-of-Sinusoids Principle

2008

Published version of an article in the journal: Wireless Personal Communications. The original publication is available at Springerlink. http://dx.doi.org/10.1007/s11277-008-9512-3 The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed …

Optimal “anti-Bayesian” parametric pattern classification for the exponential family using Order Statistics criteria

2012

Published version of a chapter in the book: Image Analysis and Recognition. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-31295-3_2 This paper reports some pioneering results in which optimal parametric classification is achieved in a counter-intuitive manner, quite opposed to the Bayesian paradigm. The paper, which builds on the results of [1], demonstrates (with both theoretical and experimental results) how this can be done for some distributions within the exponential family. To be more specific, within a Bayesian paradigm, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal Bayesian strat…

Optimal “anti-Bayesian” parametric pattern classification using Order Statistics criteria

2012

Published version of a chapter in the book: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-33275-3_1 The gold standard for a classifier is the condition of optimality attained by the Bayesian classifier. Within a Bayesian paradigm, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal Bayesian strategy would be to achieve this based on the (Mahalanobis) distance from the corresponding means. The reader should observe that, in this context, the mean, in one sense, is the most central point in the respective distrib…

The variance of the ℓnp-norm of the Gaussian vector, and Dvoretzky's theorem

2018

Let n be a large integer, and let G be the standard Gaussian vector in Rn. Paouris, Valettas and Zinn (2015) showed that for all p∈[1,clogn], the variance of the ℓnp-norm of G is equivalent, up to a constant multiple, to 2ppn2/p−1, and for p∈[Clogn,∞], to (logn)−1. Here, C,c>0 are universal constants. That result left open the question of estimating the variance for p logarithmic in n. In this paper, the question is resolved by providing a complete characterization of Var∥G∥p for all p. It is shown that there exist two transition points (windows) in which the behavior of Var∥G∥p changes significantly. Some implications of the results are discussed in the context of random Dvoretzky's theore…

Weighted local second-order statistics for complex spatio-temporal point processes

2019

Spatial, temporal, and spatio-temporal point processes, and in particular Poisson processes, are stochastic processes that are largely used to describe and model the distribution of a wealth of real phenomena. When a model is fitted to a set of random points, observed in a given multidimensional space, diagnostic measures are necessary to assess the goodness-of-fit and to evaluate the ability of that model to describe the random point pattern behaviour. The main problem when dealing with residual analysis for point processes is to find a correct definition of residuals. Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data in…