Hatem A. Fayed

A Novel Template Reduction Approach for the

The K-nearest neighbor (KNN) rule is one of the most widely used pattern classification algorithms. For large data sets, the computational demands for classifying patterns using KNN can be prohibitive. A way to alleviate this problem is through the condensing approach. This means we remove patterns that are more of a computational burden but do not contribute to better classification accuracy. In this brief, we propose a new condensing algorithm. The proposed idea is based on defining the so-called chain. This is a sequence of nearest neighbors from alternating classes. We make the point that patterns further down the chain are close to the classification boundary and based on that we set a cutoff for the patterns we keep in the training set. Experiments show that the proposed approach effectively reduces the number of prototypes while maintaining the same level of classification accuracy as the traditional KNN. Moreover, it is a simple and a fast condensing algorithm.

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Prototype classifiers are a type of pattern classifiers, whereby a number of prototypes are designed for each class so as they act as representatives of the patterns of the class. Prototype classifiers are considered among the simplest and best performers in classification problems. However, they need careful positioning of prototypes to capture the distribution of each class region and/or to define the class boundaries. Standard methods, such as learning vector quantization (LVQ), are sensitive to the initial choice of the number and the locations of the prototypes and the learning rate. In this article, a new prototype classification method is proposed, namely self-generating prototypes (SGP). The main advantage of this method is that both the number of prototypes and their locations are learned from the training set without much human intervention. The proposed method is compared with other prototype classifiers such as LVQ, self-generating neural tree (SGNT) and K-nearest neighbor (K-NN) as well as Gaussian mixture model (GMM) classifiers. In our experiments, SGP achieved the best performance in many measures of performance, such as training speed, and test or classification speed. Concerning number of prototypes, and test classification accuracy, it was considerably better than the other methods, but about equal on average to the GMM classifiers. We also implemented the SGP method on the well-known STATLOG benchmark, and it beat all other 21 methods (prototype methods and non-prototype methods) in classification accuracy.

-Nearest Neighbor Method

Abstract. This paper derives the value of the integral of the product of the error function and the normal probability density as a series of the Hermite polynomial and the normalized incomplete Gamma function. This expression is beneficial, and can be used for evaluating the bivariate normal integral as a series expansion. This expansion is a good alternative to the well-known tetrachoric series, when the correlation coefficient, ρ, is large in absolute value.

Self-generating prototypes for pattern classification

The k-center problem arises in many applications such as facility location and data clustering. Typically, it is solved using a branch and bound tree traversed using the depth first strategy. The reason is its linear space requirement compared to the exponential space requirement of the breadth first strategy. Although the depth first strategy gains useful information fast by reaching some leaves early and therefore assists in pruning the tree, it may lead to exploring too many subtrees before reaching the optimal solution, resulting in a large search cost. To speed up the arrival to the optimal solution, a mixed breadth-depth traversing strategy is proposed. The main idea is to cycle through the nodes of the same level and recursively explore along their first promising paths until reaching their leaf nodes (solutions). Thus many solutions with diverse structures are obtained and a good upper bound of the optimal solution can be achieved by selecting the minimum among them. In addition, we employ inexpensive lower and upper bounds of the enclosing balls, and this often relieves us from calling the computationally expensive exact minimum enclosing ball algorithm. Experimental work shows that the proposed strategy is significantly faster than the naked branch and bound approach, especially as the number of centers and/or the required accuracy increases.

An evaluation of the integral of the product of the error function and the normal probability density with application to the bivariate normal integral

Abstract. In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from hi to ∞ to be from −∞ to ∞ by multiplying the integrand by a periodic square wave that approximates the domain of the integral. This square wave is expressed by its Fourier series expansion. Then a Cholesky decomposition of the covariance matrix is applied to transform the integrand to a simple one that can be easily evaluated. The resultant formula has a simple pattern that is expressed as multiple series expansion of trigonometric and exponential functions.

A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems

The nearest neighbor method is one of the most widely used pattern classification methods. However its major drawback in practice is the curse of dimensionality. In this paper, we propose a new method to alleviate this problem significantly. In this method, we attempt to cover the training patterns of each class with a number of hyperspheres. The method attempts to design hyperspheres as compact as possible, and we pose this as a quadratic optimization problem. We performed several simulation experiments, and found that the proposed approach results in considerable speed-up over the k-nearest-neighbor method while maintaining the same level of accuray. It also significantly beats other prototype classification methods (Like LVQ, RCE and CCCD) in most performance aspects.

A novel series expansion for the multivariate normal probability integrals based on Fourier series

Abstract Dynamic pricing is the science of pricing a product in a time-varying way for optimising revenue. There is a slow but steady tendency over the last three decades for major businesses to move from fixed pricing to dynamic pricing. In this paper, we consider the problem of dynamic pricing for wireless broadband data. We propose a novel dynamic pricing approach, based on optimally adjusting premiums and discounts over the prevailing rate, where these adjustments are a function of traffic and demand conditions. Moreover, we propose an agent-based framework for designing and testing this or any other rate plan. In this framework, we have several offered broadband data rate plans, and we model subscribers as agents which react to the dynamic changes of the prices. The proposed framework can be used by wireless operators as a testbed to explore the success of novel dynamic rate plans, and optimise their revenue.

HYPERSPHERICAL PROTOTYPES FOR PATTERN CLASSIFICATION

The task of stance detection is to determine whether someone is in favor or against a certain topic. A person may express the same stance towards a topic using positive or negative words. In this paper, several features and classifiers are explored to find out the combination that yields the best performance for stance detection. Due to the large number of features, ReliefF feature selection method was used to reduce the large dimensional feature space and improve the generalization capabilities. Experimental analyses were performed on five datasets, and the obtained results revealed that a majority vote classifier of the three classifiers: Random Forest, linear SVM and Gaussian Naive Bayes classifiers can be adopted for stance detection task.

A framework for an agent-based dynamic pricing for broadband wireless price rate plans

Prototype classifiers are one of the simplest and most intuitive approaches in pattern classification. However, they need careful positioning of prototypes to capture the distribution of each class region. Classical methods, such as learning vector quantization (LVQ), are sensitive to the initial choice of the number and the locations of the prototypes. To alleviate this problem, a new method is proposed that represents each class region by a set of compact hyperspheres. The number of hyperspheres and their locations are determined by setting up the problem as a set of quadratic optimization problems. Experimental results show that the proposed approach significantly beats LVQ and Restricted Coulomb Energy (RCE) in most performance aspects.