some higher order methods for the simultaneous approximation of multiple polynomial zeros abstract applying newton s and halley s corrections some modified methods of higher order for the simultaneous approximation of multiple zeros of a polynomial are derived further acceleration of convergence of these methods is performed by approximating all zeros in a serial fashion using the new approximations as they become available faster convergence is attained without additional calculations lower bounds of the r order of convergence for the serial single step methods are given

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

weierstrass formula and zero finding methods classical weierstrass formula 29 has been often the subject of investigation of many authors in this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions we are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros conditions for the safe convergence of weierstrass method depending only on initial approximations are given in particular we study polynomials with interval coefficients using an interval version of weierstrass method enclosures in the form of disks for the complex valued set containing all zeros of a polynomial with varying coefficients are obtained we also present weierstrass like algorithm for approximating simultaneously all zeros of a class of analytic functions in a given closed region to demonstrate the proposed algorithms three numerical examples are included

evolutionary pursuit and its application to face recognition introduces evolutionary pursuit ep as an adaptive representation method for image encoding and classification in analogy to projection pursuit ep seeks to learn an optimal basis for the dual purpose of data compression and pattern classification it should increase the generalization ability of the learning machine as a result of seeking the trade off between minimizing the empirical risk encountered during training and narrowing the confidence interval for reducing the guaranteed risk during testing it therefore implements strategies characteristic of ga for searching the space of possible solutions to determine the optimal basis it projects the original data into a lower dimensional whitened principal component analysis pca space directed random rotations of the basis vectors in this space are searched by ga where evolution is driven by a fitness function defined by performance accuracy empirical risk and class separation confidence interval accuracy indicates the extent to which learning has been successful while separation gives an indication of expected fitness the method has been tested on face recognition using a greedy search algorithm to assess both accuracy and generalization capability the data includes for each subject images acquired at different times or under different illumination conditions ep has better recognition performance than pca eigenfaces and better generalization abilities than the fisher linear discriminant fisherfaces

on the convergence order of accelerated root iterations a gauss seidel procedure for accelerating the convergence of the generalized method of the root iterations type of the k 2 th order k n for finding polynomial complex zeros given in 7 is considered in this paper it is shown that ther order of convergence of the accelerated method is at leastk 1 n k where n k 1 is the unique positive root of the equation n k 1 0 andn is the degree of the polynomial the examples of algebraic equations in ordinary and circular arithmetic are given

new simultaneous root finding methods with accelerated convergence for analytic functions a new iterative method of the fourth order for the simultaneous determination of zeros of a class of analytic functions is proposed further improvements of the basic method are attained by using newton s and halley s corrections giving the orders of convergence five and six respectively the improved convergence is achieved with negligible number of additional calculations which significantly increases the computational efficiency of the accelerated methods numerical examples demonstrate a good convergence properties fitting very well theoretical results

an efficient discriminant based solution for small sample size problem classification of high dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size problem to address the problem of high dimensional data classification in the face of a limited number of samples a novel principal component analysis pca based feature extraction classification scheme is proposed the proposed method yields a piecewise linear feature subspace and is particularly well suited to difficult recognition problems where achievable classification rates are intrinsically low such problems are often encountered in cases where classes are highly overlapped or in cases where a prominent curvature in data renders a projection onto a single linear subspace inadequate the proposed feature extraction classification method uses class dependent pca in conjunction with linear discriminant feature extraction and performs well on a variety of real world datasets ranging from digit recognition to classification of high dimensional bioinformatics and brain imaging data

a class of simultaneous methods for the zeros of analytic functions abstract a family of iterative methods for simultaneously approximating simple zeros of analytic functions inside a simple smooth closed contour in the complex plane is presented the order of convergence of the considered methods in m 2 m 1 2 where m is the order of the highest derivative of analytic function appearing in the iterative formula a special attention is paid to the total step and single step methods with newton s and halley s corrections because of their high computational efficiency numerical examples are also included

face recognition a convolutional neural network approach we present a hybrid neural network for human face recognition which compares favourably with other methods the system combines local image sampling a self organizing map som neural network and a convolutional neural network the som provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space thereby providing dimensionality reduction and invariance to minor changes in the image sample and the convolutional neural network provides partial invariance to translation rotation scale and deformation the convolutional network extracts successively larger features in a hierarchical set of layers we present results using the karhunen loeve transform in place of the som and a multilayer perceptron mlp in place of the convolutional network for comparison we use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression pose and facial details we analyze the computational complexity and discuss how new classes could be added to the trained recognizer

real time object recognition using relational dependency based on graphical model this paper proposes a real time object recognition using the relational dependency among the objects that is represented by the graphical model when we recognize the objects it is effective to use the relational dependency in which several different objects co exist each other the relational dependency has been modeled by the transition matrix in the graphical model the transition matrix precisely represents the conditional probability of object s existence at time t given the existence of others at time t 1 we use a very fast cascaded adaboost detector in order to detect all object candidates in the image then the existence probability of the object from a given object candidate is estimated by a logistic regression using the softmax function the estimated existence probability is updated by the trained transition matrix to reflect the relational dependency of the objects the object s existence is determined by the threshold level experiment results validate that the proposed method is a very fast and effective way of recognizing the objects in terms of high recognition rate and low false alarm rate

classification of smooth congruences of low degree we give a complete classification of smooth congruences i e surfaces in the grassmann variety of lines in p 3c identified with a smooth quadric in p5 of degree at most 8 by studying which surfaces of p5can lie in a smooth quadric and proving their existence we present their ideal sheaf as a quotient of natural bundles in the grassmannian what provides a perfect knowledge of its cohomology for example postulation or linear normality as well as many information on the hilbert scheme of these families such as dimension smoothness unirationality and thus irreducibility and in some cases rationality

the distribution of bidegrees of smooth surfaces in gr 1 p3 the study of algebraic surfaces in gr 1 p3 the grassmann variety parametrising lines in projective three space was a popular one for algebraic geometers of the late nineteenth and early twentieth centuries calling them line congruences researchers such as kummer fano roth and many others published many papers on the topic classifying congruences and studying their invariants since that time the field has lain dormant until very recently the classical geometers identified two numbers associated with a given congruence the order and the class thinking of a congruence as a two dimensional family of lines the order is the number of lines in the family passing through a general point in p3 and the class the number of lines in the family contained in a general plane together these two numbers make up the bidegree of the congruence in modern terms the bidegree gives the class of the congruence in the chow ring of gr 1 p3 in this paper we consider the question for what values of a and b does there exist or not exist a smooth congruence of bidegree a b in particular we try to find restrictions on the bidegree using an approach suggested by dolgachev and reider in 8 this approach is to study the restriction of the universal bundle g of gr 1 p3 which appears in the exact sequence

tchebychef like method for the simultaneous finding zeros of analytic functions abstract using a suitable approximation in classical tchebychef s iterative method of the third order a new method for approximating simultaneously all zeros of a class of analytic functions in a given simple smooth closed contour is constructed it is proved that its order of convergence is three the analysis of numerical stability and some computational aspects including a numerical example are given also the asynchronous implementation of the proposed method on a distributed memory multicomputer is considered from a theoretical point of view assuming that the maximum delay r is bounded a convergence analysis shows that the order of convergence of this version is the unique positive root of the equation x r 1 2 x r 1 0 belonging to the interval 2 3

rapid and brief communication why direct lda is not equivalent to lda in this paper we present counter arguments against the direct lda algorithm d lda which was previously claimed to be equivalent to linear discriminant analysis lda we show from bayesian decision theory that d lda is actually a special case of lda by directly taking the linear space of class means as the lda solution the pooled covariance estimate is completely ignored furthermore we demonstrate that d lda is not equivalent to traditional subspace based lda in dealing with the small sample size problem as a result d lda may impose a significant performance limitation in general applications

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

an efficient higher order family of root finders a one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial based on a cubically convergent hansen patrick s family is studied we show that the convergence of the basic family of the fourth order can be increased to five and six using newton s and halley s corrections respectively since these corrections use the already calculated values the computational efficiency of the accelerated methods is significantly increased further acceleration is achieved by applying the gauss seidel approach single step mode one of the most important problems in solving nonlinear equations the construction of initial conditions which provide both the guaranteed and fast convergence is considered for the proposed accelerated family these conditions are computationally verifiable they depend only on the polynomial coefficients its degree and initial approximations which is of practical importance some modifications of the considered family providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions are also studied numerical examples demonstrate the convergence properties of the presented family of root finding methods

face recognition using lda based algorithms low dimensional feature representation with enhanced discriminatory power is of paramount importance to face recognition fr systems most of traditional linear discriminant analysis lda based methods suffer from the disadvantage that their optimality criteria are not directly related to the classification ability of the obtained feature representation moreover their classification accuracy is affected by the small sample size sss problem which is often encountered in fr tasks in this paper we propose a new algorithm that deals with both of the shortcomings in an efficient and cost effective manner the proposed method is compared in terms of classification accuracy to other commonly used fr methods on two face databases results indicate that the performance of the proposed method is overall superior to those of traditional fr approaches such as the eigenfaces fisherfaces and d lda methods

on some improvements of square root iteration for polynomial complex zeros abstract using newton s and halley s corrections some modifications of the simultaneous method for finding polynomial complex zeros based on square root iteration are obtained the convergence order of the proposed methods is five and six respectively further improvements of these methods are performed by applying the gauss seidel approach the lower bounds of the r order of convergence and the convergence conditions for the accelerated single step methods are given faster convergence is attained without additional calculations the considered iterative procedures are illustrated numerically in the example of an algebraic equation

fractional step dimensionality reduction linear projections for dimensionality reduction computed using linear discriminant analysis lda are commonly based on optimization of certain separability criteria in the output space the resulting optimization problem is linear but these separability criteria are not directly related to the classification accuracy in the output space consequently a trial and error procedure has to be invoked experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set often even the best weighting function among the trial choices results in poor classification of data in the subspace in this short paper we introduce the concept of fractional dimensionality and develop an incremental procedure called the fractional step lda f lda to reduce the dimensionality in fractional steps the f lda algorithm is more robust to the selection of weighting function and for any given weighting function it finds a subspace in which the classification accuracy is higher than that obtained using lda

higher order iterative methods for approximating zeros of analytic functions abstract iterative methods with extremely rapid convergence in floating point arithmetic and circular arithmetic for simultaneously approximating simple zeros of analytic functions inside a simple smooth closed contour in the complex plane are presented the r order of convergence of the basic total step and single step methods as well as their improvements which use newton s and halley s corrections is given some hybrid algorithms that combine the efficiency of ordinary floating point iterative methods with the accuracy control provided by interval arithmetic are also considered

kernel quadratic discriminant analysis for small sample size problem it is generally believed that quadratic discriminant analysis qda can better fit the data in practical pattern recognition applications compared to linear discriminant analysis lda method this is due to the fact that qda relaxes the assumption made by lda based methods that the covariance matrix for each class is identical however it still assumes that the class conditional distribution is gaussian which is usually not the case in many real world applications in this paper a novel kernel based qda method is proposed to further relax the gaussian assumption by using the kernel machine technique the proposed method solves the complex pattern recognition problem by combining the qda solution and the kernel machine technique and at the same time tackles the so called small sample size problem through a regularized estimation of the covariance matrix extensive experimental results indicate that the proposed method is a more sophisticated solution outperforming many traditional kernel based learning algorithms

on halley like algorithms for simultaneous approximation of polynomial complex zeros let p z be a polynomial of degree n with n distinct zeros iterative methods for the simultaneous inclusion of k leqq n simple or multiple zeros are given the iterative formulas presented can be regarded as an interval version of halley s iterative formula for multiple zeros realized in circular arithmetic the convergence analysis is done in the presence of multiplicity the convergence order is three for k n and four if k n applying the gauss seidel approach to the basic iterative formula the single step method with accelerated convergence is stated and the lower bound of the r order of convergence of this method is obtained the dependence of convergence rate of the basic methods on the rounding errors is also studied some numerical examples illustrate the theoretical results