an upper bound on the aperiodic autocorrelation function for a maximal length sequence corresp the magnitude of the out of phase aperiodic autocorrelation function for a maximal length linear feedback shift register sequence of period n is at most 1 2 pi n 1 1 2 ln 4n pi previously the best upper bound was n 1 1 2 ln en

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

a dna based graph encoding scheme with its applications to graph isomorphism problems abstract feynman first proposed dna based computation in 1961 but his idea was not implemented by experiment for a few decades by properly manipulating dna strands as the input instance of the hamiltonian path problem adleman succeeded in solving the problem in a test tube since the experimental demonstration of its feasibility dna based computing has been applied to a number of decision or combinatorial optimization problems in this paper we propose a dna based graph encoding scheme which can be used to solve some intractable graph problems such as the subgraph isomorphism problem and its generalized problem the maximum common subgraph problem which are known to be np complete problems in the adleman lipton model using polynomial number of basic biological operations

a generalization of the cosine sine functional equation on groups abstract the functional equation f xy f x g y g x f y h x h y is solved where f g h are complex functions defined on a group

dynamical irreducibility of polynomials modulo primes for a class of polynomials f in mathbb z x which in particular includes all quadratic polynomials and also trinomials of some special form we show that under some natural conditions necessary for quadratic polynomials the set of primes p such that all iterations of f are irreducible modulo p is of relative density zero furthermore we give an explicit bound on the rate of the decay of the density of such primes in an interval 1 q as q rightarrow infty for this class of polynomials this gives a more precise version of a recent result of ferraguti proc am math soc 146 2773 2784 2018 which applies to arbitrary polynomials but requires a certain assumption about their galois group furthermore under the generalised riemann hypothesis we obtain a stronger bound on this density

towards a generalized singular value decomposition we suggest a form for and give a constructive derivation of the generalized singular value decomposition of any two matrices having the same number of columns we outline its desirable characteristics and compare it to an earlier suggestion by van loan siam j numer anal 13 1976 pp 76 83 the present form largely follows from the work of van loan but is slightly more general and computationally more amenable than that in the paper cited we also prove a useful extension of a theorem of stewart siam rev 19 1977 pp 634 662 on unitary decompositions of submatrices of a unitary matrix

algebraic feature extraction for image recognition based on an optimal discriminant criterion abstract a novel algebraic feature extraction method for image recognition is presented the main difference between the present method and any other existing algebraic feature extraction method is that the present method uses an optimal discriminant criterion to extract algebraic features for the given training image samples a set of optimal discriminant projection vectors is calculated according to a generalized fisher criterion function on the basis of the optimal discriminant projection vector the projective feature vectors of an image i e algebraic features are extracted by projecting the image onto all optimal discriminant projection vectors the method of calculating the set of optimal discriminant projection vectors is discussed a minimum distance classifier is also proposed for classifying projective feature vectors experimental results showed that the present method has good recognition performance an important conclusion about the present method is that the foley sammon optimal set of discriminant vectors is a special case of the set of optimal discriminant projection vectors

fast computation of von neumann entropy for large scale graphs via quadratic approximations abstract the von neumann graph entropy vnge can be used as a measure of graph complexity which can be the measure of information divergence and distance between graphs however computing vnge is extensively demanding for a large scale graph we propose novel quadratic approximations for fast computing vnge various inequalities for error between the quadratic approximations and the exact vnge are found our methods reduce the cubic complexity of vnge to linear complexity computational simulations on random graph models and various real network datasets demonstrate superior performance

optimal sets of frequency hopping sequences with large linear spans frequency hopping fh is one of the basic spread coding technologies in spread spectrum communications fh sequences are needed in fh code division multiple access cdma systems for the anti jamming purpose fh sequences are required to have a large linear span a few optimal sets of fh sequences are available in the literature however their sequences have very small linear spans it is known that an optimal set of fh sequences could be transformed to another optimal set of fh sequences with large linear spans by a power permutation if the power is chosen properly see c ding and j yin ieee trans inf theory vol it 54 pp 3741 3745 2008 the objective of this paper is to investigate this idea of c ding and j yin further and determine the linear span of the fh sequences in the optimal sets obtained by applying a power permutation to some existing optimal sets of fh sequences

a new construction of frequency hopping sequences with optimal partial hamming correlation frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems in this paper lower bounds on the partial hamming correlation of fhss and fhs sets are proposed they slightly improve the known bounds by eun et al and zhou et al a construction of fhss and fhs sets having optimal partial hamming correlation with respect to the improved bounds is also presented based on the theory of generalized cyclotomy our construction yields optimal fhss and fhs sets with new and flexible parameters not covered in this paper

strictly optimal frequency hopping sequence sets with optimal family sizes frequency hopping sequences fhss with favorable partial hamming correlation properties are desirable in many synchronization and multiple access systems an fhs set is said to be strictly optimal if it has optimal partial hamming correlation for any correlation window in this paper we derive upper bounds on the family sizes of fhs sets with respect to partial hamming correlation from some classical bounds on error correcting codes we then present strictly optimal fhs sets having optimal family sizes with respect to one of the new bounds in particular our construction gives new parameters not covered in the literature

linear dimension reduction and bayes classification with unknown population parameters abstract odell and decell odell and coberly gave necessary and sufficient conditions for the smallest dimension compression matrix b such that the bayes classification regions are preserved that is they developed an explicit expression of a compression matrix b such that the bayes classification assignment are the same for both the original space x and the compressed space bx odell indicated that whenever the population parameters are unknown then the dimension of bx is the same as x with probability one furthermore odell posed the problem of finding a lower dimension q p which in some sense best fits the range space generated by the matrix m the purpose of this paper is to discuss this problem and provide a partial solution

comparing large graphs efficiently by margins of feature vectors measuring the structural similarity of graphs is a challenging and outstanding problem most of the classical approaches of the so called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs in contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs we introduce novel graph similarity and dissimilarity measures provide some properties and analyze their algorithmic complexity we find that the computational complexity of our measures is polynomial in the graph size and hence significantly better than classical methods from e g exact graph matching which are np complete numerically we provide some examples of our measure and compare the results with the well known graph edit distance

fast low rank modifications of the thin singular value decomposition this paper develops an identity for additive modivations of a singular value decomposition svd to reflect updates downdates shifts and edits of the data matrix this sets the stage for fast and ememory efficient sequential algorithms for tracking singular values and subspaces in conjunction with a fast solution for the pseudo inverse of a submatrix of an orthogonal matrix we develop a scheme for computing a thin svd of streaming data in a single pass with linear time complexity a rank r think svd of a p x q matrix can be computed in o pqr time for r less than or equal sqroot min p q linear algebra and its applications

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

an iterative construction of irreducible polynomials reducible modulo every prime abstract we give a method of constructing polynomials of arbitrarily large degree irreducible over a global field f but reducible modulo every prime of f the method consists of finding quadratic f f x whose iterates have the desired property and it depends on new criteria ensuring all iterates of f are irreducible in particular when f is a number field in which the ideal 2 is not a square we construct infinitely many families of quadratic f such that every iterate f n is irreducible over f but f n is reducible modulo all primes of f for n 2 we also give an example for each n 2 of a quadratic f z x whose iterates are all irreducible over q whose n 1 st iterate is irreducible modulo some primes and whose n th iterate is reducible modulo all primes from the perspective of galois theory this suggests that a well known rigidity phenomenon for linear galois representations does not exist for galois representations obtained by polynomial iteration finally we study the number of primes p for which a given quadratic f defined over a global field has f n irreducible modulo p for all n 1

on the odd and the aperiodic correlation properties of the kasami sequences derives a new upper bound for the odd and the aperiodic correlations of binary sequences in the small kasami family the approach is based on a technique described in s litsyn and a tietavainen 1994 that is originally due to i m vinogradov 1954 an essential ingredient in this method is a good upper bound on the discrete fourier coefficients of a shifted product of a pair of sequences the author obtains an upper bound of the order o spl radic llnl for the maximal aperiodic and odd correlation magnitudes for sequences of length l

spectral distances of graphs abstract let 1 g 2 g n g be the adjacency spectrum of a graph g on n vertices the spectral distance g 1 g 2 between n vertex graphs g 1 and g 2 is defined by g 1 g 2 i 1 n i g 1 i g 2 here we provide some initial results regarding this quantity first we give some general results concerning the spectral distances between arbitrary graphs and compute these distances in some particular cases certain relation with the theory of graph energy is identified the spectral distances bounded by a given constant are also considered next we introduce the cospectrality measure and the spectral diameter and obtain specific results indicating their relevance for the theory of cospectral graphs finally we give and discuss some computational results and conclude the paper by a list of conjectures

toward bayes optimal linear dimension reduction dimension reduction is the process of transforming multidimensional vectors into a low dimensional space in pattern recognition it is often desired that this task be performed without significant loss of classification information the bayes error is an ideal criterion for this purpose however it is known to be notoriously difficult for mathematical treatment consequently suboptimal criteria have been used in practice we propose an alternative criterion based on the estimate of the bayes error that is hopefully closer to the optimal criterion than the criteria currently in use an algorithm for linear dimension reduction based on this criterion is conceived and implemented experiments demonstrate its superior performance in comparison with conventional algorithms

algebraic constructions of optimal frequency hopping sequences frequency hopping fh spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are needed in fh code division multiple access cdma systems in this correspondence three classes of optimal frequency hopping sequences are constructed with algebraic methods the three classes are based on perfect nonlinear functions power functions and norm functions respectively both individual optimal frequency hopping sequences and optimal families of frequency hopping sequences are presented

distance between the normalized laplacian spectra of two graphs abstract let g v e be a simple graph of order n the normalized laplacian eigenvalues of graph g are denoted by 1 g 2 g n 1 g n g 0 also let g and g be two nonisomorphic graphs on n vertices define the distance between the normalized laplacian spectra of g and g as n g g i 1 n i g i g p p 1 define the cospectrality of g by c s n g min n g g g not isomorphic to g let c s n n max c s n g g a graph on n vertices in this paper we give an upper bound on c s n g in terms of the graph parameters moreover we obtain an exact value of c s n n an upper bound on the distance between the normalized laplacian spectra of two graphs has been presented in terms of randic energy as an application we determine the class of graphs which are lying closer to the complete bipartite graph than to the complete graph regarding the distance of normalized laplacian spectra

optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings we construct new sequences over finite rings having optimal hamming correlation properties these sequences are useful in frequency hopping multiple access fhma spread spectrum communication systems our constructions can be classified into linear and nonlinear categories both giving optimal hamming correlations according to lempel greenberger 1974 bound the nonlinear sequences have large linear complexity and can be seen as a generalized version of gmw sequences over fields

optimal discriminant plane for a small number of samples and design method of classifier on the plane abstract in a previous work zi quan hong and jing yu yang minimum distance classifier on the optimal discriminant plane we suggested and derived a method for constructing classifier on the optimal discriminant plane using minimum distance criteria in this paper the problem of solving optimal discriminant plane for a small number of samples is discussed which is based on the above paper by the same authors in the case of a small number of samples generalized eigenequation ax bx established for a large number of samples usually has no solution because within class scatter matrix is singular to obtain the solution of the generalized eigenequation a new method is suggested in which the singular value perturbation is added to the within class scatter matrix such that the matrix becomes a nonsingular matrix therefore the generalized eigenequation can be solved using existing algorithms we proved that the generalized eigenequations on the optimal discriminant plane are stable in respect of eigenvalues and the generalized eigenvectors are indeed the optimal discriminant directions if the perturbation is subject to some certain conditions the experimental results have shown that our method works well and the minimum distance classifier on the optimal discriminant plane can be constructed with high performance even in the case of a small number of samples

a new dissimilarity measure for comparing labeled graphs abstract we use spectral graph theory to compare graphs that share the same node set taking into account global graph structures we propose a general framework using eigendecomposition of graph laplacians we show its special cases and propose a new dissimilarity measure that avoid problems of spectral analysis the new dissimilarity emphasizes the importance of small eigenvalues which are known to carry the main information on graphs general properties of the dissimilarity are discussed the dissimilarity provides an efficient and intuitive tool for graph analysis

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

bahadur efficiency of tests of separate hypotheses and adaptive test statistics the notion of separability of hypotheses was first introduced by cox 1961 two families of hypotheses are separate if no distribution in one family can be obtained as a limit of distributions from the other family for testing separate hypotheses cox 1961 1962 suggested the test based on the comparison of the logarithm of the likelihood ratio with its expected value or estimate thereof under each hypothesis the tests of such hypotheses are required to have high power against the specified alternatives when nuisance parameters are present this concept leads to the notion of an adaptive test which by definition must be asymptotically efficient for any value of the unknown nuisance parameter a testing problem of separate hypotheses for an exponential family is studied from the standpoint of bahadur asymptotic optimality a formula for the bahadur exact slope of any smooth test statistic is obtained and in the example of testing lognormality versus exponentiality it is shown that cox s test can

a hybrid incomplete exponential sum with application to aperiodic hamming correlation of some frequency hopping sequences in this paper an upper bound for a hybrid incomplete exponential sum over finite fields is derived this bound is then used to obtain lower and upper bounds for aperiodic hamming correlation of frequency hopping sequences based on power functions

distance between spectra of graphs richard brualdi proposed in stevanivic 2007 10 the following problem problem awgs 4 let gngn and gn be two nonisomorphic graphs on n vertices with spectra 1 2 nand 1 2 n respectively define the distance between the spectra of gngn and gn as gn gn i 1n i i 2 or use i 1n i i define the cospectrality of gngn by cs gn min gn gn gn not isomorphic to gn let csn max cs gn gn a graph on n vertices problem a investigate cs gn cs gn for special classes of graphs problem b find a good upper bound on csncsn in this paper we completely answer problem b by proving that csn 2csn 2 for all n 2n 2 whenever csncsn is computed with respect to any lplp norm with 1 p 1 p and csn 1csn 1 with respect to the l l norm the cospectrality cs km n cs km n of the complete bipartite graph km nkm n for all positive integers m and n with m n m 1 2m 1 is computed as a consequence of the latter result it is proved that in general there is no constant upper bound on e e e e where e and e e denote the number of edges of the graphs g and g g respectively such that cs g g g cs g g g in contrast we show that for such graphs g and g g we have e e 1 in particular e e 3e e e 3e

global similarity tests of physical designs of circuits a complex network approach abstract similarity testing for circuits is an important task in the identification of possible infringement of intellectual property rights in this paper we propose a novel procedure for global similarity measurement between circuit topologies networks and apply this procedure to the comparison of physical designs of circuits we first construct networks to describe the way in which circuit elements interact then we evaluate the properties of each node from the resulting networks by calculating the cumulative distribution of characteristic parameters such as degree clustering coefficient etc based on the maximum vertical distance of each pair of distributions global similarity testing methods are proposed with consideration of the inhomogeneity of parameter distributions and the scale of the networks simulation results show the effectiveness of the strategy in terms of robustness and topological information mining the methodology described here can be applied to the identification of physical designs of circuits that may contain suspected patent infringement and it is suitable for a wide range of circuits and systems

best conditional tests for separate families of hypotheses we consider from the viewpoint of hypotheses testing the problem of assigning the probability density function of a random variable x to one of two separate families of distributions our aim is to study the possibility of constructing best similar tests for this we characterize sufficient statistics for the union of the two families completeness is also studied we state conditions under which the test statistics are easily obtainable when both families are of the generalized exponential type the relative merits of the exact best test and of asymptotic tests are empirically investigated in small samples when testing for the log normal versus the gamma distribution

structural multiple empirical kernel learning multiple kernel learning mkl can boost classification performance through using multiple kernels rather than a single fixed one unlike the traditional mkl with the implicit kernels multiple empirical kernel learning mekl explicitly maps input data into multiple feature spaces this paper focuses on mekl and proposes an effective threefold structural mekl tsmekl the first fold structure is the space structural information between different mapped feature spaces the second one is the class discriminant information within each mapped feature space the third one is the cluster structural information of samples in each mapped feature space the classical mekl mainly pays attention to the first two structures but neglects the last one the proposed tsmekl introduces the cluster structural information into mekl doing so can simultaneously utilize the space the class and the cluster information in the way from globality to locality therefore tsmekl utilizes threefold structural information to result in the improvement of classification performance to the best of our knowledge it is the first time to introduce the cluster information into the mekl framework the main advantage of the developed tsmekl is considering different folds of data information to improve classification performance the experimental results validate the feasibility and effectiveness of tsmekl moreover we discuss the theoretical and experimental generalization risk bound of the proposed algorithm in terms of the rademacher complexity

graph distance measures based on topological indices revisited graph distance measures based on topological indices have been already explored by dehmer et al also inequalities for those graph distance measures have been proved in this paper we continue studying such comparative graph measures based on the well known wiener index graph energy and randic index respectively we prove extremal properties of the graph distance measures for some special classes of graphs to demonstrate useful properties of the measures we also discuss numerical results to conclude the paper we state some open problems

new classes of frequency hopping sequences with optimal partial correlation in this paper the partial hamming correlation properties of frequency hopping sequences fhss are discussed the peng fan bounds on sets of fhss are generalized to the case of partial correlation both individual fhss with optimal partial autocorrelation and sets of fhss with optimal partial correlation are presented the former has more new parameters compared with the known individual fhss with optimal partial autocorrelation while the later is obtained in the literature for the first time

an optimization criterion for generalized discriminant analysis on undersampled problems an optimization criterion is presented for discriminant analysis the criterion extends the optimization criteria of the classical linear discriminant analysis lda through the use of the pseudoinverse when the scatter matrices are singular it is applicable regardless of the relative sizes of the data dimension and sample size overcoming a limitation of classical lda the optimization problem can be solved analytically by applying the generalized singular value decomposition gsvd technique the pseudoinverse has been suggested and used for undersampled problems in the past where the data dimension exceeds the number of data points the criterion proposed in this paper provides a theoretical justification for this procedure an approximation algorithm for the gsvd based approach is also presented it reduces the computational complexity by finding subclusters of each cluster and uses their centroids to capture the structure of each cluster this reduced problem yields much smaller matrices to which the gsvd can be applied efficiently experiments on text data with up to 7 000 dimensions show that the approximation algorithm produces results that are close to those produced by the exact algorithm

lower bounds on the hamming auto and cross correlations of frequency hopping sequences frequency hopping fh sequences have found wide applications in various modern fh spread spectrum communications and radar systems in fh spread spectrum communications the interference occurs when two distinct transmitters use the same frequency simultaneously in order to evaluate the goodness of fh sequence design the hamming correlation function is used as an important measure in this correspondence by considering separately the maximum hamming autocorrelation sidelobe h sub a and the maximum hamming cross correlation h sub c several new lower bounds on the size p of the frequency slot set f the sequence length l the family size m and correlation properties are established the new periodic bounds include the known lempel greenberger bounds as special case when m 2 and are tighter than the seay bounds under certain conditions when m 2 furthermore the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the lempel greenberger bounds and seay bounds besides the aperiodic fh bounds which have not yet been previously reported are also presented and discussed in this correspondence

measures of distance between probability distributions abstract in statistical estimation problems measures between probability distributions play significant roles hellinger coefficient jeffreys distance chernoff coefficient directed divergence and its symmetrization j divergence are examples of such measures here these and like measures are characterized through a composition law and the sum form they possess the functional equations f pr qs f ps qr r s f p q p q f r s and f pr qs f ps qr f p q f r s are instrumental in their deduction

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

novel fisher discriminant classifiers at the present several applications need to classify high dimensional points belonging to highly unbalanced classes unfortunately when the training set cardinality is small compared to the data dimensionality small sample size problem the classification performance of several well known classifiers strongly decreases similarly the classification accuracy of several discriminative methods decreases when non linearly separable and unbalanced classes are treated in this paper we firstly survey state of the art methods that employ improved versions of linear discriminant analysis lda to deal with the above mentioned problems secondly we propose a family of classifiers based on the fisher subspace estimation which efficiently deal with the small sample size problem non linearly separable classes and unbalanced classes the promising results obtained by the proposed techniques on benchmark datasets and the comparison with state of the art predictors show the efficacy of the proposed techniques

asymptotic power comparisons of tests of separate parametric families by bahadur s approach summary the paper investigates asymptotic power comparisons of tests of separate parametric families when the size of the test is allowed to tend to zero as the sample size tends to infinity it shows that bahadur s method of asymptotic comparison by means of the approximate slope of the tests can be extended to the case of separate parametric families the paper contains a number of applications

a comparative analysis of the tanimoto index and graph edit distance for measuring the topological similarity of trees abstract in this paper we explore interrelations between the tanimoto index and the graph edit distance ged for measuring the topological similarity distance of graphs to do so we discuss cumulative similarity distance distributions of these measures and other data analysis methods also we explore properties of the tanimoto index by using sets of chemical alkane trees and exhaustively generated ordinary trees as subgraphs in particular we discuss numerical results for exploring the approximation behavior of the tanimoto index by ged

a combinatorial construction for strictly optimal frequency hopping sequences frequency hopping sequences fhss with favorable partial hamming correlation properties have important applications in many synchronization and multiple access systems strictly optimal fhss are those fhss with optimal partial hamming autocorrelation irrespective of the correlation window length in this paper strictly optimal fhss are investigated from a combinatorial approach a generic connection between strictly optimal fhss and disjoint cyclic perfect mendelsohn difference families is established by virtue of this connection new strictly optimal fhss are generated from some disjoint cpmdfs these strictly optimal fhss have new parameters not covered in the literature

a new method for testing separate families of hypotheses abstract theoretical and empirical evidence are reported showing that the tests given in cox 1961 and williams 1970a b for the problem of testing separate families of hypotheses suffer from fundamental difficulties neither test is guaranteed to be asymptotically level a even for very smooth problems a new method proposed here as an alternative works adaptively by repeated application of the parametric bootstrap idea over slowly shrinking confidence regions theoretical properties of the method are derived and its finite sample behavior is studied in a number of examples

essence of kernel fisher discriminant in this paper the method of kernel fisher discriminant kfd is analyzed and its nature is revealed i e kfd is equivalent to kernel principal component analysis kpca plus fisher linear discriminant analysis lda based on this result a more transparent kfd algorithm is proposed that is kpca is first performed and then lda is used for a second feature extraction in the kpca transformed space finally the effectiveness of the proposed algorithm is verified using the cenparmi handwritten numeral database

integrated fisher linear discriminants this paper studies fisher linear discriminants flds based on classification accuracies for imbalanced datasets an optimal threshold is found out from a series of empirical formulas developed which is related not only to sample sizes but also to distribution regions a mixed binary decimal coding system is suggested to make the very dense datasets sparse and enlarge the class margins on condition that the neighborhood relationships of samples are nearly preserved the within class scatter matrices being or approximately singular should be moderately reduced in dimensionality but not added with tiny perturbations the weight vectors can be further updated by a kind of epoch limited three at most iterative learning strategy provided that the current training error rates come down accordingly putting the above ideas together this paper proposes a type of integrated flds the extensive experimental results over real world datasets have demonstrated that the integrated flds have obvious advantages over the conventional flds in the aspects of learning and generalization performances for the imbalanced datasets an optimal threshold is found out from a series of empirical threshold formulas developed for fisher linear discriminants based on classification accuracies weight vectors and thresholds are updated by an epoch limited iterative learning strategy the singular within class scatter matrices are reduced in dimensionality but not added with perturbations a coding system enlarges class margins and approximately preserves neighborhood relationships an integrated learning algorithm improves the learning and generalization performances of fisher linear discriminants

cospectral graphs and the generalized adjacency matrix abstract let j be the all ones matrix and let a denote the adjacency matrix of a graph an old result of johnson and newman states that if two graphs are cospectral with respect to yj a for two distinct values of y then they are cospectral for all y here we will focus on graphs cospectral with respect to yj a for exactly one value y of y we call such graphs y cospectral it follows that y is a rational number and we prove existence of a pair of y cospectral graphs for every rational y in addition we generate by computer all y cospectral pairs on at most nine vertices recently chesnokov and the second author constructed pairs of y cospectral graphs for all rational y 0 1 where one graph is regular and the other one is not this phenomenon is only possible for the mentioned values of y and by computer we find all such pairs of y cospectral graphs on at most eleven vertices

upper bound for a hybrid sum over galois rings with applications to aperiodic correlation of some q ary sequences an upper bound for a hybrid exponential sum over galois rings is derived this bound is then used to obtain an upper bound for the maximum aperiodic correlation of some sequence families over galois rings the bound is of the order of spl radic qlnq where q 1 is the period of the sequences

linear dimensionality reduction via a heteroscedastic extension of lda the chernoff criterion we propose an eigenvector based heteroscedastic linear dimension reduction ldr technique for multiclass data the technique is based on a heteroscedastic two class technique which utilizes the so called chernoff criterion and successfully extends the well known linear discriminant analysis lda the latter which is based on the fisher criterion is incapable of dealing with heteroscedastic data in a proper way for the two class case the between class scatter is generalized so to capture differences in co variances it is shown that the classical notion of between class scatter can be associated with euclidean distances between class means from this viewpoint the between class scatter is generalized by employing the chernoff distance measure leading to our proposed heteroscedastic measure finally using the results from the two class case a multiclass extension of the chernoff criterion is proposed this criterion combines separation information present in the class mean as well as the class covariance matrices extensive experiments and a comparison with similar dimension reduction techniques are presented

optimal frequency hopping sequences auto and cross correlation properties frequency hopping fh sequences play a key role in frequency hopping spread spectrum communication systems in order to evaluate the performance of fh sequences lempel and greenberger 1974 and peng and fan 2004 derived lower bounds on their hamming auto and cross correlations in this paper we construct families of fh sequences with hamming correlations meeting those bounds by combinatorial and algebraic techniques we first construct optimal families consisting of a single fh sequence with maximum hamming correlation equal to 2 from a combinatorial approach then we investigate families consisting of multiple fh sequences we provide a combinatorial characterization for such families and present a recursive method to construct them by means of this characterization we also describe two algebraic constructions for such families of fh sequences generalizing those of ding moisio and yuan 2007 as a consequence many new optimal families of fh sequences are obtained

frequency hopping sequences with optimal partial autocorrelation properties we classify some p sup k ary p prime k integer generalized m sequences and generalized gordon mills welch gmw sequences of period p sup 2k 1 over a residue class ring r gf p spl xi spl xi sup k having optimal partial hamming autocorrelation properties in frequency hopping fh spread spectrum systems these sequences are useful for synchronizing process suppose for example that a transmitting p sup k ary fh patterns of period p sup 2k 1 are correlated at a receiver usually the length of a correlation window denoted by l is shorter than the pattern s overall period in that case the maximum value of the out of phase hamming autocorrelation is lower bounded by spl lceil l p sup k 1 spl rceil but the classified sequences achieve this bound with equality for any positive integer l

comparing large scale graphs based on quantum probability theory abstract in this paper a new measurement to compare two large scale graphs based on the theory of quantum probability is proposed an explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established our proposed distance between two graphs is defined as the distance between the corresponding moment matrices of their spectral distributions it is shown that the spectral distributions of their adjacency matrices in a vector state includes information not only about their eigenvalues but also about the corresponding eigenvectors moreover we prove that the proposed distance is graph invariant and sub structure invariant examples with various graphs are given and distances between graphs with few vertices are checked computational results for real large scale graphs show that its accuracy is better than any existing methods and time cost is extensively cheap

on a quadratic trigonometric functional equation and some applications our main goal is to determine the general solution of the functional equation fl xy f2 xy 1 f3 x f4 y f5 x f6 y fi txy fi tyx i 1 2 where fi are complex valued functions defined on a group this equation contains among others an equation of h swiatak whose general solution was not known until now and an equation studied by k s lau in connection with a characterization of rao s quadratic entropies special cases of this equation also include the pexider quadratic d alembert and wilson equations

a similarity measure for graphs with low computational complexity we present and analyze an algorithm to measure the structural similarity of generalized trees a new graph class which includes rooted trees for this we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings we prove that the obtained graph similarity measures are so called backward similarity measures from this we find that the time complexity of our algorithm is polynomial and hence significantly better than the time complexity of classical graph similarity methods based on isomorphic relations

new constructions for optimal sets of frequency hopping sequences in this paper two generic constructions of optimal frequency hopping sequence fhs sets employing d form functions with difference balanced property are presented they generalize the previous constructions of optimal fhs sets using m sequences and produce new optimal fhs sets that cannot be produced by the earlier constructions by choosing appropriate d form functions with difference balanced property both constructions lead to fhss with large linear complexity in addition one of the proposed constructions gives new optimal parameters of fhs sets

a study of graph spectra for comparing graphs and trees the spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure it has also been employed as a graph representation for pattern matching since it is invariant to the labelling of the graph there are however a number of potential drawbacks in using the spectrum as a representation of a graph firstly more than one graph may share the same spectrum it is well known for example that very few trees can be uniquely specified by their spectrum secondly the spectrum may change dramatically with a small change structure there are a wide variety of graph matrix representations from which the spectrum can be extracted among these are the adjacency matrix combinatorial laplacian normalised laplacian and unsigned laplacian spectra can also be derived from the heat kernel matrix and path length distribution matrix the choice of matrix representation clearly has a large effect on the suitability of spectrum in a number of pattern recognition tasks in this paper we investigate the performance of the spectra as a graph representation in a variety of situations firstly we investigate the cospectrality of the various matrix representations over large graph and tree sets extending the work of previous authors we then show that the euclidean distance between spectra tracks the edit distance between graphs over a wide range of edit costs and we analyse the accuracy of this relationship we then use the spectra to both cluster and classify the graphs and demonstrate the effect of the graph matrix formulation on error rates these results are produced using both synthetic graphs and trees and graphs derived from shape and image data

generalized burr pareto logistic distributions with applications to a uranium exploration data set a distribution developed previously cook and johnson 1981 has been generalizedu sing morgenstern s distribution to include more useful dependence structures the new distribution provides better fits to a uranium survey data set the effectiveness of atkinson s 1982 graphical aid for discriminating separate models is also demonstrated in comparing the usual normal model with the new distribution having normal marginal distributions