on copositive matrices abstract a criterion for copositive matrices is given and for n 3 the set of all copositive matrices is determined in terms of matrix elements copositive matrices are applied to the problem of excluding periodic solutions of certain algebraic differential equations

graph theoretic methods for matrix completion problems abstract a pattern is a list of positions in an n n real matrix a matrix completion problem for the class of matrices asks whether every partial matrix whose specified entries are exactly the positions of the pattern can be completed to a matrix we survey the current state of research on matrix completion problems for many subclasses of p 0 matrices including positive definite matrices m matrices inverse m matrices p matrices and matrices defined by various sign symmetry and positivity conditions on p 0 and p matrices graph theoretic techniques used to study completion problems are discussed several new results are also presented including the solution to the m 0 matrix completion problem and the sign symmetric p 0 matrix completion problem

discriminative sparsity preserving projections for image recognition previous works have demonstrated that image classification performance can be significantly improved by manifold learning however performance of manifold learning heavily depends on the manual selection of parameters resulting in bad adaptability in real world applications in this paper we propose a new dimensionality reduction method called discriminative sparsity preserving projections dspp different from the existing sparse subspace algorithms which manually construct a penalty adjacency graph dspp employs sparse representation model to adaptively build both intrinsic adjacency graph and penalty graph with weight matrix and then integrates global within class structure into the discriminant manifold learning objective function for dimensionality reduction extensive experimental results on four image databases demonstrate the effectiveness of the proposed approach we analyzed the vertex points of penalty graph using sparse representation we adaptively constructed both penalty adjacency graph and intrinsic graph our method simultaneously considered the global and local geometric structure of data

some properties of schur complements and diagonal schur complements of diagonally dominant matrices in this paper we prove that the diagonal schur complement of a strictly doubly diagonally dominant matrix is strictly doubly diagonally dominant matrix the same holds for the diagonal schur complement of a strictly generalized doubly diagonally dominant matrix and a nonsingular h matrix we point out that under certain assumptions the diagonal schur complement of a strictly doubly doubly product diagonally dominant matrix is also strictly doubly doubly product diagonally dominant further we provide the distribution of the real parts of eigenvalues of a diagonal schur complement of h matrix we also show that the schur complement of a diagonally dominant matrix is not always diagonally dominant by a numerical example and then obtain a sufficient condition to ensure that the schur complement of a diagonally dominant matrix is diagonally dominant

two dimensional supervised local similarity and diversity projection this paper presents a novel manifold learning method namely two dimensional supervised local similarity and diversity projection 2dslsdp for feature extraction the proposed method defines two weighted adjacency graphs namely similarity graph and diversity graph the affinity matrix of similarity graph is determined by the spatial relationship between vertices of this graph while affinity matrix of diversity graph is determined by the diversity information of vertices of its graph using these two graphs the proposed method constructs local similarity scatter and diversity scatter respectively a concise feature extraction criterion is then raised via minimizing the ratio of the local similarity scatter to local diversity scatter thus 2dslsdp can well preserve not only the adjacency similarity structure but also the diversity of data points which is important for the classification experiments on the ar and umist databases show the effectiveness of the proposed method

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

sign patterns of inverse nonnegative matrices abstract we determine here the 0 sign patterns which occur among the inverses of nonsingular entrywise nonnegative matrices these results complete a sequence of work which began with the characterization of all possible sign patterns which occur among inverses of positive matrices and the characterization in this general case is more involved to state than the earlier ones

robust adaptive asymptotic tracking of nonlinear systems with additive disturbance this note deals with the tracking control of multiple input multiple output mimo nonlinear parametric strict feedback systems in the presence of additive disturbances and parametric uncertainties for such systems c sup 0 robust adaptive controllers usually cannot ensure asymptotic tracking or even regulation in this work under the assumption the disturbances are c sup 2 with bounded time derivatives we present a c sup 0 robust adaptive control construction that guarantees the tracking error is asymptotically driven to zero

stable orthogonal local discriminant embedding for linear dimensionality reduction manifold learning is widely used in machine learning and pattern recognition however manifold learning only considers the similarity of samples belonging to the same class and ignores the within class variation of data which will impair the generalization and stableness of the algorithms for this purpose we construct an adjacency graph to model the intraclass variation that characterizes the most important properties such as diversity of patterns and then incorporate the diversity into the discriminant objective function for linear dimensionality reduction finally we introduce the orthogonal constraint for the basis vectors and propose an orthogonal algorithm called stable orthogonal local discriminate embedding experimental results on several standard image databases demonstrate the effectiveness of the proposed dimensionality reduction approach

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

the real positive definite completion problem for a simple cycle abstract we consider the question of whether a real partial positive definite matrix in which the specified off diagonal entries consist of a full n cycle has a positive definite completion this lies in contrast to the previously studied chordal case we give two solutions in one we describe about n 2 independent conditions on angles associated with a normalization of the data that are necessary and sufficient the second is more computational and allows presentation of all positive definite completions as well as answering the existence question

two dimensional maximum local variation based on image euclidean distance for face recognition manifold learning concerns the local manifold structure of high dimensional data and many related algorithms are developed to improve image classification performance none of them however consider both the relationships among pixels in images and the geometrical properties of various images during learning the reduced space in this paper we propose a linear approach called two dimensional maximum local variation 2dmlv for face recognition in 2dmlv we encode the relationships among pixels in images using the image euclidean distance instead of conventional euclidean distance in estimating the variation of values of images and then incorporate the local variation which characterizes the diversity of images and discriminating information into the objective function of dimensionality reduction extensive experiments demonstrate the effectiveness of our approach

nonnegative matrices with power invariant zero patterns abstract if a is a nonsingular m matrix the elements of the sequence a k all have the same zero pattern using the drazin inverse we show that a similar zero pattern invariance property holds for a class of matrices which is larger than the generalized m matrices

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

on the inverse of a special schur complement abstract the inverse of a schur complement is a very useful tool in many algorithms for the computation of the matrix inversion in this paper we study the inverse of a special schur complement cd 1 b we proved that always exist some x and y such that xdy is a inverse of cd 1 b furthermore using minimal rank properties we give some explicit expressions for x y and the inverse of cd 1 b numerical examples also given

deep adaptive feature embedding with local sample distributions for person re identification person re identification re id aims to match pedestrians observed by disjoint camera views it attracts increasing attention in computer vision due to its importance to surveillance systems to combat the major challenge of cross view visual variations deep embedding approaches are proposed by learning a compact feature space from images such that the euclidean distances correspond to their cross view similarity metric however the global euclidean distance cannot faithfully characterize the ideal similarity in a complex visual feature space because features of pedestrian images exhibit unknown distributions due to large variations in poses illumination and occlusion moreover intra personal training samples within a local range which are robust to guide deep embedding against uncontrolled variations cannot be captured by a global euclidean distance in this paper we study the problem of person re id by proposing a novel sampling to mine suitable positives i e intra class within a local range to improve the deep embedding in the context of large intra class variations our method is capable of learning a deep similarity metric adaptive to local sample structure by minimizing each sample s local distances while propagating through the relationship between samples to attain the whole intra class minimization to this end a novel objective function is proposed to jointly optimize similarity metric learning local positive mining and robust deep feature embedding this attains local discriminations by selecting local ranged positive samples and the learned features are robust to dramatic intra class variations experiments on benchmarks show state of the art results achieved by our method c 2017 elsevier ltd all rights reserved

inverse m matrices ii this is an update of the 1981 survey by the first author in the meantime a considerable amount has been learned about the very special structure of the important class of inverse m matrices developments since the earlier survey are emphasized but we have tried to be somewhat complete and some results have not previously been published some proofs are given where appropriate and references are given for others after some elementary preliminaries results are grouped by certain natural categories

generalized ultrametric matrices a class of inverse m matrices abstract recently marti nez michon and san marti n introduced the new class of symmetric strictly ultrametric matrices they proved that the inverse of a strictly ultrametric matrix is a strictly row and strictly column diagonally dominant stieltjes matrix here we generalize their result by introducing a class of nonsymmetric matrices calledgeneralized ultrametric matrices we give a necessary and sufficient condition for the regularity of these matrices and prove that the inverse of a nonsingular generalized ultrametric matrix is a row and column diagonally dominant m matrix we establish that a nonnegative matrix is a generalized ultrametric matrix if and only if the matrix is a certain sum of at most rank two matrices moreover we give a characterization of generalized ultrametric matrices based on weighted trees the entries of generalized ultrametric matrices then arise as certain distances between the leaves and the root of the tree

characterizations of inverse m matrices with special zero patterns in this paper we provide some characterizations of inverse m matrices with special zero patterns in particular we give necessary and sufficient conditions for k diagonal matrices and symmetric k diagonal matrices to be inverse m matrices in addition results for triadic matrices tridiagonal matrices and symmetric 5 diagonal matrices are presented as corollaries

notes on completely positive matrices abstract let a be a n n symmetric matrix and in the closure of inverse m matrices then a can be factored as a bb t for some nonnegative lower triangular n n matrix b and cp rank a n if a is a positive semidefinite 0 1 matrix then a is completely positive and cp rank a rank a if a is a nonnegative symmetric h matrix then a is completely positive and cp rank a n n 1 2 n n where is the number of connected components of the graph g a

tridiagonal and upper triangular inverse m matrices abstract in this paper we characterize the nonnegative nonsingular tridiagonal matrices belonging to the class of inverse m matrices we give a geometric equivalence for a nonnegative nonsingular upper triangular matrix to be in this class this equivalence is extended to include some reducible matrices

inverse h matrices abstract the notion of inverse m matrices has been quite well studied and many of their properties have been documented in the literature in this article a proposal to consider the larger class of inverse h matrices is made first certain special types of real matrices are identified as inverse h matrices while these matrices are not inverse m matrices in general their definitions are inspired by matrices that are known to be inverse m matrices in the rest of the article motivated by results that hold for inverse m matrices the endeavor will be to attempt at proving corresponding results for inverse h matrices it is shown that for the full class of inverse h matrices many of these extensions are false nevertheless two subclasses of real inverse h matrices are identified where these generalizations are shown to hold

monotonicity and positivity of coefficients of power series expansions associated with newton and halley methods for the matrix pth root abstract if a is a matrix with all eigenvalues in the disk z 1 1 the principal pth root of a can be computed by newton s method or halley s method the study of newton s method and halley s method for the matrix pth root can be done through a study of power series expansions of some sequences of scalar functions in this paper we prove monotonicity results for the coefficients in the power series expansions for both newton s method and halley s method and for all integer p 2 the sign patterns of these coefficients can be seen directly from the monotonicity results we then use these monotonicity results and their consequences to obtain some new error estimates in the matrix case to obtain a monotonic convergence result when a is a nonsingular m matrix and to obtain a structure preserving result when a is a nonsingular m matrix or a real nonsingular h matrix with positive diagonal entries

matrices and the linear complementarity problem the paper is a collection of results on the linear complementarity problem q m the results are stated in terms of the matrix m

criteria for sign regularity of sets of matrices abstract we consider matrix intervals with respect to a certain checkerboard partial ordering we show that every real matrix contained in a matrix interval is sign regular if two special matrices taken from that matrix interval are sign regular

local inversion of matrices with sparse inverses abstract we demonstrate that subject to certain regularity conditions any invertible matrix whose inverse is subordinate to a chordal graph g may be inverted via a simple formula involving only the inverses of its principal submatrices corresponding to the maximal cliques and minimal vertex separators of the graph g the resulting formula is reminiscent of known formulae for the determinant and inertia of matrices whose inverses are subordinate to a chordal graph

rapid and brief communication two dimensional fld for face recognition this paper presents a new scheme of face image feature extraction namely the two dimensional fisher linear discriminant experiments on the orl and the umist face databases show that the new scheme outperforms the pca and the conventional pca fld schemes not only in its computational efficiency but also in its performance for the task of face recognition

a new class of nonlinear robust adaptive controllers recently a new class of adaptive control schemes motivated from nonlinear systems theory has been proposed for minimum phase linear time invariant plants under certain assumptions on the plant transfer function these schemes guarantee uniform signal boundedness and good transient and steady state response for the regulation or tracking error despite the good performance properties of the proposed schemes their practicality relies very much on their robustness properties with respect to plant model uncertainties these robustness properties have to be established and understood for application purposes the purpose of this paper is to analyse the stability properties of this new class of adaptive controllers in the presence of reasonable classes of plant model uncertainties we first indicate that the same non robust behaviour that appears in the case of the traditional adaptive controllers without modifications may be exhibited by this new class of adaptive controller we then propose design mod

the symmetric m matrix and symmetric inverse m matrix completion problems abstract the symmetric m matrix and symmetric m 0 matrix completion problems are solved and results of johnson and smith linear algebra appl 290 1999 193 are extended to solve the symmetric inverse m matrix completion problem 1 a pattern i e a list of positions in an n n matrix has symmetric m completion i e every partial symmetric m matrix specifying the pattern can be completed to a symmetric m matrix if and only if the principal subpattern r determined by its diagonal is permutation similar to a pattern that is block diagonal with each diagonal block complete or in graph theoretic terms if and only if each component of the graph of r is a clique 2 a pattern has symmetric m 0 completion if and only if the pattern is permutation similar to a pattern that is block diagonal with each diagonal block either complete or omitting all diagonal positions or in graph theoretic terms if and only if every principal subpattern corresponding to a component of the graph of the pattern either omits all diagonal positions or includes all positions 3 a pattern has symmetric inverse m completion if and only if its graph is block clique and no diagonal position is omitted that corresponds to a vertex in a graph block of order 2 the techniques used are also applied to matrix completion problems for other classes of symmetric matrices

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

regularized generalized eigen decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis we propose a general technique for obtaining sparse solutions to generalized eigenvalue problems and call it regularized generalized eigen decomposition rged for decades fisher s discriminant criterion has been applied in supervised feature extraction and discriminant analysis and it is formulated as a generalized eigenvalue problem thus rged can be applied to effectively extract sparse features and calculate sparse discriminant directions for all variants of fisher discriminant criterion based models particularly rged can be applied to matrix based and even tensor based discriminant techniques for instance 2d linear discriminant analysis 2d lda furthermore an iterative algorithm based on the alternating direction method of multipliers is developed the algorithm approximately solves rged with monotonically decreasing convergence and at an acceptable speed for results of modest accuracy numerical experiments based on four data sets of different types of images show that rged has competitive classification performance with existing multidimensional and sparse techniques of discriminant analysis highlightswe propose a new technique called regularized generalized eigen decomposition rged rged solves generalized eigenvalue problems and obtains sparse solutions it is easy and straightforward applying rged to sparse discriminant analysis and feature extraction an algorithm is developed to solve it with monotonically decreasing convergence rged has competitive classification performance comparing with other methods

on inverse m matrices abstract we generalize a previous result of lewin and neumann and present a characterization of inverse m matrices the approach is mainly graph theoretical

global plus local linear discriminant analysis lda is one of the most popular supervised feature extraction techniques used in machine learning and pattern classification however lda only captures global geometrical structure information of the data and ignores the geometrical structure information of local data points though many articles have been published to address this issue most of them are incomplete in the sense that only part of the local information is used we show here that there are total three kinds of local information namely local similarity information local intra class pattern variation and local inter class pattern variation we first propose a new method called enhanced within class lda ewlda algorithm to incorporate the local similarity information and then propose a complete framework called complete global local lda cglda algorithm to incorporate all these three kinds of local information experimental results on two image databases demonstrate the effectiveness of our algorithms there are three kinds of local information that exist for linear discriminant analysis for incorporating the local similarity information we propose the ewlda algorithm for incorporating the three kinds of local information we propose the cglda algorithm

the symmetric inverse m matrix completion problem necessary and sufficient conditions are given on the data for completability of a partial symmetric inverse m matrix the graph of whose specified entries is a cycle and these conditions coincide with those we identify to be necessary in the general nonsymmetric case graphs for which all partial symmetric inverse m matrices have symmetric inverse m matrix completions are identified and these include those that arise in the general positionally symmetric case however the identification of all such graphs is more subtle than the general case finally we show that our new cycle conditions are sufficient for completability of all partial symmetric inverse m matrices the graph of whose specified entries is a block graph

matrix completion problems for pairs of related classes of matrices abstract for a class x of real matrices a list of positions in an n n matrix a pattern is said to have x completion if every partial x matrix that specifies exactly these positions can be completed to an x matrix if x and x0 are classes that satisfy the conditions any partial x matrix is a partial x0 matrix for any x0 matrix a and e 0 a ei is a x matrix and for any partial x matrix a there exists 0 such that a i is a partial x matrix where is the partial identity matrix specifying the same pattern as a then any pattern that has x0 completion must also have x completion however there are usually patterns that have x completion that fail to have x0 completion this result applies to many pairs of subclasses of p and p0 matrices defined by the same restriction on entries including the classes p p0 matrices weakly sign symmetric p p0 matrices and non negative p p0 matrices it also applies to other related pairs of subclasses of p0 matrices such as the pairs classes of p p0 1 matrices weakly sign symmetric p p0 1 matrices and non negative p p0 1 matrices furthermore any pattern that has weakly sign symmetric sign symmetric non negative p0 completion must also have weakly sign symmetric sign symmetric non negative p0 1 completion although these pairs of classes do not satisfy condition 3 similarly the class of inverse m matrices and its topological closure do not satisfy condition 3 but the conclusion remains true and the matrix completion problem for the topological closure of the class of inverse m matrices is solved for patterns containing the diagonal

z matrices and inverse z matrices abstract we consider z matrices and inverse z matrices i e those nonsingular matrices whose inverses are z matrices recently fiedler and markham introduced a classification of z matrices this classification directly leads to a classification of inverse z matrices among all classes of z matrices and inverse z matrices the classes of m matrices n 0 matrices f 0 matrices and inverse m matrices inverse n 0 matrices and inverse f 0 matrices respectively have been studied in detail here we discuss each single class of z matrices and inverse z matrices as well as considering the whole classes of z matrices and inverse z matrices we establish some common properties of the classes such as eigenvalue bounds and determinant inequalities and we give a new characterization of some classes of z matrices and inverse z matrices moreover we prove that other classes besides those of m matrices n 0 matrices and f 0 matrices consist of matrices whose determinants have the same sign some of the results generalize known results for m matrices n 0 matrices and f 0 matrices and for inverse m matrices inverse n 0 matrices and inverse f 0 matrices however we also show that some properties of the specific classes mentioned above do not hold for all classes of z matrices and inverse z matrices

the completion problem for m matrices and inverse m matrices abstract the completion problems for m matrices and inverse m matrices are discussed the former has a simple solution but is not at all analogous to the positive definite completion problem the latter is more subtle and is analogous to the positive definite problem a graph theoretic completion result as well as a determinant maximizing completion that is characterized by having a zero entry in the inverse in every position in which the partial matrix has an unspecified entry is given for the inverse m matrix problem these mirror to some extent the positive definite case but the methodology is necessarily different

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

theory and design of robust direct and indirect adaptive control schemes a general approach for designing and the theory for analysing robust direct and indirect adaptive control schemes for continuous time plants is presented the design approach involves the development of a general robust adaptive law and the use of the certainty equivalence principle to combine it with robust model reference and pole placement control structures the global stability properties and robustness of the developed adaptive control schemes are established by using a general theory which relates the properties of signals in the mean sense over intervals of time the developed theory and design approach are used to analyse and compare the robustness properties and performance of a wide class of robust adaptive laws which employ a dead zone fixed e1 and a switching modification as well as their variations

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

rapid and brief communication two dimensional locality preserving projections 2dlpp with its application to palmprint recognition this paper proposes a novel algorithm for image feature extraction namely the two dimensional locality preserving projections 2dlpp which directly extracts the proper features from image matrices based on locality preserving criterion experimental results on the polyu palmprint database show the effectiveness of the proposed algorithm

discussion comment on two dimensional locality preserving projections 2dlpp with its application to palmprint recognition this paper proposes a novel algorithm for image feature extraction namely the two dimensional locality preserving projections 2dlpp which directly extracts the proper features from image matrices based on locality preserving criterion experimental results on the polyu palmprint database show the effectiveness of the proposed algorithm

almost principal minors of inverse m matrices abstract it is well known that if an inverse m matrix has a 0 entry then it must be reducible and thus have many more 0 entries this property is actually a special case of a deeper phenomenon that might be loosely described as relations among vanishing almost principal minors in an inverse m matrix this phenomenon encompasses both minors of nested dimension a certain loose monotonicity and minors of the same size in loosely related positions this phenomenon is limited to almost principal minors and where possible converses and examples are given to show the limit of the extent of this phenomenon it is also shown that if one almost principle minor is contained in another then the magnitude of the former is larger than that of the latter

copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints abstract a symmetric matrix c is called copositive if the quadratic form x cx is nonnegative for all nonnegative values of the variables x 1 x 2 x n x a known sufficient condition for a quadratic form x qx to be positive unless x 0 subject to the linear inequality constraints ax 0 is that there should exist a copositive matrix c such that q a ca is positive definite the main result of this paper establishes the necessity of this condition for x qx to be merely nonnegative subject to ax 0 the situation is less straightforward the necessity of the existence of a copositive matrix c such that q a ca is positive semidefinite is proved only under various additional hypotheses regarding the size or rank of a and counterexamples are given to show that in general no such matrix may exist even when slater s constraint qualification holds our approach to these existence questions also furnishes certain tests for positivity or mere nonnegativity of x qx subject to ax 0 in which specific symmetric matrices constructed by rational operations from a and q and depending upon a single real parameter v must be tested for positive definiteness or strict copositivity for large values of v this technique is illustrated by several examples

automated induction of heterogeneous proximity measures for supervised spectral embedding spectral embedding methods have played a very important role in dimensionality reduction and feature generation in machine learning supervised spectral embedding methods additionally improve the classification of labeled data using proximity information that considers both features and class labels however these calculate the proximity information by treating all intraclass similarities homogeneously for all classes and similarly for all interclass samples in this paper we propose a very novel and generic method which can treat all the intra and interclass sample similarities heterogeneously by potentially using a different proximity function for each class and each class pair to handle the complexity of selecting these functions we employ evolutionary programming as an automated powerful formula induction engine in addition for computational efficiency and expressive power we use a compact matrix tree representation equipped with a broad set of functions that can build most currently used similarity functions as well as new ones model selection is data driven because the entire model is symbolically instantiated using only problem training data and no user selected functions or parameters are required we perform thorough comparative experimentations with multiple classification datasets and many existing state of the art embedding methods which show that the proposed algorithm is very competitive in terms of classification accuracy and generalization ability

adaptive data embedding framework for multiclass classification the objective of this paper is the design of an engine for the automatic generation of supervised manifold embedding models it proposes a modular and adaptive data embedding framework for classification referred to as defc which realizes in different stages including initial data preprocessing relation feature generation and embedding computation for the computation of embeddings the concepts of friend closeness and enemy dispersion are introduced to better control at local level the relative positions of the intraclass and interclass data samples these are shown to be general cases of the global information setup utilized in the fisher criterion and are employed for the construction of different optimization templates to drive the defc model generation for model identification we use a simple but effective bilevel evolutionary optimization which searches for the optimal model and its best model parameters the effectiveness of defc is demonstrated with experiments using noisy synthetic datasets possessing nonlinear distributions and real world datasets from different application fields

theorems on schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems abstract we firstly consider the block dominant degree for i ii block strictly diagonally dominant matrix and their schur complements showing that the block dominant degree for the schur complement of an i ii block strictly diagonally dominant matrix is greater than that of the original grand block matrix then as application we present some disc theorems and some bounds for the eigenvalues of the schur complement by the elements of the original matrix further by means of matrix partition and the schur complement of block matrix based on the derived disc theorems we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and the numerical example illustrates that the iteration can compute out the results faster

enhanced fisher discriminant criterion for image recognition many previous studies have shown that image recognition can be significantly improved by fisher linear discriminant analysis flda technique however flda ignores the variation of data points from the same class which characterizes the most important modes of variability of patterns and helps to improve the generalization capability of flda thus the performance of flda on testing data is not good enough in this paper we propose an enhanced fisher discriminant criterion efdc efdc explicitly considers the intra class variation and incorporates the intra class variation into the fisher discriminant criterion to build a robust and efficient dimensionality reduction function efdc obtains a subspace which best detects the discriminant structure and simultaneously preserves the modes of variability of patterns which will result in stable intraclass representation experimental results on four image database show a clear improvement over the results of flda based methods

on the spectra of matrices having nonnegative sums of principal minors abstract the localization of the eigenvalues of matrices with nonnegative sums of principal minors is studied the discussion is carried out in particular for p matrices such matrices for which almost all the eigenvalues lie on the left half plane are constructed

rapid and brief communication local structure based supervised feature extraction in the past few years the computer vision and pattern recognition community has witnessed the rapid growth of a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among them locality preserving projection lpp is one of the most promising feature extraction techniques however when lpp is applied to the classification tasks it shows some limitations such as the ignorance of the label information in this paper we propose a novel feature extraction method called locally discriminating projection ldp ldp utilizes class information to guide the procedure of feature extraction in ldp the local structure of the original data is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information the similarity has several good properties which help to discover the true intrinsic structure of the data and make ldp a robust technique for the classification tasks we compare the proposed ldp approach with lpp as well as other feature extraction methods such as pca and lda on the public available data sets feret and ar experimental results suggest that ldp provides a better representation of the class information and achieves much higher recognition accuracies