multiple kernel learning for dimensionality reduction in solving complex visual learning tasks adopting multiple descriptors to more precisely characterize the data has been a feasible way for improving performance the resulting data representations are typically high dimensional and assume diverse forms hence finding a way of transforming them into a unified space of lower dimension generally facilitates the underlying tasks such as object recognition or clustering to this end the proposed approach termed mkl dr generalizes the framework of multiple kernel learning for dimensionality reduction and distinguishes itself with the following three main contributions first our method provides the convenience of using diverse image descriptors to describe useful characteristics of various aspects about the underlying data second it extends a broad set of existing dimensionality reduction techniques to consider multiple kernel learning and consequently improves their effectiveness third by focusing on the techniques pertaining to dimensionality reduction the formulation introduces a new class of applications with the multiple kernel learning framework to address not only the supervised learning problems but also the unsupervised and semi supervised ones

existence of maximal surfaces in asymptotically flat spacetimes we prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition this uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the dirichlet problem

gtm the generative topographic mapping latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent or hidden variables a familiar example is factor analysis which is based on a linear transformations between the latent space and the data space in this paper we introduce a form of non linear latent variable model called the generative topographic mapping for which the parameters of the model can be determined using the em algorithm gtm provides a principled alternative to the widely used self organizing map som of kohonen 1982 and overcomes most of the significant limitations of the som we demonstrate the performance of the gtm algorithm on a toy problem and on simulated data from flow diagnostics for a multi phase oil pipeline

extending metric multidimensional scaling with bregman divergences sum of weighted square distance errors has been a popular way of defining stress function for metric multidimensional scaling mmds like the sammon mapping in this paper we generalise this popular mmds with bregman divergences as an example we show that the sammon mapping can be thought of as a truncated bregman mmds bmmds and we show that the full bmmds improves upon the sammon mapping on some standard data sets and investigate the reasons underlying this improvement we then extend a well known family of mmds that deploy a strategy of focusing on small distances with bmmds and investigate limitations of the strategy empirically then an opposite strategy is introduced to create another family of bmmds that gives increasing mapping quality a data preprocessing method and a distance matrix preprocessing are introduced

the statistics of eigenvector components of random band matrices analytical results by using a supersymmetric formalism the authors calculate analytically all higher moments pq sigma n mod psi n mod 2q generalizing the inverse participation ratio p2 where psi n 1 or n or n stands for the nth component of an eigenvector of a large random matrix with a band structure on this basis they reconstruct the whole probability distribution function of eigenvector components the relation with known numerical results is discussed

improved data visualisation through multiple dissimilarity modelling popular dimension reduction and visualisation algorithms rely on the assumption that input dissimilarities are typically euclidean for instance metric multidimensional scaling t distributed stochastic neighbour embedding and the gaussian process latent variable model it is well known that this assumption does not hold for most datasets and often high dimensional data sits upon a manifold of unknown global geometry we present a method for improving the manifold charting process coupled with elastic mds such that we no longer assume that the manifold is euclidean or of any particular structure we draw on the benefits of different dissimilarity measures allowing for the relative responsibilities under a linear combination to drive the visualisation process

curvilinear component analysis a self organizing neural network for nonlinear mapping of data sets we present a new strategy called curvilinear component analysis cca for dimensionality reduction and representation of multidimensional data sets the principle of cca is a self organized neural network performing two tasks vector quantization vq of the submanifold in the data set input space and nonlinear projection p of these quantizing vectors toward an output space providing a revealing unfolding of the submanifold after learning the network has the ability to continuously map any new point from one space into another forward mapping of new points in the input space or backward mapping of an arbitrary position in the output space

improved data visualisation through nonlinear dissimilarity modelling inherent to state of the art dimension reduction algorithms is the assumption that global distances between observations are euclidean despite the potential for altogether non euclidean data manifolds we demonstrate that a non euclidean manifold chart can be approximated by implementing a universal approximator over a dictionary of dissimilarity measures building on recent developments in the field this approach is transferable across domains such that observations can be vectors distributions graphs and time series for instance our novel dissimilarity learning method is illustrated with four standard visualisation datasets showing the benefits over the linear dissimilarity learning approach

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

statistics of transfer matrices for disordered quantum thin metallic slabs in the quantum transport problem of a tight binding anderson model the statistics of eigenvalues for the transfer matrices of thin disordered slabs is studied numerical simulations indicate that the probability distribution of nearest neighbor eigenvalue spacing and the 3 statistics have already become close to that of the gaussian orthogonal ensemble for sample lengths of the order of the mean free path provided that transverse localization effects are not important an intuitive argument is given why this should occur independently of the size of the matrix therefore good mixing of the channels is not essential for obtaining gaussian orthogonal ensemble type statistics and universal conductance fluctuations

parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes spacelike hypersurfaces of prescribed mean curvature in cosmological spacetimes are constructed as asymptotic limits of a geometric evolution equation in particular an alternative constructive proof is given for the existence of maximal and constant mean curvature slices

proof of the positive mass theorem ii the positive mass theorem states that for a nontrivial isolated physical system the total energy which includes contributions from both matter and gravitation is positive this assertion was demonstrated in our previous paper in the important case when the space time admits a maximal slice here this assumption is removed and the general theorem is demonstrated abstracts of the results of this paper appeared in 11 and 13

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

distribution of singular values of random band matrices marchenko pastur law and more we consider the limiting spectral distribution of matrices of the form frac 1 2b n 1 r x r x where x is an n times n band matrix of bandwidth b n and r is a non random band matrix of bandwidth b n we show that the stieltjes transform of esd of such matrices converges to the stieltjes transform of a non random measure and the limiting stieltjes transform satisfies an integral equation for r 0 the integral equation yields the stieltjes transform of the marchenko pastur law

on maximal surfaces in asymptotically flat space times existenc of maximal and almost maximal hypersurfaces in asymptotically flat space times is established under boundary conditions weaker than those considered previously we show in particular that every vacuum evolution of asymptotically flat data for the einstein equations can be foliated by slices maximal outside a spatially compact set and that every strictly stationary asymptotically flat space time can be foliated by maximal hypersurfaces amongst other uniqueness results we show that maximal hypersurfaces can be used to partially fix an asymptotic poincare group

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

shape classification by manifold learning in multiple observation spaces manifold learning is a non linear method with the aim of finding a constructive way to embed the data from a high dimensional space into a low dimensional one the improvement of shape classification is the major approach in this paper which is based on the continuity in feature space in accordance with the continuity in semantic one in this regard a non linear approach is employed to map the shape feature vectors to a new space while their semantics become similar with human opinion the euclidean distance between two feature vectors would be closed shapes are described by four contour based and region based techniques by the proposed method in other word they are described in four observation spaces furthermore a parameter space is learnt from multiple observation spaces based on fusion of dissimilarities in a supervised manner experimental results show the validity and efficiency of the proposed approach for shape classification over a variety of standard shape datasets

spacelike hypersurfaces with prescribed boundary values and mean curvature we consider the boundary value problem for the mean curvature operator in minkowski space and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions our main results hold for non constant mean curvature and make no assumptions about the smoothness of the boundary or boundary data

stable maximal hypersurfaces in lorentzian spacetimes abstract we study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions for instance the timelike convergence condition tcc we characterize stability when the target space has constant sectional curvature as well as give sufficient conditions on the geometry of the ambient spacetime e g the validity of tcc to ensure stability some rigidity results and height estimates are also proven in grw spacetimes in the last part of the paper we consider k stability of spacelike hypersurfaces a concept related to mean curvatures of higher orders

multiple kernel learning algorithms in recent years several methods have been proposed to combine multiple kernels instead of using a single one these different kernels may correspond to using different notions of similarity or may be using information coming from multiple sources different representations or different feature subsets in trying to organize and highlight the similarities and differences between them we give a taxonomy of and review several multiple kernel learning algorithms we perform experiments on real data sets for better illustration and comparison of existing algorithms we see that though there may not be large differences in terms of accuracy there is difference between them in complexity as given by the number of stored support vectors the sparsity of the solution as given by the number of used kernels and training time complexity we see that overall using multiple kernels instead of a single one is useful and believe that combining kernels in a nonlinear or data dependent way seems more promising than linear combination in fusing information provided by simple linear kernels whereas linear methods are more reasonable when combining complex gaussian kernels