matching pursuits dissimilarity measure for shape based comparison and classification of high dimensional data in this paper a new matching pursuits dissimilarity measure mpdm is presented that compares two signals using the information provided by their matching pursuits mp approximations without requiring any prior domain knowledge mpdm is a flexible and differentiable measure that can be used to perform shape based comparisons and fuzzy clustering of very high dimensional possibly compressed data a novel prototype based classification algorithm which is termed the computer aided minimization procedure camp is also proposed the camp algorithm uses the mpdm with the competitive agglomeration ca fuzzy clustering algorithm to build reliable shape based prototypes for classification mp is a well known sparse signal approximation technique which is commonly used for video and image coding the dictionary and coefficient information produced by mp has previously been used to define features to build discrimination and prototype based classifiers however existing mp based classification applications are quite problem domain specific thus making their generalization to other problems quite difficult the proposed camp algorithm is the first mp based classification system that requires no assumptions about the problem domain and builds a bridge between the mp and fuzzy clustering algorithms experimental results also show that the camp algorithm is more resilient to outliers in test data than the multilayer perceptron mlp and support vector machine svm classifiers as well as prototype based classifiers using the euclidean distance as their dissimilarity measure

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

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

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

connectedness properties of limit sets we study convergence group actions on continua and give a criterion which ensures that every global cut point is a parabolic fixed point we apply this result to the case of boundaries of relatively hyperbolic groups and consider implications for connectedness properties of such spaces

using support vector machines to enhance the performance of elastic graph matching for frontal face authentication a novel method for enhancing the performance of elastic graph matching in frontal face authentication is proposed the starting point is to weigh the local similarity values at the nodes of an elastic graph according to their discriminatory power powerful and well established optimization techniques are used to derive the weights of the linear combination more specifically we propose a novel approach that reformulates fisher s discriminant ratio to a quadratic optimization problem subject to a set of inequality constraints by combining statistical pattern recognition and support vector machines svm both linear and nonlinear svm are then constructed to yield the optimal separating hyperplanes and the optimal polynomial decision surfaces respectively the method has been applied to frontal face authentication on the m2vts database experimental results indicate that the performance of morphological elastic graph matching is highly improved by using the proposed weighting technique

stable actions of groups on real trees this paper further develops rips s work on real trees we study a class of actions called stable which includes actions with trivial arc stabilizers and small actions of hyperbolic groups

jsj splittings for finitely presented groups over slender groups we generalize the jsj splitting of rips and sela to give decompositions of finitely presented groups which capture splittings over certain classes of small subgroups such classes include the class of all 2 ended groups and the class of all virtually z z groups the approach called track zipping is relatively elementary and differs from the rips sela approach in that it does not rely on the theory of r trees but rather on an understanding of certain embedded 1 complexes called patterns in a presentation 2 complex for the ambient group

exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification in this paper two supervised methods for enhancing the classification accuracy of the nonnegative matrix factorization nmf algorithm are presented the idea is to extend the nmf algorithm in order to extract features that enforce not only the spatial locality but also the separability between classes in a discriminant manner the first method employs discriminant analysis in the features derived from nmf in this way a two phase discriminant feature extraction procedure is implemented namely nmf plus linear discriminant analysis lda the second method incorporates the discriminant constraints inside the nmf decomposition thus a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived the introduced methods have been applied to the problem of frontal face verification using the well known xm2vts database both methods greatly enhance the performance of nmf for frontal face verification

the approximate solution of a class of fredholm integral equations with a weakly singular kernel a method for finding the numerical solution of a weakly singular fredholm integral equation of the second kind is presented the taylor series is used to remove singularity and legendre polynomials are used as a basis furthermore the legendre function of the second kind is used to remove singularity in the cauchy type integral equation the integrals that appear in this method are computed in terms of gamma and beta functions and some of these integrals are computed in the cauchy principal value sense without using numerical quadratures four examples are given to show the accuracy of the method

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

solving a system of linear volterra integral equations using the new reproducing kernel method in this paper we present a new numerical technique to obtain the approximation solution for linear volterra integral equations of the second kind based on reproducing kernel theory the approximation solution is expressed by n term summation of reproducing kernel functions the merit of the new method includes 1 it is easy to implement this method 2 high accuracy the numerical examples compared with other methods show that the new method is more efficient

peripheral fillings of relatively hyperbolic groups in this paper a group theoretic version of dehn surgery is studied starting with an arbitrary relatively hyperbolic group g we define a peripheral filling procedure which produces quotients of g by imitating the effect of the dehn filling of a complete finite volume hyperbolic 3 manifold m on the fundamental group 1 m the main result of the paper is an algebraic counterpart of thurston s hyperbolic dehn surgery theorem we also show that peripheral subgroups of g almost have the congruence extension property and the group g is approximated in an algebraic sense by its quotients obtained by peripheral fillings

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

variable transformations in the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels extensions to fredholm integral equations abstract a number of techniques that use variable transformations in numerical integration have been developed recently cf sidi numerical integration iv h brass g hammerlin eds birkhauser basel 1993 pp 359 373 laurie j comput appl math 66 1996 337 344 the use of these transformations resulted in increasing the order of convergence of the trapezoidal and the midpoint quadrature rule in this paper the application of variable transformation techniques of sidi and laurie type to the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels is considered since the transformations are such that the end points of integration need not be used as mesh points the methods introduced can be used for vie with both continuous and weakly singular kernel in a uniform way the methods have also the advantages of simplicity of application and of achieving high order of convergence the application of the idea to fredholm integral equations with continuous and weakly singular equations is also considered numerical results are included and they verify the expected increased order of convergence they were obtained by using the trapezoidal formula for the evaluation of the transformed integrals

gabor based kernel pca with doubly nonlinear mapping for face recognition with a single face image in this paper a novel gabor based kernel principal component analysis pca with doubly nonlinear mapping is proposed for human face recognition in our approach the gabor wavelets are used to extract facial features then a doubly nonlinear mapping kernel pca dkpca is proposed to perform feature transformation and face recognition the conventional kernel pca nonlinearly maps an input image into a high dimensional feature space in order to make the mapped features linearly separable however this method does not consider the structural characteristics of the face images and it is difficult to determine which nonlinear mapping is more effective for face recognition in this paper a new method of nonlinear mapping which is performed in the original feature space is defined the proposed nonlinear mapping not only considers the statistical property of the input features but also adopts an eigenmask to emphasize those important facial feature points therefore after this mapping the transformed features have a higher discriminating power and the relative importance of the features adapts to the spatial importance of the face images this new nonlinear mapping is combined with the conventional kernel pca to be called doubly nonlinear mapping kernel pca the proposed algorithm is evaluated based on the yale database the ar database the orl database and the yaleb database by using different face recognition methods such as pca gabor wavelets plus pca and gabor wavelets plus kernel pca with fractional power polynomial models experiments show that consistent and promising results are obtained

a splitting iterative method for solving second kind integral equations in reproducing kernel spaces abstract in the present paper we propose a new iterative method to solve integral equations of the second kind in reproducing kernel hilbert spaces rkhs at first we make appropriate splitting in second kind integral equations and according to this splitting the iterative method will be constructed then bases of rkhs and reproducing kernel spaces properties are used to convert this problem to linear system of equations we move between reproducing kernel spaces by changing bases in order to achieve more accurate approximate solutions classically in iterative rkhs method the number of iterations should be the same as the number of points here we present a type of iterative rkhs method without this limitation convergence of the proposed method is investigated and the efficiency of the method is demonstrated through various examples

mathematical programming methods in the numerical solution of volterra integral and integro differential equations with weakly singular kernel abstract nonlinear volterra integral and integro differential equations with weakly singular kernel are considered and solved numerically using nonlinear mathematical programming methods based on minimax approximations in both cases polynomial and multiquadric approximation are used

error analysis of reproducing kernel hilbert space method for solving functional integral equations this paper is devoted to error analysis of reproducing kernel hilbert space method for solving linear and nonlinear volterra integral equations in some reproducing kernel hilbert spaces finally some examples are given to illustrate and confirm error analysis of the method

the exact solution of a class of volterra integral equation with weakly singular kernel abstract in this paper the weakly singular volterra integral equations with an infinite set of solutions are investigated among the set of solutions only one particular solution is smooth and all others are singular at the origin the numerical solutions of this class of equations have been a difficult topic to analyze and have received much previous investigation the aim of this paper is to present a numerical technique for giving the approximate solution to the only smooth solution based on reproducing kernel theory applying weighted integral we provide a new definition for reproducing kernel space and obtain reproducing kernel function using the good properties of reproducing kernel function the only smooth solution is exactly expressed in the form of series the n term approximate solution is obtained by truncating the series meanwhile we prove that the derivative of approximation converges to the derivative of exact solution uniformly the final numerical examples compared with other methods show that the method is efficient

morphological elastic graph matching applied to frontal face authentication under well controlled and real conditions abstract in this paper morphological elastic graph matching is applied to frontal face authentication on databases ranging from small to large multimedia ones collected under either well controlled or real world conditions it is shown that the morphological elastic graph matching achieves a very low equal error rate on databases collected under well controlled conditions however its performance deteriorates when it is applied to databases recorded in real world scenarios the compensation for variable recording conditions such as changes in illumination scale differences and varying face position prior to the application of morphological elastic matching is proposed

the exact solution of a linear integral equation with weakly singular kernel a space w21 a b which is proved to be a reproducing kernel space with simple reproducing kernel is defined the expression of its reproducing kernel function is given subsequently a class of linear volterra integral equation vie with weakly singular kernel is discussed in the new reproducing kernel space the reproducing kernel method of linear operator equation au f which request the image space of operator a is w21 a b and operator a is bounded is improved namely the request for the image space is weakened to be l2 a b and the boundedness of operator a is also not required as a result the exact solution of the equation is obtained the numerical experiments show the efficiency of our method

redundancy reduction as a strategy for unsupervised learning a redundancy reduction strategy which can be applied in stages is proposed as a way to learn as efficiently as possible the statistical properties of an ensemble of sensory messages the method works best for inputs consisting of strongly correlated groups that is features with weaker statistical dependence between different features this is the case for localized objects in an image or for words in a text a local feature measure determining how much a single feature reduces the total redundancy is derived which turns out to depend only on the probability of the feature and of its components but not on the statistical properties of any other features the locality of this measure makes it ideal as the basis for a neural implementation of redundancy reduction and an example of a very simple non hebbian algorithm is given the effect of noise on learning redundancy is also discussed

independent component analysis of gabor features for face recognition we present an independent gabor features igfs method and its application to face recognition the novelty of the igf method comes from 1 the derivation of independent gabor features in the feature extraction stage and 2 the development of an igf features based probabilistic reasoning model prm classification method in the pattern recognition stage in particular the igf method first derives a gabor feature vector from a set of downsampled gabor wavelet representations of face images then reduces the dimensionality of the vector by means of principal component analysis and finally defines the independent gabor features based on the independent component analysis ica the independence property of these gabor features facilitates the application of the prm method for classification the rationale behind integrating the gabor wavelets and the ica is twofold on the one hand the gabor transformed face images exhibit strong characteristics of spatial locality scale and orientation selectivity these images can thus produce salient local features that are most suitable for face recognition on the other hand ica would further reduce redundancy and represent independent features explicitly these independent features are most useful for subsequent pattern discrimination and associative recall experiments on face recognition using the face recognition technology feret and the orl datasets where the images vary in illumination expression pose and scale show the feasibility of the igf method in particular the igf method achieves 98 5 correct face recognition accuracy when using 180 features for the feret dataset and 100 accuracy for the orl dataset using 88 features

the numerical solution of weakly singular volterra integral equations by collocation on graded meshes since the solution of a second kind volterra integral equation with weakly singular kernel has in general unbounded derivatives at the left endpoint of the interval of integration its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates in this paper we investigate the convergence rates with respect to graded meshes and we discuss the problem of how to select the quadrature formulas to obtain the fully discretized collocation equation

boundaries of geometrically finite groups we show that the limit set of a relatively hyperbolic group with no separating horoball is locally connected if it is connected on the other hand if there is a separating horoball centred on a parabolic point one obtains a non trivial splitting of the group over a parabolic subgroup relative to the maximal parabolic subgroups together with results from elsewhere one deduces that if gamma is a relatively hyperbolic group such that each maximal parabolic subgroup is one or two ended finitely presented and contains no infinite torsion subgroup then the boundary of gamma is locally connected if it is connected as a corollary we see that the limit set of a geometrically finite group acting on a complete simply connected manifold of pinched negative curvature must be locally connected if it is connected

peripheral splittings of groups we define the notion of a peripheral splitting of a group this is essentially a representation of the group as the fundamental group of a bipartite graph of groups where all the vertex groups of one colour are held fixed the peripheral subgroups we develop the theory of such splittings and prove an accessibility result the theory mainly applies to relatively hyperbolic groups with connected boundary where the peripheral subgroups are precisely the maximal parabolic subgroups we show that if such a group admits a non trivial peripheral splitting then its boundary has a global cut point moreover the non peripheral vertex groups of such a splitting are themselves relatively hyperbolic these results together with results from elsewhere show that under modest constraints on the peripheral subgroups the boundary of a relatively hyperbolic group is locally connected if it is connected in retrospect one further deduces that the set of global cut points in such a boundary has a simplicial treelike structure

in plane rotation and scale invariant clustering using dictionaries in this paper we present an approach that simultaneously clusters images and learns dictionaries from the clusters the method learns dictionaries and clusters images in the radon transform domain the main feature of the proposed approach is that it provides both in plane rotation and scale invariant clustering which is useful in numerous applications including content based image retrieval cbir we demonstrate the effectiveness of our rotation and scale invariant clustering method on a series of cbir experiments experiments are performed on the smithsonian isolated leaf kimia shape and brodatz texture datasets our method provides both good retrieval performance and greater robustness compared to standard gabor based and three state of the art shape based methods that have similar objectives

acylindrical accessibility for groups we define the notion of acylindrical graph of groups of a group we bound the combinatorics of these graphs of groups for f g freely indecomposable groups our arguments imply the finiteness of acylindrical surfaces in closed 3 manifolds ha finiteness of isomorphism classes of small splittings of torsion free freely indecomposable hyperbolic groups as well as finiteness results for small splittings of f g kleinian and semisimple discrete groups acting on non positively curved simply connected manifolds in order to get our accessibility for f g groups we generalize parts of rips analysis of stable actions of f p groups on real trees to f g groups the concepts we present play an essential role in constructing the canonical jsj decomposition se1 ri se2 in obtaining the hopf property for hyperbolic groups se2 and in our study of sets of solutions to equations in a free group se3

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

a shape and texture based enhanced fisher classifier for face recognition this paper introduces a new face coding and recognition method the enhanced fisher classifier efc which employs the enhanced fisher linear discriminant model efm on integrated shape and texture features shape encodes the feature geometry of a face while texture provides a normalized shape free image the dimensionalities of the shape and the texture spaces are first reduced using principal component analysis constrained by the efm for enhanced generalization the corresponding reduced shape and texture features are then combined through a normalization procedure to form the integrated features that are processed by the efm for face recognition experimental results using 600 face images corresponding to 200 subjects of varying illumination and facial expressions show that 1 the integrated shape and texture features carry the most discriminating information followed in order by textures masked images and shape images and 2 the new coding and face recognition method efc performs the best among the eigenfaces method using l sub 1 or l sub 2 distance measure and the mahalanobis distance classifiers using a common covariance matrix for all classes or a pooled within class covariance matrix in particular efc achieves 98 5 recognition accuracy using only 25 features

dehn fillings and elementary splittings we consider conditions on relatively hyperbolic groups about the non existence of certain kinds of splittings and show these properties persist in long dehn fillings we deduce that certain connectivity properties of the bowditch boundary persist un

constructive proof for existence of nonlinear two point boundary value problems owing to the importance of differential equations in physics the existence of solutions for differential equations has been paid much attention in this paper the existence of solution are obtained for the nonlinear second order two point boundary value problem in the reproducing kernel space under certain assumptions on right hand side we propose constructive proof for the existence result and a method is presented to obtain the exact solution expressed by the form of series this paper is a extension of previous paper wei jiang minggen cui the exact solution and stability analysis for integral equation of third or first kind with singular kernel appl math comput 202 2 2008 666 674 which extends a method of solving linear problems to present method for solving nonlinear problems

pattern classification using projection pursuit abstract this article discusses the adaptation of recently developed regression techniques to classifier design apart from finite sample effects projection pursuit pp regression may be used to model a desired response class as a sum of ridge functions according to a minimum expected squared error criterion this approach can be shown to furnish an optimal discriminant function which can satisfy the neyman pearson criterion over all possible thresholds basis function expansions are used instead of smoothed histograms to reduce computation since good approximation of a discriminant by a linear combination of moderate number of ridge functions may not be easy we introduce an improved method utilizing a nonlinear weighting function

matching pursuit filters applied to face identification we present a face identification algorithm that automatically processes an unknown image by locating and identifying the face the heart of the algorithm is the use of pursuit filters a matching pursuit filter is an adapted wavelet expansion where the expansion is adapted to both the data and the pattern recognition problem being addressed for identification the filters find the features that differentiate among faces whereas for detection the filters encode the similarities among faces the filters are designed though a simultaneous decomposition of a training set into a two dimensional 2 d wavelet expansion this yields a representation that is explicitly 2 d and encodes information locally the algorithm uses coarse to fine processing to locate a small set of key facial features which are restricted to the nose and eye regions of the face the result is an algorithm that is robust to variations in facial expression hair style and the surrounding environment based on the locations of the facial features the identification module searches the data base for the identity of the unknown face using matching pursuit filters to make the identification the algorithm was demonstrated on three sets of images the first set was images from the feret data base the second set was infrared and visible images of the same people this demonstration was done to compare performance on infrared and visible images individually and on fusing the results from both modalities the third set was mugshot data from a law enforcement application

a new method for solving hilbert type singular integral equations abstract a simple method for solving hilbert type singular integral equations is proposed using the reproducing kernel as the basis of w 2 1 0 2 the singularity of the considered equation is removed skillfully since the problem is discussed in space w 2 1 0 2 which only require the absolute continuity of the considered function our method is effective not only for smooth solutions but also for non smooth solutions the final numerical examples show the efficiency of the proposed method

capitalize on dimensionality increasing techniques for improving face recognition grand challenge performance this paper presents a novel pattern recognition framework by capitalizing on dimensionality increasing techniques in particular the framework integrates gabor image representation a novel multiclass kernel fisher analysis kfa method and fractional power polynomial models for improving pattern recognition performance gabor image representation which increases dimensionality by incorporating gabor filters with different scales and orientations is characterized by spatial frequency spatial locality and orientational selectivity for coping with image variabilities such as illumination variations the kfa method first performs nonlinear mapping from the input space to a high dimensional feature space and then implements the multiclass fisher discriminant analysis in the feature space the significance of the nonlinear mapping is that it increases the discriminating power of the kfa method which is linear in the feature space but nonlinear in the input space the novelty of the kfa method comes from the fact that 1 it extends the two class kernel fisher methods by addressing multiclass pattern classification problems and 2 it improves upon the traditional generalized discriminant analysis gda method by deriving a unique solution compared to the gda solution which is not unique the fractional power polynomial models further improve performance of the proposed pattern recognition framework experiments on face recognition using both the feret database and the frgc face recognition grand challenge databases show the feasibility of the proposed framework in particular experimental results using the feret database show that the kfa method performs better than the gda method and the fractional power polynomial models help both the kfa method and the gda method improve their face recognition performance experimental results using the frgc databases show that the proposed pattern recognition framework improves face recognition performance upon the bee baseline algorithm and the lda based baseline algorithm by large margins

convergent algorithm for sensory receptive field development an unsupervised developmental algorithm for linear maps is derived which reduces the pixel entropy using the measure introduced in previous work at every update and thus removes pairwise correlations between pixels since the measure of pixel entropy has only a global minimum the algorithm is guaranteed to converge to the minimum entropy map such optimal maps have recently been shown to possess cognitively desirable properties and are likely to be used by the nervous system to organize sensory information the algorithm derived here turns out to be one proposed by goodall for pairwise decorrelation it is biologically plausible since in a neural network implementation it requires only data available locally to a neuron in training over ensembles of two dimensional input signals with the same spatial power spectrum as natural scenes networks develop output neurons with center surround receptive fields similar to those of ganglion cells in the retina some technical issues pertinent to developmental algorithms of this sort such as symmetry fixing are also discussed

cohomology of group theoretic dehn fillings i cohen lyndon type theorems abstract this is the first paper of three papers in a row aiming to study cohomology of group theoretic dehn fillings in the present paper we prove a particular free product structure which is termed the cohen lyndon property of dehn filling kernels as an application we describe the structure of relative relation modules of dehn fillings

word hyperbolic dehn surgery in the late 1970 s thurston dramatically changed the nature of 3 manifold theory with the introduction of his geometrisation conjecture and by proving it in the case of haken 3 manifolds 23 the conjecture for general closed orientable 3 manifolds remains perhaps the most important unsolved problem in the subject a weaker form of the conjecture 19 deals with the fundamental group of a closed orientable 3 manifold it proposes that either it contains z z as a subgroup or it is word hyperbolic in the sense of gromov 11 word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality they are of fundamental importance in geometric group theory and have very many useful properties

from projection pursuit and cart to adaptive discriminant analysis while many efforts have been put into the development of nonlinear approximation theory and its applications to signal and image compression encoding and denoising there seems to be very few theoretical developments of adaptive discriminant representations in the area of feature extraction selection and signal classification in this paper we try to advocate the idea that such developments and efforts are worthwhile based on the theoretical study of a data driven discriminant analysis method on a simple yet instructive example we consider the problem of classifying a signal drawn from a mixture of two classes using its projections onto low dimensional subspaces unlike the linear discriminant analysis lda strategy which selects subspaces that do not depend on the observed signal we consider an adaptive sequential selection of projections in the spirit of nonlinear approximation and classification and regression trees cart at each step the subspace is enlarged in a direction that maximizes the mutual information with the unknown class we derive explicit characterizations of this adaptive discriminant analysis ada strategy in two situations when the two classes are gaussian with the same covariance matrix but different means the adaptive subspaces are actually nonadaptive and can be computed with an algorithm similar to orthonormal matching pursuit when the classes are centered gaussians with different covariances the adaptive subspaces are spanned by eigen vectors of an operator given by the covariance matrices just as could be predicted by regular lda however we prove that the order of observation of the components along these eigen vectors actually depends on the observed signal numerical experiments on synthetic data illustrate how data dependent features can be used to outperform lda on a classification task and we discuss how our results could be applied in practice

sparse representation for coarse and fine object recognition this paper offers a sparse multiscale representation of objects it captures the object appearance by selection from a very large dictionary of gaussian differential basis functions the learning procedure results from the matching pursuit algorithm while the recognition is based on polynomial approximation to the bases turning image matching into a problem of polynomial evaluation the method is suited for coarse recognition between objects and by adding more bases also for fine recognition of the object pose the advantages over the common representation using pca include storing sampled points for recognition is not required adding new objects to an existing data set is trivial because retraining other object models is not needed and significantly in the important case where one has to scan an image over multiple locations in search for an object the new representation is readily available as opposed to pca projection at each location the experimental result on the coil 100 data set demonstrates high recognition accuracy with real time performance