approximate tree kernels convolution kernels for trees provide simple means for learning with tree structured data the computation time of tree kernels is quadratic in the size of the trees since all pairs of nodes need to be compared thus large parse trees obtained from html documents or structured network data render convolution kernels inapplicable in this article we propose an effective approximation technique for parse tree kernels the approximate tree kernels atks limit kernel computation to a sparse subset of relevant subtrees and discard redundant structures such that training and testing of kernel based learning methods are significantly accelerated we devise linear programming approaches for identifying such subsets for supervised and unsupervised learning tasks respectively empirically the approximate tree kernels attain run time improvements up to three orders of magnitude while preserving the predictive accuracy of regular tree kernels for unsupervised tasks the approximate tree kernels even lead to more accurate predictions by identifying relevant dimensions in feature space

a linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions a sequential algorithm is presented for computing the exact euclidean distance transform dt of a k dimensional binary image in time linear in the total number of voxels n the algorithm which is based on dimensionality reduction and partial voronoi diagram construction can be used for computing the dt for a wide class of distance functions including the l sub p and chamfer metrics at each dimension level the dt is computed by constructing the intersection of the voronoi diagram whose sites are the feature voxels with each row of the image this construction is performed efficiently by using the dt in the next lower dimension the correctness and linear time complexity are demonstrated analytically and verified experimentally the algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast not only does it run in o n time but the time constant is small a simple modification of the algorithm computes the weighted euclidean dt which is useful for images with anisotropic voxel dimensions a parallel version of the algorithm runs in o n p time with p processors

svm decision boundary based discriminative subspace induction we study the problem of linear dimension reduction for classification with a focus on sufficient dimension reduction i e finding subspaces without loss of discrimination power first we formulate the concept of sufficient subspace for classification in parallel terms as for regression then we present a new method to estimate the smallest sufficient subspace based on an improvement of decision boundary analysis dba the main idea is to combine dba with support vector machines svm to overcome the inherent difficulty of dba in small sample size situations while keeping dba s estimation simplicity the compact representation of svm boundary results in a significant gain in both speed and accuracy over previous dba implementations alternatively this technique can be viewed as a way to reduce the run time complexity of svm itself comparative experiments on one simulated and four real world benchmark datasets highlight the superior performance of the proposed approach

rotation invariant texture classification using a complete space frequency model a method of rotation invariant texture classification based on a complete space frequency model is introduced a polar analytic form of a two dimensional 2 d gabor wavelet is developed and a multiresolution family of these wavelets is used to compute information conserving microfeatures from these microfeatures a micromodel which characterizes spatially localized amplitude frequency and directional behavior of the texture is formed the essential characteristics of a texture sample its macrofeatures are derived from the estimated selected parameters of the micromodel classification of texture samples is based on the macromodel derived from a rotation invariant subset of macrofeatures in experiments comparatively high correct classification rates were obtained using large sample sets

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

scaled and rotated texture classification using a class of basis functions abstract three classes of basis functions are considered for classifying scaled and rotated textured images the first is the orthonormal compactly supported daubechies and the discrete haar bases the second is the biorthogonal basis and the third is the non orthogonal gabor basis textures are scaled and rotated and the basis functions are used to expand them features are computed on a combination of inter resolution coefficients experimental results show that the daubechies orthonormal basis perform well in recognizing transformed textures followed by the haar basis the concept of multiresolution representation and orthogonality are shown to be useful for invariant texture classificaiton

on the minimal dimension of sufficient statistics the minimal dimension of sufficient continuous statistics for a finite family of continuous probability density functions is determined the relation between sufficient statistics and optimal statistics in the context of pattern recognition systems is studied and the application of the main result to the case of exponential families is discussed

gaussian mrf rotation invariant features for image classification features based on markov random field mrf models are sensitive to texture rotation this paper develops an anisotropic circular gaussian mrf acgmrf model for retrieving rotation invariant texture features to overcome the singularity problem of the least squares estimate method an approximate least squares estimate method is designed and implemented rotation invariant features are obtained from the acgmrf model parameters using the discrete fourier transform the acgmrf model is demonstrated to be a statistical improvement over three published methods the three methods include a laplacian pyramid an isotropic circular gmrf icgmrf and gray level cooccurrence probability features

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

output frequency response characteristics of nonlinear systems part ii overlapping effects and commensurate multi tone excitations the output response of nonlinear systems is strongly dependent on the extent to which different input frequency combinations intermodulations overlap one another and contribute to a common output frequency component this makes it hard to determine the actual number of output frequencies or to determine which of the many possible combinations contribute to a specified output frequency of interest systematic algorithms are presented for resolving these issues in a manner which is both efficient and straightforward to implement on a computer three broad classes of input are considered multi tone but nominally incommensurate sinusoids multi tone harmonically related sinusoids and multi tone excitations that are equi spaced in frequency the considered inputs also admit the possibility of a dc bias component since this can significantly affect the system response the algorithms are therefore applicable to a broad range of practical inputs and their use and benefits are illustrated with several examples

output frequency response characteristics of nonlinear systems part i general multi tone inputs a systematic algorithm for determining the output frequencies generated by a nonlinear system subject to a general multi tone input including a bias input is presented the algorithm is very efficient and circumvents many of the difficulties of duplicate frequencies that are often generated using previous methods the inclusion of the dc bias component in the analysis is also important because of the significant effect that non zero mean inputs can have on nonlinear system response the algorithm is straightforward to implement on a computer and the results are illustrated by means of an example

toward a theory of statistical tree shape analysis to develop statistical methods for shapes with a tree structure we construct a shape space framework for tree shapes and study metrics on the shape space this shape space has singularities which correspond to topological transitions in the represented trees we study two closely related metrics on the shape space ted and qed qed is a quotient euclidean distance arising naturally from the shape space formulation while ted is the classical tree edit distance using gromov s metric geometry we gain new insight into the geometries defined by ted and qed we show that the new metric qed has nice geometric properties that are needed for statistical analysis geodesics always exist and are generically locally unique following this we can also show the existence and generic local uniqueness of average trees for qed ted while having some algorithmic advantages does not share these advantages along with the theoretical framework we provide experimental proof of concept results on synthetic data trees as well as small airway trees from pulmonary ct scans this way we illustrate that our framework has promising theoretical and qualitative properties necessary to build a theory of statistical tree shape analysis

a nonparametric regression model with tree structured response developments in science and technology over the last two decades has motivated the study of complex data objects in this article we consider the topological properties of a population of tree structured objects our interest centers on modeling the relationship between a tree structured response and other covariates for tree structured objects this poses serious challenges since most regression methods rely on linear operations in euclidean space we generalize the notion of nonparametric regression to the case of a tree structured response variable in addition we develop a fast algorithm and give its theoretical justification we implement the proposed method to analyze a dataset of human brain artery trees an important lesson is that smoothing in the full tree space can reveal much deeper scientific insights than the simple smoothing of summary statistics this article has supplementary materials online

an optimal transformation for discriminant and principal component analysis a general method is proposed to describe multivariate data sets using discriminant analysis and principal component analysis first the problem of finding k discriminant vectors in an l class data set is solved and compared to the solution proposed in the literature for two class problems and the classical solution for l class data sets it is shown that the method proposed is better than the classical method for l classes and is a generalization of the optimal set of discriminant vectors proposed for two class problems then the method is combined with a generalized principal component analysis to permit the user to define the properties of each successive computed vector all the methods were tested using measurements made on various kinds of flowers iris data

object oriented data analysis sets of trees object oriented data analysis is the statistical analysis of populations of complex objects in the special case of functional data analysis these data objects are curves where standard euclidean approaches such as principal component analysis have been very successful recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non euclidean spaces such as lie groups and symmetric spaces or of strongly non euclidean spaces such as spaces of tree structured data objects these new contexts for object oriented data analysis create several potentially large new interfaces between mathematics and statistics this point is illustrated through the careful development of a novel mathematical framework for statistical analysis of populations of tree structured objects

clustering tree structured data on manifold tree structured data usually contain both topological and geometrical information and are necessarily considered on manifold instead of euclidean space for appropriate data parameterization and analysis in this study we propose a novel tree structured data parameterization called topology attribute matrix t a matrix so the data clustering task can be conducted on matrix manifold we incorporate the structure constraints embedded in data into the non negative matrix factorization method to determine meta trees from the t a matrix and the signature vector of each single tree can then be extracted by meta tree decomposition the meta tree space turns out to be a cone space in which we explore the distance metric and implement the clustering algorithm based on the concepts like frechet mean finally the t a matrix based clustering tambac framework is evaluated and compared using both simulated data and real retinal images to illustrate its efficiency and accuracy

face recognition based on the uncorrelated discriminant transformation abstract the extraction of discriminant features is the most fundamental and important problem in face recognition this paper presents a method to extract optimal discriminant features for face images by using the uncorrelated discriminant transformation and kl expansion experiments on the orl database and the nust603 database have been performed experimental results show that the uncorrelated discriminant transformation is superior to the foley sammon discriminant transformation and the new method to extract uncorrelated discriminant features for face images is very effective an error rate of 2 5 is obtained with the experiments on the orl database an average error rate of 1 2 is obtained with the experiments on the nust603 database experiments show that by extracting uncorrelated discriminant features face recognition could be performed with higher accuracy on lower than 16 16 resolution mosaic images it is suggested that for the uncorrelated discriminant transformation the optimal face image resolution can be regarded as the resolution m n which makes the dimensionality n mn of the original image vector space be larger and closer to the number of known face classes

principal components analysis in the space of phylogenetic trees phylogenetic analysis of dna or other data commonly gives rise to a collection or sample of inferred evolutionary trees principal components analysis pca cannot be applied directly to collections of trees since the space of evolutionary trees on a fixed set of taxa is not a vector space this paper describes a novel geometrical approach to pca in tree space that constructs the first principal path in an analogous way to standard linear euclidean pca given a data set of phylogenetic trees a geodesic principal path is sought that maximizes the variance of the data under a form of projection onto the path due to the high dimensionality of tree space and the nonlinear nature of this problem the computational complexity is potentially very high so approximate optimization algorithms are used to search for the optimal path principal paths identified in this way reveal and quantify the main sources of variation in the original collection of trees in terms of both topology and branch lengths the approach is illustrated by application to simulated sets of trees and to a set of gene trees from metazoan animal species

bayes error estimation using parzen and k nn procedures the use of k nearest neighbor k nn and parzen density estimates to obtain estimates of the bayes error is investigated under limited design set conditions by drawing analogies between the k nn and parzen procedures new procedures are suggested and experimental results are given which indicate that these procedures yield a significant improvement over the conventional k nn and parzen procedures we show that by varying the decision threshold many of the biases associated with the k nn or parzen density estimates may be compensated and successful error estimation may be performed in spite of these biases experimental results are given which demonstrate the effect of kernel size and shape parzen the size of k k nn and the number of samples in the design set

bayes optimality motivated linear and multilayered perceptron based dimensionality reduction dimensionality reduction is the process of mapping high dimension patterns to a lower dimension subspace when done prior to classification estimates obtained in the lower dimension subspace are more reliable for some classifiers there is also an improvement in performance due to the removal of the diluting effect of redundant information a majority of the present approaches to dimensionality reduction are based on scatter matrices or other statistics of the data which do not directly correlate to classification accuracy the optimality criteria of choice for the purposes of classification is the bayes error usually however bayes error is difficult to express analytically we propose an optimality criteria based on an approximation of the bayes error and use it to formulate a linear and a nonlinear method of dimensionality reduction the nonlinear method we propose relies on using a multilayered perceptron which produces as output the lower dimensional representation it thus differs from autoassociative like multilayered perceptrons which have been proposed and used for dimensionality reduction our results show that the nonlinear method is as anticipated superior to the linear method in that it can perform unfolding of a nonlinear manifold in addition the nonlinear method we propose provides substantially better lower dimension representation for classification purposes than fisher s linear discriminant fld and two other nonlinear methods of dimensionality reduction that are often used

optimization methods on riemannian manifolds and their application to shape space we extend the scope of analysis for linesearch optimization algorithms on possibly infinite dimensional riemannian manifolds to the convergence analysis of the bfgs quasi newton scheme and the fletcher reeves conjugate gradient iteration numerical implementations for exemplary problems in shape spaces show the practical applicability of these methods

finding defects in texture using regularity and local orientation abstract we address basic aspects of detection of structural defects in regular and flow like patterns textures humans are able to find such defects without prior knowledge of the defect free pattern this capability to perceive local disorder has not attracted proper attention in machine vision despite its obvious relation to various application areas e g industrial texture inspection instead numerous ad hoc techniques have been developed to locate particular sorts of defects for particular tasks although useful these techniques do not help us understand the nature of structural defects which is the primary goal of our study in no attempt to compete with the existing dedicated algorithms we approach texture defects based on two fundamental structural properties regularity and local orientation anisotropy the two properties belong to a hierarchy of structural descriptions with the former being a higher level one than the latter both properties have great perceptual value in this study they are assumed to underlie recognition of structural defects defects are viewed as inhomogeneities in regularity and orientation fields two distinct but conceptually related approaches are presented the first one defines structural defects as regions of abruptly falling regularity the second one as perturbations in the dominant orientation both methods are general in the sense that each of them is applicable to a variety of patterns and defects however they are better suited to different kinds of patterns two tests are presented to assess and compare the two methods in the first test diverse textures are processed individually and defects are searched in each pattern in the second test classified defects in groups of textiles are considered conclusions concerning the scopes of the two approaches are drawn

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

local frequency features for texture classification abstract we propose a texture feature extraction method which allows very small training sets and due to its very local nature is suitable for classification of small textured structures the method is based on detection of local extremas along a set of direction vectors in the spatial image representation the local extremas are interpreted as identifying local frequencies and used to design features corresponding to the basal frequency characteristics amplitude and wavelength the good texture discrimination ability of these features is demonstrated on two images and in a quantitative comparison with features from gabor filtered images and co occurrence matrix features of the three images used in the quantitative comparison the local frequency features performed best on two of them we conclude that the new method is a promising feature extraction method for non stochastic textures and that it should be further explored

polynomial time metrics for attributed trees we address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree the proposed measures are general and defined on trees endowed with either symbolic or continuous valued attributes and can be applied to rooted as well as unrooted trees we prove that our measures satisfy the metric constraints and provide a polynomial time algorithm to compute them this is a remarkable and attractive property since the computation of traditional edit distance based metrics is in general np complete at least in the unordered case we experimentally validate the usefulness of our metrics on shape matching tasks and compare them with an approximation of edit distance

the gauss bonnet theorem for cone manifolds and volumes of moduli spaces this paper generalizes the gauss bonnet formula to a class of stratied spaces called riemannian cone manifolds as an application we compute the volumes of the moduli spacesm0 n with respect to the complex hyperbolic metrics introduced by picard deligne mostow and thurston

multiclass linear dimension reduction by weighted pairwise fisher criteria we derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the well known k class fisher criterion associated with linear discriminant analysis lda it can be seen that lda weights contributions of individual class pairs according to the euclidean distance of the respective class means we generalize upon lda by introducing a different weighting function

invariant and adaptive geometrical texture features for defect detection and classification automatic texture defect detection is highly important for many fields of visual inspection we introduce novel geometrical texture features for this task which are euclidean motion invariant and texture adaptive an algebraic function rational pade or polynomial is integrated over intensities in local circular neighborhoods on the image including an anisotropical texture analysis adaptiveness is achieved through the optimization of this feature kernel and further coefficients based on a simplex energy minimization constrained by a measure of texture discrimination fisher criterion a backpropagation trained multilayer perceptron network classifies the textures locally our approach contains new properties usually not common in feature theories theoretically implicit multiple invariances and an automatic and specific adaptation of the features to the texture images experiments with a fabric data set and brodatz textures reveal up to 98 6 recognition accuracy

automatic computation of polyharmonic balance equations for non linear differential systems an automated algorithm is presented which enables the harmonic balance equations for any polynomial type pure or cross product non linear differential system to be written down directly in terms of the coefficients of the governing equation and the complex amplitudes of a general harmonic waveform the system frequency response in the form of a multi input amplitude dependent describing function is therefore readily computed the method is illustrated by means of an example and the results validated against detailed numeric simulation

orthogonalized fisher discriminant abstract the foley sammon discriminant fsd exhibits higher performance in face recognition than the fisher linear discriminant due to its elimination of dependences among discriminant vectors but its theory is complex and the calculation is time expensive the orthogonalized fisher discriminant ofd which also derives a set of orthogonal discriminant vectors is very simple and easy to implement experiments show that ofd is more effective and efficient than fsd in pattern recognition

brief review of invariant texture analysis methods this paper considers invariant texture analysis texture analysis approaches whose performances are not affected by translation rotation affine and perspective transform are addressed existing invariant texture analysis algorithms are carefully studied and classified into three categories statistical methods model based methods and structural methods the importance of invariant texture analysis is presented first each approach is reviewed according to its classification and its merits and drawbacks are outlined the focus of possible future work is also suggested

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

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