learning the kernel with hyperkernels this paper addresses the problem of choosing a kernel suitable for estimation with a support vector machine hence further automating machine learning this goal is achieved by defining a reproducing kernel hilbert space on the space of kernels itself such a formulation leads to a statistical estimation problem similar to the problem of minimizing a regularized risk functional we state the equivalent representer theorem for the choice of kernels and present a semidefinite programming formulation of the resulting optimization problem several recipes for constructing hyperkernels are provided as well as the details of common machine learning problems experimental results for classification regression and novelty detection on uci data show the feasibility of our approach

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

a common fixed point theorem for compatible quasi contractive self mappings in metric spaces a common fixed point theorem for weakly commuting quasi contractive self mappings with contracting orbital diameters in metric spaces v berinde a common fixed point theorem for quasi contractive type mappings ann univ sci budapest 46 2003 81 90 is extended to the more general class of compatible quasi contractive self mappings our result does extend and generalize numerous related results in literature

rapid and brief communication learning the kernel parameters in kernel minimum distance classifier choosing appropriate values for kernel parameters is one of the key problems in many kernel based methods because the values of these parameters have significant impact on the performances of these methods in this paper a novel approach is proposed to learn the kernel parameters in kernel minimum distance kmd classifier where the values of the kernel parameters are computed through optimizing an objective function designed for measuring the classification reliability of kmd experiments on both artificial and real world datasets show that the proposed approach works well on learning kernel parameters of kmd

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

kernel based equiprobabilistic topographic map formation we introduce a new unsupervised competitive learning rule the kernel based maximum entropy learning rule kmer which performs equiprobabilistic topographic map formation in regular fixed topology lattices for use with nonparametric density estimation as well as nonparametric regression analysis the receptive fields of the formal neurons are overlapping radially symmetric kernels compatible with radial basis functions rbfs but unlike other learning schemes the radii of these kernels do not have to be chosen in an ad hoc manner the radii are adapted to the local input density together with the weight vectors that define the kernel centers so as to produce maps of which the neurons have an equal probability to be active equiprobabilistic maps both an online and a batch version of the learning rule are introduced which are applied to nonparametric density estimation and regression respectively the application envisaged is blind source separation bss from nonlinear noisy mixtures

locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image we present a novel method of nonlinear discriminant analysis involving a set of locally linear transformations called locally linear discriminant analysis llda the underlying idea is that global nonlinear data structures are locally linear and local structures can be linearly aligned input vectors are projected into each local feature space by linear transformations found to yield locally linearly transformed classes that maximize the between class covariance while minimizing the within class covariance in face recognition linear discriminant analysis lida has been widely adopted owing to its efficiency but it does not capture nonlinear manifolds of faces which exhibit pose variations conventional nonlinear classification methods based on kernels such as generalized discriminant analysis gda and support vector machine svm have been developed to overcome the shortcomings of the linear method but they have the drawback of high computational cost of classification and overfitting our method is for multiclass nonlinear discrimination and it is computationally highly efficient as compared to gda the method does not suffer from overfitting by virtue of the linear base structure of the solution a novel gradient based learning algorithm is proposed for finding the optimal set of local linear bases the optimization does not exhibit a local maxima problem the transformation functions facilitate robust face recognition in a low dimensional subspace under pose variations using a single model image the classification results are given for both synthetic and real face data

optimizing the kernel in the empirical feature space in this paper we present a method of kernel optimization by maximizing a measure of class separability in the empirical feature space an euclidean space in which the training data are embedded in such a way that the geometrical structure of the data in the feature space is preserved employing a data dependent kernel we derive an effective kernel optimization algorithm that maximizes the class separability of the data in the empirical feature space it is shown that there exists a close relationship between the class separability measure introduced here and the alignment measure defined recently by cristianini extensive simulations are carried out which show that the optimized kernel is more adaptive to the input data and leads to a substantial sometimes significant improvement in the performance of various data classification algorithms

optimizing the data dependent kernel under a unified kernel optimization framework the kernel functions play a central role in kernel methods accordingly over the years the optimization of kernel functions has been a promising research area ideally fisher discriminant criteria can be used as an objective function to optimize the kernel function to augment the margin between different classes unfortunately fisher criteria are optimal only in the case that all the classes are generated from underlying multivariate normal distributions of common covariance matrix but different means and each class is expressed by a single cluster due to the assumptions fisher criteria obviously are not a suitable choice as a kernel optimization rule in some applications such as the multimodally distributed data in order to solve this problem recently many improved discriminant criteria dc have been also developed therefore to apply these discriminant criteria to kernel optimization in this paper based on a data dependent kernel function we propose a unified kernel optimization framework which can use any discriminant criteria formulated in a pairwise manner as the objective functions under the kernel optimization framework to employ different discriminant criteria one has to only change the corresponding affinity matrices without having to resort to any complex derivations in feature space experimental results based on some benchmark data demonstrate the efficiency of our method

measurement of the hyperelastic properties of ex vivo brain tissue slices abstract the elastic and hyperelastic properties of brain tissue are of interest to the medical research community as there are several applications where accurate characterization of these properties is crucial for an accurate outcome the linear response is applicable to brain elastography while the non linear response is of interest for surgical simulation programs because of the biological differences between gray and white matter it is reasonable to expect a difference in their mechanical properties the goal of this work is to characterize the elastic and hyperelastic properties of the brain gray and white matter in this method force displacement data of these tissues were acquired from 25 different brain samples using an indentation apparatus these data were processed with an inverse problem algorithm using finite element method as the forward problem solver young s modulus and the hyperelastic parameters corresponding to the commonly used polynomial yeoh arruda boyce and ogden models were obtained the parameters characterizing the linear and non linear mechanical behavior of gray and white matters were found to be significantly different young s modulus was 1787 186 and 1195 157 pa for white matter and gray matter respectively among hyperelastic models due to its accuracy fewer parameters and shorter computational time requirements yeoh model was found to be the most suitable due to the significant differences between the linear and non linear tissue response we conclude that incorporating these differences into brain biomechanical models is necessary to increase accuracy

nonlinear contraction theorems in probabilistic spaces abstract in this paper first we prove a common fixed point theorem in menger probabilistic metric spaces then we present a nonlinear contraction case of jungck s common fixed point theorem in menger probabilistic metric spaces finally we prove a common fixed point theorem for six self maps in a menger probabilistic metric space

group differences in measures of voice production and revised values of maximum airflow declination rate in previous reports aerodynamic and acoustic measures of voice production were presented for groups of normal male and female speakers holmberg et al j acoust soc am 84 511 529 1988 j voice 3 294 305 1989 that were used as norms in studies of voice disorders hillman et al j speech hear res 32 373 392 1989 j voice 4 52 63 1990 several of the measures were extracted from glottal airflow waveforms that were derived by inverse filtering a high time resolution oral airflow signal recently the methods have been updated and a new study of additional subjects has been conducted this report presents previous 1988 and current 1993 group mean values of sound pressure level fundamental frequency maximum airflow declination rate ac flow peak flow minimum flow ac dc ratio inferred subglottal air pressure average flow and glottal resistance statistical tests indicate overall group differences and differences for values of several individual parameters between the 1988 and 1993 studies some inter study differences in parameter values may be due to sampling effects and minor methodological differences however a comparative test of 1988 and 1993 inverse filtering algorithms shows that some lower 1988 values of maximum flow declination rate were due at least in part to excessive low pass filtering in the 1988 algorithm the observed differences should have had a negligible influence on the conclusions of our studies of voice disorders

logarithm bispectrum based approach to radar range profile for automatic target recognition abstract the paper starts by the definition of logarithm bispectrum and the presentation of its properties relative to target recognition a relationship is established between the logarithm bispectrum feature of a target and that of its high resolution range profile as a result the criterion for target recognition based on the relationship is induced and its scheme and pseudocode for implementation are given simulation with some acquired outfield data is given to show that the approach is effective and advantageous in both rapid recognition and easy computation

radar hrrp target recognition based on higher order spectra radar high resolution range profile hrrp is very sensitive to time shift and target aspect variation therefore hrrp based radar automatic target recognition ratr requires efficient time shift invariant features and robust feature templates although higher order spectra are a set of well known time shift invariant features direct use of them except for power spectrum is impractical due to their complexity a method for calculating the euclidean distance in higher order spectra feature space is proposed in this paper which avoids calculating the higher order spectra effectively reducing the computation complexity and storage requirement moreover according to the widely used scattering center model theoretical analysis and experimental results in this paper show that the feature vector extracted from the average profile in a small target aspect sector has better generalization performance than the average feature vector in the same sector when both of them are used as feature templates in hrrp based ratr the proposed euclidean distance calculation method and average profile based template database are applied to two classification algorithms the template matching method tmm and the radial basis function network rbfn to evaluate the recognition performances of higher order spectra features experimental results for measured data show that the power spectrum has the best recognition performance among higher order spectra

some common fixed point theorems for weakly compatible mappings abstract jungck s g jungck compatible mappings and common fixed points int j math math sci 9 1986 771 779 notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non self mappings in complete convex metric spaces we improve on the method of proof used by rhoades b e rhoades a fixed point theorem for non self set valued mappings int j math math sci 20 1997 9 12 and ahmed and rhoades a ahmed b e rhoades some common fixed point theorems for compatible mappings indian j pure appl math 32 2001 1247 1254 and obtain generalization of some known results in particular a theorem by rhoades b e rhoades a fixed point theorem for non self set valued mappings int j math math sci 20 1997 9 12 is generalized and improved

adaptive quasiconformal kernel nearest neighbor classification nearest neighbor classification assumes locally constant class conditional probabilities this assumption becomes invalid in high dimensions due to the curse of dimensionality severe bias can be introduced under these conditions when using the nearest neighbor rule we propose an adaptive nearest neighbor classification method to try to minimize bias we use quasiconformal transformed kernels to compute neighborhoods over which the class probabilities tend to be more homogeneous as a result better classification performance can be expected the efficacy of our method is validated and compared against other competing techniques using a variety of data sets

from sample similarity to ensemble similarity probabilistic distance measures in reproducing kernel hilbert space this paper addresses the problem of characterizing ensemble similarity from sample similarity in a principled manner using a reproducing kernel as a characterization of sample similarity we suggest a probabilistic distance measure in the reproducing kernel hilbert space rkhs as the ensemble similarity assuming normality in the rkhs we derive analytic expressions for probabilistic distance measures that are commonly used in many applications such as chernoff distance or the bhattacharyya distance as its special case kullback leibler divergence etc since the reproducing kernel implicitly embeds a nonlinear mapping our approach presents a new way to study these distances whose feasibility and efficiency is demonstrated using experiments with synthetic and real examples further we extend the ensemble similarity to the reproducing kernel for ensemble and study the ensemble similarity for more general data representations

pulse wave propagation in a model human arterial network assessment of 1 d visco elastic simulations against in vitro measurements a numerical model based on the nonlinear one dimensional 1 d equations of pressure and flow wave propagation in conduit arteries is tested against a well defined experimental 1 1 replica of the human arterial tree the tree consists of 37 silicone branches representing the largest central systemic arteries in the human including the aorta carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs the set up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow terminal branches end in simple resistance models consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure the parameters required by the numerical algorithm are directly measured in the in vitro set up and no data fitting is involved comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1 d time domain formulation to capture the main features of pulse wave propagation measured throughout the system test as a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation the experimental set up generates waveforms at terminal branches with additional non physiological oscillations the frequencies of these oscillations are well captured by the 1 d model even though amplitudes are overestimated adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect suggesting that wall visco elasticity might play an important role in the experimental results nevertheless average relative root mean square errors between simulations and experimental waveforms are smaller than 4 for pressure and 19 for the flow at all 70 locations studied

infinite max margin factor analysis via data augmentation this paper addresses the bayesian estimation of the discriminative probabilistic latent models especially the mixture models we develop the max margin factor analysis mmfa model which utilizes the latent variable support vector machine lvsvm as the classification criterion in the latent space to learn a discriminative subspace with max margin constraint furthermore to deal with multimodally distributed data we further extend mmfa to infinite gaussian mixture model and develop the infinite max margin factor analysis immfa model via the consideration of dirichlet process mixtures dpm it jointly learns clustering max margin classifiers and the discriminative latent space in a united framework to improve the prediction performance moreover both of mmfa and immfa are natural to handle outlier rejection problem since the observations are described by a single or a mixture of gaussian distributions additionally thanks to the conjugate property the parameters in the two models can be inferred efficiently via the simple gibbs sampler finally we implement our models on synthesized and real world data including multimodally distributed datasets and measured radar echo data to validate the classification and rejection performance of the proposed models jointly learning fa and svm mmfa is proposed to get a discriminative subspace clustering the dataset in the subspace by dpm mmfa is extended to immfa thanks to the jointly learning framework they gain good prediction performance having the data description ability the proposed models can reject outlier samples in bayesian framework parameters can be inferred efficiently by the gibbs sampler

coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces abstract in this paper we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems under contractive conditions for self maps in partially ordered complete probabilistic metric spaces

nonlinear kernel based statistical pattern analysis the eigenstructure of the second order statistics of a multivariate random population can be inferred from the matrix of pairwise combinations of inner products of the samples therefore it can be also efficiently obtained in the implicit high dimensional feature spaces defined by kernel functions we elaborate on this property to obtain general expressions for immediate derivation of nonlinear counterparts of a number of standard pattern analysis algorithms including principal component analysis data compression and denoising and fisher s discriminant the connection between kernel methods and nonparametric density estimation is also illustrated using these results we introduce the kernel version of mahalanobis distance which originates nonparametric models with unexpected and interesting properties and also propose a kernel version of the minimum squared error mse linear discriminant function this learning machine is particularly simple and includes a number of generalized linear models such as the potential functions method or the radial basis function rbf network our results shed some light on the relative merit of feature spaces and inductive bias in the remarkable generalization properties of the support vector machine svm although in most situations the svm obtains the lowest error rates exhaustive experiments with synthetic and natural data show that simple kernel machines based on pseudoinversion are competitive in problems with appreciable class overlapping

a kernel optimization method based on the localized kernel fisher criterion it is widely recognized that whether the selected kernel matches the data determines the performance of kernel based methods ideally it is expected that the data is linearly separable in the kernel induced feature space therefore fisher linear discriminant criterion can be used as a cost function to optimize the kernel function however the data may not be linearly separable even after kernel transformation in many applications e g the data may exist as multimodally distributed structure in this case a nonlinear classifier is preferred and obviously fisher criterion is not a suitable choice as kernel optimization rule motivated by this issue we propose a localized kernel fisher criterion instead of traditional fisher criterion as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space experimental results based on some benchmark data and measured radar high resolution range profile hrrp data show that the classification performance can be improved by using the proposed method

a comparison of cross validation techniques in density estimation in the setting of nonparametric multivariate density estimation theorems are established which allow a comparison of the kullback leibler and the least squares cross validation methods of smoothing parameter selection the family of delta sequence estimators including kemel orthogonal series histogram and histospline estimators is considered these theorems also show that either type of cross validation can be used to compare different estimators e g kernel versus orthogonal series 1 introduction consider the problem of trying to estimate a d dimensional probability density function f x using a random sample xl xn from f most proposed estimators of f depend on a smoothing parameter say x e dr whose selection is crucial to the performance of the estimator in this paper for the large class of delta sequence estimators theorems are obtained which allow comparison of two smoothing parameter selectors which are known to be asymptotically optimal an important consequence of these results is that either smoothing parameter selector may be used for a data based comparison of two density estimators for example kernel versus orthogonal series another attractive feature of these results is that they are set in a quite general framework special cases of which provide simpler proofs of several recent asymptotic optimality results in sections 2 and 3 the family of delta sequence estimators and the smoothing parameter selectors are given the theorems are stated in section 4 with some remarks in section 5 the rest of the paper consists of proofs

a coupled coincidence point result in partially ordered metric spaces for compatible mappings abstract in this paper we introduce the notion of compatibility of mappings in a partially ordered metric space and use this notion to establish a coupled coincidence point result our work extends the work of bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 an example is also given

common fixed point theorems of compatible and weakly compatible maps in menger spaces abstract in this paper we prove some new common fixed point theorems for compatible and weakly compatible self maps on menger space under contractive conditions our results improve and generalize the results of singh and jain b singh s jain a fixed point theorem in menger space through weak compatibility j math anal appl 301 2005 439 448 razani and shirdaryazdi a razani m shirdaryazdi a common fixed point theorem of compatible maps in menger space chaos solitons fractals 32 2007 26 34 and others

nonlinear coupled coincidence and coupled fixed point theorems for not necessary commutative contractive mappings in partially ordered probabilistic metric spaces in this paper we introduce the notion of compatibility of mappings in partially ordered probabilistic metric spaces and use this notion to establish a coupled coincidence point result very recently hu and ma xin qi hu xiao yan ma coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces nonlinear anal 74 2011 6451 6458 proved coupled coincidence point theorems for commuting mappings in partially ordered probabilistic metric spaces in this paper we proved results of hu and ma under a different set of conditions precisely we establish our results by assuming that two mappings on a partially ordered probabilistic metric spaces are compatible not necessary commutative and satisfy a more general contractive condition than the contractive condition in the main theorem of hu and ma our results improve and extend a coupled coincidence point theorem due to hu and ma as well as a coupled fixed point theorem due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 an example is given to support our result

effect of low pass filtering on joint moments from inverse dynamics implications for injury prevention analyses of joint moments are important in the study of human motion and are crucial for our understanding of e g how and why acl injuries occur such analyses may be affected by artifacts due to inconsistencies in the equations of motion when force and movement data are filtered with different cut off frequencies the purpose of this study was to quantify the effect of these artifacts and compare joint moments calculated with the same or different cut off frequency for the filtering of force and movement data 123 elite handball players performed sidestep cutting while the movement was recorded by eight 240 hz cameras and the ground reaction forces were recorded by a 960 hz force plate knee and hip joint moments were calculated through inverse dynamics with four different combinations of cut off frequencies for signal filtering movement 10 hz force 10 hz 10 10 movement 15 hz force 15 hz movement 10 hz force 50 hz 10 50 movement 15 hz force 50 hz the results revealed significant differences especially between conditions with different filtering of force and movement mean sd peak knee abduction moment for the 10 10 and 10 50 condition were 1 27 0 53 and 1 64 0 68 nm kg respectively ranking of players based on knee abduction moments were affected by filtering condition out of 20 players with peak knee abduction moment higher than mean 1 sd with the 10 50 condition only 11 were still above mean 1 sd when the 10 10 condition was applied hip moments were very sensitive to filtering cut off mean sd peak hip flexion moment was 3 64 0 75 and 5 92 1 80 under the 10 10 and 10 50 conditions respectively based on these findings force and movement data should be processed with the same filter conclusions from previous inverse dynamics studies where this was not the case should be treated with caution

dynamic stability of human walking in visually and mechanically destabilizing environments abstract understanding how humans remain stable during challenging locomotor activities is critical to developing effective tests to diagnose patients with increased fall risk this study determined if different continuous low amplitude perturbations would induce specific measureable changes in measures of dynamic stability during walking we applied continuous pseudo random oscillations of either the visual scene or support surface in either the anterior posterior or mediolateral directions to subjects walking in a virtual environment with speed matched optic flow floquet multipliers and short term local divergence exponents both increased indicating greater instability during perturbed walking these responses were generally much stronger for body movements occurring in the same directions as the applied perturbations likewise subjects were more sensitive to both visual and mechanical perturbations applied in the mediolateral direction than to those applied in the anterior posterior direction consistent with previous experiments and theoretical predictions these responses were likewise consistent with subjects anecdotal perceptions of which perturbation conditions were most challenging contrary to the floquet multipliers and short term local divergence exponents which both increased long term local divergence exponenets decreased during perturbed walking however this was consistent with specific changes in the mean log divergence curves which indicated that subjects movements reached their maximum local divergence limits more quickly during perturbed walking overall the floquet multipliers were less sensitive but reflected greater specificity in their responses to the different perturbation conditions conversely the short term local divergence exponents exhibited less specificity in their responses but were more sensitive measures of instability in general

learning the kernel matrix with semidefinite programming kernel based learning algorithms work by embedding the data into a euclidean space and then searching for linear relations among the embedded data points the embedding is performed implicitly by specifying the inner products between each pair of points in the embedding space this information is contained in the so called kernel matrix a symmetric and positive semidefinite matrix that encodes the relative positions of all points specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space classical model selection problems in machine learning in this paper we show how the kernel matrix can be learned from data via semidefinite programming sdp techniques when applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm using the labeled part of the data one can learn an embedding also for the unlabeled part the similarity between test points is inferred from training points and their labels importantly these learning problems are convex so we obtain a method for learning both the model class and the function without local minima furthermore this approach leads directly to a convex method for learning the 2 norm soft margin parameter in support vector machines solving an important open problem

fixed point theorems in partially ordered metric spaces and applications abstract we prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order using a weak contractivity type of assumption besides including several recent developments our theorem can be used to investigate a large class of problems as an application we discuss the existence and uniqueness of solution for a periodic boundary value problem

the generic modeling fallacy average biomechanical models often produce non average results computational biomechanics models constructed using nominal or average input parameters are often assumed to produce average results that are representative of a target population of interest to investigate this assumption a stochastic monte carlo analysis of two common biomechanical models was conducted consistent discrepancies were found between the behavior of average models and the average behavior of the population from which the average models input parameters were derived more interestingly broadly distributed sets of non average input parameters were found to produce average or near average model behaviors in other words average models did not produce average results and models that did produce average results possessed non average input parameters these findings have implications on the prevalent practice of employing average input parameters in computational models to facilitate further discussion on the topic the authors have termed this phenomenon the generic modeling fallacy the mathematical explanation of the generic modeling fallacy is presented and suggestions for avoiding it are provided analytical and empirical examples of the generic modeling fallacy are also given

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data