bmo spaces associated with semigroups of operators we study bmo spaces associated with semigroup of operators on noncommutative function spaces i e von neumann algebras and apply the results to boundedness of fourier multipliers on non abelian discrete groups we prove an interpolation theorem for bmo spaces and prove the boundedness of a class of fourier multipliers on noncommutative lp spaces for all 1 p with optimal constants in p

performance of a distributed stochastic approximation algorithm in this paper a distributed stochastic approximation algorithm is studied applications of such algorithms include decentralized estimation optimization control or computing the algorithm consists in two steps a local step where each node in a network updates a local estimate using a stochastic approximation algorithm with decreasing step size and a gossip step where a node computes a local weighted average between its estimates and those of its neighbors convergence of the estimates toward a consensus is established under weak assumptions the approach relies on two main ingredients the existence of a lyapunov function for the mean field in the agreement subspace and a contraction property of the random matrices of weights in the subspace orthogonal to the agreement subspace a second order analysis of the algorithm is also performed under the form of a central limit theorem the polyak averaged version of the algorithm is also considered

nonconvergence to unstable points in urn models and stochastic approximations a particle in mathbf r d moves in discrete time the size of the n th step is of order 1 n and when the particle is at a position mathbf v the expectation of the next step is in the direction mathbf f mathbf v for some fixed vector function mathbf f of class c 2 it is well known that the only possible points mathbf p where mathbf v n may converge are those satisfying mathbf f mathbf p mathbf 0 this paper proves that convergence to some of these points is in fact impossible as long as the noise the difference between each step and its expectation is sufficiently omnidirectional the points where convergence is impossible are the unstable critical points for the autonomous flow d dt mathbf v t mathbf f v t this generalizes several known results that say convergence is impossible at a repelling node of the flow

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

kernelized multiview projection for robust action recognition conventional action recognition algorithms adopt a single type of feature or a simple concatenation of multiple features in this paper we propose to better fuse and embed different feature representations for action recognition using a novel spectral coding algorithm called kernelized multiview projection kmp computing the kernel matrices from different features views via time sequential distance learning kmp can encode different features with different weights to achieve a low dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative more crucially kmp is linear for the reproducing kernel hilbert space which allows it to be competent for various practical applications we demonstrate kmp s performance for action recognition on five popular action datasets and the results are consistently superior to state of the art techniques

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

controllability is not necessary for adaptive pole placement control the key issue for adaptive pole placement control of linear time invariant systems is the possible singularity of the sylvester matrix corresponding to the coefficient estimate however to overcome the difficulty the estimate is modified by several methods which are either nonrecursive and with high computational load or recursive but with random search involved all of the previous works are done under the assumption that the system is controllable this paper gives the necessary and sufficient condition which is weaker than controllability for the system to be adaptively stabilizable first a nonrecursive algorithm is proposed to modify the estimates and the algorithm is proved to terminate in finitely many steps then with the help of stochastic approximation a recursive algorithm is proposed for obtaining the modification parameters it is proved that these modification parameters turn out to be a constant vector in a finite number of steps this leads to the convergence of the modified coefficient estimates for both algorithms the sylvester matrices corresponding to the modified coefficient estimates are asymptotically uniformly nonsingular thus the adaptive pole placement control problem can be solved i e the system can be adaptively stabilized

rapidly decreasing functions in reduced algebras of groups let r be a group we associate to any length function l on r the space h r of rapidly decreasing functions on r with respect to l which coincides with the space of smooth functions on the k dimensional torus when r zk we say that r has property rd if there exists a length function l on r such that h r is contained in the reduced c algebra c r of r we study the stability of property rd with respect to some constructions of groups such as subgroups over groups of finite index semidirect and amalgamated products finally we show that the following groups have property rd 1 finitely generated groups of polynomial growth 2 discrete cocompact subgroups of the group of all isometries of any hyperbolic space

a dynamical system approach to stochastic approximations it is known that some problems of almost sure convergence for stochastic approximation processes can be analyzed via an ordinary differential equation ode obtained by suitable averaging the goal of this paper is to show that the asymptotic behavior of such a process can be related to the asymptotic behavior of the ode without any particular assumption concerning the dynamics of this ode the main results are as follows a the limit sets of trajectory solutions to the stochastic approximation recursion are under classical assumptions almost surely nonempty compact connected sets invariant under the flow of the ode and contained in its set of chain recurrence b if the gain parameter goes to zero at a suitable rate depending on the expansion rate of the ode any trajectory solution to the recursion is almost surely asymptotic to a forward trajectory solution to the ode

asymptotic properties of sign algorithms for adaptive filtering this paper develops asymptotic properties of a class of sign error algorithms with expanding truncation bounds for adaptive filtering under merely stationary ergodicity and finite second moments of the reference and output signals and using trajectory subsequence ts method it is proved that the algorithm convergers almost surely then a mean squares estimate is derived for the estimation error and a suitably scaled sequence of the estimation error is shown to converge to a diffusion process the scaling factor together with the stationary covariance gives the rate of convergence result moreover an algorithm under mean squares criterion with expanding truncation bounds is also examined compared with the existing results in the literature sufficient conditions for almost sure convergence are much relaxed a simple example is provided for demonstration purpose

general results on the convergence of stochastic algorithms a deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the nonnecessarily continuous mean field emphasis is placed on the case where more than one stationary point exists we also use this approach to prove the convergence of a stochastic algorithm with markovian dynamics

stability and instability of limit points for stochastic approximation algorithms it is shown that the limit points of a stochastic approximation sa algorithm consist of a connected set conditions are given to guarantee the uniqueness of the limit point for a given initial value examples are provided wherein x sub n of sa algorithm converges to a limit x independent of initial values but x is unstable for the differential equation x spl dot f x with a nonnegative lyapunov function finally sufficient conditions are given for stability of x spl dot f x at x if x sub n tends to x for any initial values

discriminative elastic net regularized linear regression in this paper we aim at learning compact and discriminative linear regression models linear regression has been widely used in different problems however most of the existing linear regression methods exploit the conventional zero one matrix as the regression targets which greatly narrows the flexibility of the regression model another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability to this end we present an elastic net regularized linear regression enlr framework and develop two robust linear regression models which possess the following special characteristics first our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix second a robust elastic net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix third the resulting optimization problem of enlr has a closed form solution in each iteration which can be solved efficiently finally rather than directly exploiting the projection matrix for recognition our methods employ the transformed features as the new discriminate representations to make final image classification compared with the traditional linear regression model and some of its variants our method is much more accurate in image classification extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state of the art methods the matlab codes of our methods can be available at http www yongxu org lunwen html

on the best constants in noncommutative khintchine type inequalities we obtain new proofs with improved constants of the khintchine type inequality with matrix coefficients in two cases the first case is the pisier and lust piquard noncommutative khintchine inequality for p 1 where we obtain the sharp lower bound of 12 in the complex gaussian case and for the sequence of functions ei2nt n 1 the second case is junge s recent khintchine type inequality for subspaces of the operator space r c which he used to construct a cb embedding of the operator hilbert space oh into the predual of a hyperfinite factor also in this case we obtain a sharp lower bound of 12 as a consequence it follows that any subspace of a quotient of r c is cb isomorphic to a subspace of the predual of the hyperfinite factor of type iii1 with cb isomorphism constant 2 in particular the operator hilbert space oh has this property

pathwise convergence of recursive identification algorithms for hammerstein systems this paper gives estimates for 1 coefficients contained in the linear part of the hammerstein system 2 the value of the nonlinear function f u in the hammerstein system at any u 3 ef u sub k and eu sub k f u sub k with u sub k denoting the system input no assumption is made on structure of f spl middot the estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one two numerical examples are given

on ergodic theorems for free group actions on noncommutative spaces we extend in a noncommutative setting the individual ergodic theorem of nevo and stein concerning measure preserving actions of free groups and averages on spheres s 2 n of even radius here we study state preserving actions of free groups on a von neumann algebra a and the behaviour of s 2 n x for x in noncommutative spaces l p a for the cesaro means this problem was solved by walker our approach is based on ideas of bufetov we prove a noncommutative version of rota alternierende verfahren theorem to this end we introduce specific dilations of the powers of some noncommutative markov operators

rosenthal type inequalities for free chaos let a denote the reduced amalgamated free product of a family a 1 a 2 an of von neumann algebras over a von neumann subalgebra b with respect to normal faithful conditional expectations e k a k b we investigate the norm in lp a of homogeneous polynomials of a given degree d we first generalize voiculescu s inequality to arbitrary degree d 1 and indices 1 p this can be regarded as a free analogue of the classical rosenthal inequality our second result is a length reduction formula from which we generalize recent results of pisier ricard and the authors all constants in our estimates are independent of n so that we may consider infinitely many free factors as applications we study square functions of free martingales more precisely we show that in contrast with the khintchine and rosenthal inequalities the free analogue of the burkholder gundy inequalities does not hold in l a at the end of the paper we also consider khintchine type inequalities for shlyakhtenko s generalized circular systems

multi view intact space learning it is practical to assume that an individual view is unlikely to be sufficient for effective multi view learning therefore integration of multi view information is both valuable and necessary in this paper we propose the multi view intact space learning misl algorithm which integrates the encoded complementary information in multiple views to discover a latent intact representation of the data even though each view on its own is insufficient we show theoretically that by combing multiple views we can obtain abundant information for latent intact space learning employing the cauchy loss a technique used in statistical learning as the error measurement strengthens robustness to outliers we propose a new definition of multi view stability and then derive the generalization error bound based on multi view stability and rademacher complexity and show that the complementarity between multiple views is beneficial for the stability and generalization misl is efficiently optimized using a novel iteratively reweight residuals irr technique whose convergence is theoretically analyzed experiments on synthetic data and real world datasets demonstrate that misl is an effective and promising algorithm for practical applications

noncommutative maximal ergodic theorems this paper is devoted to the study of various maximal ergodic theorems in noncommutative spaces in particular we prove the noncommutative analogue of the classical dunford schwartz maximal ergodic inequality for positive contractions on and the analogue of stein s maximal inequality for symmetric positive contractions we also obtain the corresponding individual ergodic theorems we apply these results to a family of natural examples which frequently appear in von neumann algebra theory and in quantum probability

local feature discriminant projection in this paper we propose a novel subspace learning algorithm called local feature discriminant projection lfdp for supervised dimensionality reduction of local features lfdp is able to efficiently seek a subspace to improve the discriminability of local features for classification we make three novel contributions first the proposed lfdp is a general supervised subspace learning algorithm which provides an efficient way for dimensionality reduction of large scale local feature descriptors second we introduce the differential scatter discriminant criterion dsdc to the subspace learning of local feature descriptors which avoids the matrix singularity problem third we propose a generalized orthogonalization method to impose on projections leading to a more compact and less redundant subspace extensive experimental validation on three benchmark datasets including uiuc sports scene 15 and mit indoor demonstrates that the proposed lfdp outperforms other dimensionality reduction methods and achieves state of the art performance for image classification

hetero manifold regularisation for cross modal hashing recently cross modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi modal data to address both challenges in this paper we propose a novel method termed hetero manifold regularisation hmr to supervise the learning of hash functions for efficient cross modal search a hetero manifold integrates multiple sub manifolds defined by homogeneous data with the help of cross modal supervision information taking advantages of the hetero manifold the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero manifold furthermore a novel cumulative distance inequality defined on the hetero manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes by using the inequality cross modal hashing is transformed into a problem of hetero manifold regularised support vector learning therefore the performance of cross modal search can be significantly improved by seamlessly combining the integrated information of the hetero manifold and the strong generalisation of the support vector machine comprehensive experiments show that the proposed hmr achieve advantageous results over the state of the art methods in several challenging cross modal tasks

brief paper recursive identification for multivariate errors in variables systems the recursive algorithm is given for estimating matrix coefficients of the multivariate errors in variables eiv systems it is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the yule walker equation satisfied by the true coefficients of the system the sufficient conditions guaranteeing the uniqueness of the solution to the yule walker equation are given in this case the estimate provided by the recursive algorithm is strongly consistent

multiple operator integrals and higher operator derivatives abstract in this paper we consider the problem of the existence of higher derivatives of the function t a tk where is a function on the real line a is a self adjoint operator and k is a bounded self adjoint operator we improve earlier results by sten kin in order to do this we give a new approach to multiple operator integrals this approach improves the earlier approach given by sten kin we also consider a similar problem for unitary operators

supervised matrix factorization hashing for cross modal retrieval the target of cross modal hashing is to embed heterogeneous multimedia data into a common low dimensional hamming space which plays a pivotal part in multimedia retrieval due to the emergence of big multimodal data recently matrix factorization has achieved great success in cross modal hashing however how to effectively use label information and local geometric structure is still a challenging problem for these approaches to address this issue we propose a cross modal hashing method based on collective matrix factorization which considers both the label consistency across different modalities and the local geometric consistency in each modality these two elements are formulated as a graph laplacian term in the objective function leading to a substantial improvement on the discriminative power of latent semantic features obtained by collective matrix factorization moreover the proposed method learns unified hash codes for different modalities of an instance to facilitate cross modal search and the objective function is solved using an iterative strategy the experimental results on two benchmark data sets show the effectiveness of the proposed method and its superiority over state of the art cross modal hashing methods

self tuning control based on multi innovation stochastic gradient parameter estimation abstract this paper uses the multi innovation stochastic gradient misg algorithm to estimate the parameters of discrete time systems and presents an misg based self tuning control scheme furthermore we prove that the parameter estimation error converges to zero under persistent excitation and the parameter estimation based control algorithm can asymptotically achieve virtually optimal control and ensure that the closed loop systems are stable and globally convergent the simulation example is included

dual diversified dynamical gaussian process latent variable model for video repairing in this paper we propose a dual diversified dynamical gaussian process latent variable model text d 3 gplvm to tackle the video repairing issue for preservation purposes videos have to be conserved on media however storing on media such as films and hard disks can suffer from unexpected data loss for instance physical damage so repairing of missing or damaged pixels is essential for better video maintenance most methods seek to fill in missing holes by synthesizing similar textures from local patches the neighboring pixels consecutive frames or the whole video however these can introduce incorrect contexts especially when the missing hole or number of damaged frames is large furthermore simple texture synthesis can introduce artifacts in undamaged and recovered areas to address aforementioned problems we introduce two diversity encouraging priors to both of inducing points and latent variables for considering the variety in existing videos in text d 3 gplvm the inducing points constitute a smaller subset of observed data while latent variables are a low dimensional representation of observed data since they have a strong correlation with the observed data it is essential that both of them can capture distinct aspects of and fully represent the observed data the dual diversity encouraging priors ensure that the trained inducing points and latent variables are more diverse and resistant for context aware and artifacts free based video repairing the defined objective function in our proposed model is initially not analytically tractable and must be solved by variational inference finally experimental testing results illustrate the robustness and effectiveness of our method for damaged video repairing

large margin multi viewinformation bottleneck in this paper we extend the theory of the information bottleneck ib to learning from examples represented by multi view features we formulate the problem as one of encoding a communication system with multiple senders each of which represents one view of the data based on the precise components filtered out from multiple information sources through a bottleneck a margin maximization approach is then used to strengthen the discrimination of the encoder by improving the code distance within the frame of coding theory the resulting algorithm therefore inherits all the merits of the ib principle and coding theory it has two distinct advantages over existing algorithms namely that our method finds a tradeoff between the accuracy and complexity of the multi view model and that the encoded multi view data retains sufficient discrimination for classification we also derive the robustness and generalization error bound of the proposed algorithm and reveal the specific properties of multi view learning first the complementarity of multi view features guarantees the robustness of the algorithm second the consensus of multi view features reduces the empirical rademacher complexity of the objective function enhances the accuracy of the solution and improves the generalization error bound of the algorithm the resulting objective function is solved efficiently using the alternating direction method experimental results on annotation classification and recognition tasks demonstrate that the proposed algorithm is promising for practical applications

a noncommutative version of the john nirenberg theorem we prove a noncommutative version of the john nirenberg theorem for nontracial filtrations of von neumann algebras as an application we obtain an analogue of the classical large deviation inequality for elements of the associated bmo space

zero shot visual recognition via bidirectional latent embedding zero shot learning for visual recognition e g object and action recognition has recently attracted a lot of attention however it still remains challenging in bridging the semantic gap between visual features and their underlying semantics and transferring knowledge to semantic categories unseen during learning unlike most of the existing zero shot visual recognition methods we propose a stagewise bidirectional latent embedding framework of two subsequent learning stages for zero shot visual recognition in the bottom up stage a latent embedding space is first created by exploring the topological and labeling information underlying training data of known classes via a proper supervised subspace learning algorithm and the latent embedding of training data are used to form landmarks that guide embedding semantics underlying unseen classes into this learned latent space in the top down stage semantic representations of unseen class labels in a given label vocabulary are then embedded to the same latent space to preserve the semantic relatedness between all different classes via our proposed semi supervised sammon mapping with the guidance of landmarks thus the resultant latent embedding space allows for predicting the label of a test instance with a simple nearest neighbor rule to evaluate the effectiveness of the proposed framework we have conducted extensive experiments on four benchmark datasets in object and action recognition i e awa cub 200 2011 ucf101 and hmdb51 the experimental results under comparative studies demonstrate that our proposed approach yields the state of the art performance under inductive and transductive settings

duplex metric learning for image set classification image set classification has attracted much attention because of its broad applications despite the success made so far the problems of intra class diversity and inter class similarity still remain two major challenges to explore a possible solution to these challenges this paper proposes a novel approach termed duplex metric learning dml for image set classification the proposed dml consists of two progressive metric learning stages with different objectives used for feature learning and image classification respectively the metric learning regularization is not only used to learn powerful feature representations but also well explored to train an effective classifier at the first stage we first train a discriminative stacked autoencoder dsae by layer wisely imposing a metric learning regularization term on the neurons in the hidden layers and meanwhile minimizing the reconstruction error to obtain new feature mappings in which similar samples are mapped closely to each other and dissimilar samples are mapped farther apart at the second stage we discriminatively train a classifier and simultaneously fine tune the dsae by optimizing a new objective function which consists of a classification error term and a metric learning regularization term finally two simple voting strategies are devised for image set classification based on the learnt classifier in the experiments we extensively evaluate the proposed framework for the tasks of face recognition object recognition and face verification on several commonly used data sets and state of the art results are achieved in comparison with existing methods

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

noncommutative riesz transforms a probabilistic approach for 2 p 0 in the classical setting this is certainly satisfied for the maps tt f f 1 t where t is a semigroup of measure preserving maps on a probability space in that case n l then the maps tt act on all noncommutative lp spaces lp n and in particular on the hilbert space l2 l2 n let a be the negative generator i e tt e ta for technical reasons we have to assume that there is a weakly dense algebra a n which lies in the domain of the unbounded operator a i e a a a the algebra a plays the role of smooth functions in the classical setting this assumption might be too restrictive for some classical applications but it is easily verified in the new noncommutative examples for elements x y a we may define the gradient form 2 x y a x y x a y a x y the correct definition of is the one given by sauvageot as a bilinear form with values in l1 again our arguments require stronger assumptions in fact in all our examples we will assume that the tt s are selfadjoint i e ttxy xtty and unital i e tt 1 1 then a is indeed a positive unbounded operator under these circumstances we can formulate p a meyer s problem is it true that x x 2 p c p a 1 2 x p 0 1 holds for all selfadjoint elements x a let us illustrate this question by considering the laplace operator a f f where i 2 x2 i then it is easily verified that

dense trajectories and motion boundary descriptors for action recognition this paper introduces a video representation based on dense trajectories and motion boundary descriptors trajectories capture the local motion information of the video a dense representation guarantees a good coverage of foreground motion as well as of the surrounding context a state of the art optical flow algorithm enables a robust and efficient extraction of dense trajectories as descriptors we extract features aligned with the trajectories to characterize shape point coordinates appearance histograms of oriented gradients and motion histograms of optical flow additionally we introduce a descriptor based on motion boundary histograms mbh which rely on differential optical flow the mbh descriptor shows to consistently outperform other state of the art descriptors in particular on real world videos that contain a significant amount of camera motion we evaluate our video representation in the context of action classification on nine datasets namely kth youtube hollywood2 ucf sports ixmas uiuc olympic sports ucf50 and hmdb51 on all datasets our approach outperforms current state of the art results

learning a multiple kernel similarity metric for kinship verification abstract kinship verification kv has recently caught much attention in the computer vision community due to its potential applications ranging from missing children search to social media analysis most of the related work focuses either on developing hand crafted feature representations to describe the faces or on learning the mahalanobis distance metric to measure the similarity between facial images instead in this paper we propose a novel multiple kernel similarity metric mksm in which different from the mahalanobis metric the similarity computation is essentially based on an implicit nonlinear feature transformation the overall mksm is a weighted combination of basic similarities and therefore possesses the capacity for feature fusion the basic similarities are derived from base kernels and local features and the weights are obtained by solving a constrained linear programming lp problem that originates from a large margin lm criterion particularly the lm criterion not only guarantees the generalization on unseen samples when the training set is small but also leads to sparsity in the weight vector which in turn boosts the efficiency at the prediction stage extensive experiments on four publicly available datasets demonstrate the effectiveness of the proposed method

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