choice of kernel order in density estimation the selection of the order i e number of vanishing moments of the kernel in a kernel density estimator is considered from two points of view first theoretical properties are investigated by a mean integrated squared error analysis of the problem second and perhaps more importantly cross validation is proposed as a practical method of choice and theoretical backing for this is provided through an asymptotic optimality result

variational superposed gaussian approximation for time dependent solutions of langevin equations we propose a variational superposed gaussian approximation vsga for dynamical solutions of langevin equations subject to applied signals determining time dependent parameters of superposed gaussian distributions by the variational principle we apply the proposed vsga to systems driven by a chaotic signal where the conventional fourier method cannot be adopted and calculate the time evolution of probability density functions pdfs and moments both white and colored gaussian noises terms are included to describe fluctuations our calculations show that time dependent pdfs obtained by vsga agree excellently with those obtained by monte carlo simulations the correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises

applications of cumulants to array processing iv direction finding in coherent signals case for pt iii see ibid vol 45 no 9 p 2253 64 1997 we present a subspace based direction finding method for coherent signal environments using an antenna array our method which uses fourth order statistics is capable of resolving more signals than a comparable second order statistics based subspace method and is applicable to a larger class of arrays the maximum number of signals resolvable with our method may exceed the number of sensors in the array only a uniform linear subarray is needed the rest of the array may have arbitrary and unknown response and does not require calibration on the other hand the comparable second order statistics based method is limited to uniform linear arrays only no search procedure is needed in our method simulation experiments supporting our conclusions are provided

clustering based on gaussian processes in this letter we develop a gaussian process model for clustering the variances of predictive values in gaussian processes learned from a training data are shown to comprise an estimate of the support of a probability density function the constructed variance function is then applied to construct a set of contours that enclose the data points which correspond to cluster boundaries to perform clustering tasks of the data points an associated dynamical system is built and its topological invariant property is investigated the experimental results show that the proposed method works successfully for clustering problems with arbitrary shapes

frsvc towards making support vector clustering consume less abstract in spite of with great advantage of discovering arbitrary shapes of clusters support vector clustering svc is frustrated by large scale data especially on resource limited platform it is due to pricey storage and computation consumptions from solving dual problem and labeling clusters upon the pre computed kernel matrix and sampling point pairs respectively towards on it we first present a dual coordinate descent method to reformulate the solver that leads to a flexible training phase carried out on any runtime platform with without sufficient memory then a novel labeling phase who does connectivity analysis between two nearest neighboring decomposed convex hulls referring to clusters is proposed in which a new designed strategy namely sample once connected checking first tries to reduces the scope of sampling analysis by integrating them together a faster and reformulated svc frsvc is created with less consumption achieved according to comparative analysis of time and space complexities furthermore experimental results confirm a significant improvement on flexibility of selective efficiency without losing accuracy with which a balance can be easily reached on the basis of resources a platform equipped

statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks dynamical stochastic models of single neurons and neural networks often take the form of a system of n 2 coupled stochastic differential equations we consider such systems under the assumption that third and higher order central moments are relatively small in the general case a system of 1 n n13 generally nonlinear coupled ordinary differential equations holds for the approximate means variances and covariances for the general linear system the solutions of these equations give exact results this is illustrated in a simple case generally the moment equations can be solved numerically results are given for a spiking fitzhugh nagumo model neuron driven by a current with additive white noise differential equations are obtained for the means variances and covariances of the dynamical variables in a network of n connected spiking neurons in the presence of noise s1063 651x 96 03511 8 pacs number s 87 10 1e 05 40 1j 02 50 2r

population dynamics under the laplace assumption in this paper we describe a generic approach to modelling dynamics in neuronal populations this approach models a full density on the states of neuronal populations but finesses this high dimensional problem by re formulating density dynamics in terms of ordinary differential equations on the sufficient statistics of the densities considered c f the method of moments the particular form for the population density we adopt is a gaussian density c f the laplace assumption this means population dynamics are described by equations governing the evolution of the population s mean and covariance we derive these equations from the fokker planck formalism and illustrate their application to a conductance based model of neuronal exchanges one interesting aspect of this formulation is that we can uncouple the mean and covariance to furnish a neural mass model which rests only on the populations mean this enables us to compare equivalent mean field and neural mass models of the same populations and evaluate quantitatively the contribution of population variance to the expected dynamics the mean field model presented here will form the basis of a dynamic causal model of observed electromagnetic signals in future work

exact mean integrated squared error an exact and easily computable expression for the mean integrated squared error mise for the kernel estimator of a general normal mixture density is given for gaussian kernels of arbitrary order this provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis the family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes a number of applications of this method giving important new insights into kernel density estimation are presented among these is the discovery that the usual asymptotic approximations to the mise can be quite inaccurate especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes 1 introduction substantial research has been devoted to kernel density estimation this is because it provides a simple yet appealing context in which to study problems and issues that arise in all types of nonparametric curve estimation this includes regression spectral density and hazard estimation and also a variety of other estimators including histograms splines and orthogonal series three important and useful tools for understanding the behavior of nonparametric curve estimators are asymptotic analysis simulation and numerical calculation of error criteria each of these methods provides many useful insights into the complicated structure present in the study of curve estimation however each has its limitations as well rhe strength of asymptotic analysis is that it frequently allows simultaneous study of many different specific examples through general results applying to entire classes of settings the weakness of asymptotics is that they only describe behavior in the limit this is still very useful in many situations because the asymptotics describe the actual situation quite well however it is less useful when the asymptotics have not yet kicked in that is in studying situations where the asymptotically dominant effect has not taken over yet perhaps the biggest drawback to asymptotics is that it is very difficult to determine in a given situation which of these possibilities is occurring

learning representative exemplars using one class gaussian process regression abstract an exemplar is an observation that represents a group of similar observations exemplars from data are examined to divide entire heterogeneous data into several homogeneous subgroups wherein each subgroup is represented by an exemplar with its inherent sparsity an exemplar based learning model provides a parsimonious model to represent or cluster large scale data a novel exemplar learning method using one class gaussian process gp regression is proposed in this study the proposed method constructs data distribution support from one class gp regression using automatic relevance determination prior and heterogeneous gp noise exemplars that correspond to the basis vectors of the constructed support function are then automatically located during the training process the proposed method is applied to various data sets to examine its operability characteristics of data representation and cluster analysis the exemplars of some real data generated by the proposed method are also reported

population rate codes carried by mean fluctuation and synchrony of neuronal firings abstract a population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons in order to examine this possibility we have studied responses of neuronal ensembles to three kinds of inputs mean fluctuation and synchrony driven inputs the generalized rate code model including additive and multiplicative noise h hasegawa phys rev e 75 2007 051904 has been studied by direct simulations dss and the augmented moment method amm in which equations of motion for mean firing rate fluctuation and synchrony are derived results calculated by the amm are in good agreement with those by dss the independent component analysis ica of our results has shown that mean firing rate fluctuation or variability and synchrony may carry independent information in the population rate code model the input output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise as recently observed in prefrontal cortex a comparison is made between results obtained by the integrate and fire if model and our rate code model

mean field approximation of two coupled populations of excitable units the analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of n stochastic excitable units each is performed by studying an approximate system obtained by replacing each population with the corresponding mean field model in the exact system one has the units within an ensemble communicating via the time delayed linear couplings whereas the interensemble terms involve the nonlinear time delayed interaction mediated by the appropriate global variables the aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system governed by a set of 4n stochastic delay differential equations for the microscopic dynamics can accurately be reproduced by a flow containing just four deterministic delay differential equations which describe the evolution of the mean field based variables in particular the considered issues include determining the parameter domains where the stationary state is stable the scenarios for the onset and the time delay induced suppression of the collective mode as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state we show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations like those with symmetrical or asymmetrical interpopulation couplings

applications of cumulants to array processing iii blind beamforming for coherent signals for pt ii see ibid vol 43 no 7 p 1663 7 1995 we provide a cumulant based blind beamforming method for recovery of statistically independent narrowband source signals in the presence of coherent or perfectly correlated multipath propagation our method is based on the fact that for a blind beamformer the presence of coherent multipaths is equivalent to the case of independent sources with a different steering matrix our approach is applicable to any array configuration having unknown response signal sources must have nonzero fourth order cumulants there is no need to estimate the directions of arrival our method maximizes signal to interference plus noise ratio sinr a comparable result does not exist using just second order statistics

dynamics of a modified hindmarsh rose neural model with random perturbations moment analysis and firing activities abstract in this paper an attempt has been made to understand the activity of mean membrane voltage and subsidiary system variables with moment equations i e mean variance and covariance s under noisy environment we consider a biophysically plausible modified hindmarsh rose h r neural system injected by an applied current exhibiting spiking bursting phenomenon the effects of predominant parameters on the dynamical behavior of a modified h r system are investigated numerically it exhibits period doubling period halving bifurcation and chaos phenomena further a nonlinear system has been analyzed for the first and second order moments with additive stochastic perturbations it has been solved using fourth order runge kutta method and noisy systems by euler s scheme it has been demonstrated that the firing properties of neurons to evoke an action potential in a certain parameter space of the large exact systems can be estimated using an approximated model strong stimulation can cause a change in increase or decrease of the firing patterns corresponding to a fixed set of parameter values the firing behavior and dynamical differences of the collective variables of a large exact and approximated systems are investigated

inhibition and modulation of rhythmic neuronal spiking by noise we investigated the effects of noise on periodic firing in the hodgkin huxley nonlinear system with mean input current mu as a bifurcation parameter a bifurcation to repetitive spiking occurs at a critical value microc approximately 6 44 the firing behavior was studied as a function of the mean and variance of the input current firstly with initial resting conditions noise of a small amplitude can turn off the spiking for values of micro close to microc and the number of spikes undergoes a minimum as a function of the noise level the robustness of these phenomena was confirmed by simulations with random initial conditions and with random time of commencement of the noise furthermore their generality was indicated by their occurrence when additive noise was replaced by conductance based noise for long periods of observation many frequent transitions may occur from spiking to nonspiking activity when the noise is sufficiently strong explanations of the above phenomena are sought in terms of the underlying bifurcation structure and the probabilities that noise shifts the process from the basin of attraction of a stable limit cycle to that of a stable rest state the waiting times for such transitions depend strongly on the values of mu and sigma and on the forms of the basins of attraction the observed effects of noise are expected to occur in diverse fields in systems with the same underlying dynamical structure

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

bias analysis of the music location estimator the authors present a rigorous bias analysis of the music location estimator and they derive an accurate and concise bias expression the analysis is based on the second order taylor series expansion of the derivative of the null spectrum properties of the null spectrum and statistics of the estimated signal eigenvectors it is proven that in the derivation the remainder term in the second order taylor series can be dropped but the second order terms cannot be simulations verify that the bias expression is valid over a wide range of signal to noise ratios snrs extending down into the resolution threshold region of music although asymptotic this expression can be accurately applied to a limited number of snapshot cases the utility of the expression is shown by using it in a study of music location estimator characteristics estimate bias and standard deviation are compared for variations in snr numbers of sensors and snapshots and source correlation music resolvability and estimator performance bounds are addressed accounting for bias

an alternative method of cross validation for the smoothing of density estimates cross validation with kullback leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation a framework for this problem is constructed and used to derive an alternative method of cross validation based on integrated squared error recently also proposed by rudemo 1982 hall 1983 has established the consistency and asymptotic optimality of the new method for small and moderate sized samples the performances of the two methods of cross validation are compared on simulated data and specific examples

moment analysis of the hodgkin huxley system with additive noise abstract we consider a classical space clamped hodgkin huxley hh model neuron stimulated by a current which has a mean together with additive gaussian white noise of amplitude a system of 14 deterministic first order nonlinear differential equations is derived for the first and second order moments means variances and covariances of the voltage v and the subsidiary variables n m and h the system of equations is integrated numerically with a fourth order runge kutta method as long as the variances as determined by these deterministic equations remain small the latter accurately approximate the first and second order moments of the stochastic hodgkin huxley system describing spiking neurons on the other hand for certain values of when rhythmic spiking is inhibited by larger amplitude noise the solutions of the moment equation strongly overestimate the moments of the voltage a more refined analysis of the nature of such irregularities leads to precise insights about the effects of noise on the hodgkin huxley system for suitable values of which enable rhythmic spiking we analyze by numerical examples from both simulation and solutions of the moment equations the three factors which tend to promote its cessation namely the increasing variance the nature and shape of the basins of attraction of the limit cycle and stable equilibrium point and the speed of the process

support vector clustering we present a novel clustering method using the approach of support vector machines data points are mapped by means of a gaussian kernel to a high dimensional feature space where we search for the minimal enclosing sphere this sphere when mapped back to data space can separate into several components each enclosing a separate cluster of points we present a simple algorithm for identifying these clusters the width of the gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters the structure of a dataset is explored by varying the two parameters maintaining a minimal number of support vectors to assure smooth cluster boundaries we demonstrate the performance of our algorithm on several datasets

a dynamical trajectory based methodology for systematically computing multiple optimal solutions of general nonlinear programming problems in this paper a novel dynamical trajectory based methodology is developed for systematically computing multiple local optimal solutions of general nonlinear programming problems with disconnected feasible components satisfying nonlinear equality inequality constraints the proposed methodology deterministic in nature exploits trajectories of two different nonlinear dynamical systems to find multiple local optimal solutions the methodology consists of two phases phase i starts from an arbitrary infeasible initial point and finds systematically multiple or all the disconnected feasible components phase ii finds an adjacent local optimal solution from a local optimum via a decomposition point thereby systematically locating multiple local optimal solutions which lie within each feasible component found in phase i by alternating between these two phases the methodology locates multiple or all the local optimal solutions which lie in all the disconnected feasible components a theoretical foundation for the proposed methodology is also developed the methodology is illustrated with a numerical example with promising results

the space clamped hodgkin huxley system with random synaptic input inhibition of spiking by weak noise and analysis with moment equations we consider a classical space clamped hodgkin huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by ornstein uhlenbeck processes using numerical solutions of the stochastic model system obtained by an euler method it is found that with excitation only there is a critical value of the steady state excitatory conductance for repetitive spiking without noise and for values of the conductance near the critical value small noise has a powerfully inhibitory effect for a given level of inhibition there is also a critical value of the steady state excitatory conductance for repetitive firing and it is demonstrated that noise in either the excitatory or inhibitory processes or both can powerfully inhibit spiking furthermore near the critical value inverse stochastic resonance was observed when noise was present only in the inhibitory input process the system of deterministic differential equations for the approximate first and second order moments of the model is derived they are solved using runge kutta methods and the solutions are compared with the results obtained by simulation for various sets of parameters including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex the mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels in the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells the assumptions underlying the moment equation approach are not satisfied the simulation results show that noisy synaptic input of either an excitatory or inhibitory character or both may lead to the suppression of firing in neurons operating near a critical point and this has possible implications for cortical networks although suppression of firing is corroborated for the system of moment equations there seem to be substantial differences between the dynamical properties of the original system of stochastic differential equations and the much larger system of moment equations

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

spontaneous spiking in an autaptic hodgkin huxley setup the effect of intrinsic channel noise is investigated for the dynamic response of a neuronal cell with a delayed feedback loop the loop is based on the so called autapse phenomenon in which dendrites establish connections not only to neighboring cells but also to its own axon the biophysical modeling is achieved in terms of a stochastic hodgkin huxley model containing such a built in delayed feedback the fluctuations stem from intrinsic channel noise being caused by the stochastic nature of the gating dynamics of ion channels the influence of the delayed stimulus is systematically analyzed with respect to the coupling parameter and the delay time in terms of the interspike interval histograms and the average interspike interval the delayed feedback manifests itself in the occurrence of bursting and a rich multimodal interspike interval distribution exhibiting a delay induced reduction in the spontaneous spiking activity at characteristic frequencies moreover a specific frequency locking mechanism is detected for the mean interspike interval

extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems the analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena like decision making and bistable perception to investigate the role of noise in a multistable neurodynamical system described by coupled differential equations one usually considers numerical simulations which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system an alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations however the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal gaussian shape we extend in this paper the classical moments method to the case of bimodal distribution of the state variables such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability

analysis of inverse stochastic resonance and the long term firing of hodgkin huxley neurons with gaussian white noise abstract in order to explain the occurrence of a minimum in firing rate which occurs for certain mean input levels as noise level increases inverse stochastic resonance isr in hodgkin huxley hh systems we analyze the underlying transitions from a stable equilibrium point to limit cycle and vice versa for a value of at which isr is pronounced properties of the corresponding stable equilibrium point are found a linearized approximation around this point has oscillatory solutions from whose maxima spikes tend to occur a one dimensional diffusion is also constructed for small noise properties of the basin of attraction of the limit cycle spike are investigated heuristically long term trials of duration 500000 ms are carried out for values of from 0 to 2 0 the graph of mean spike count versus is divided into 4 regions r 1 r 4 where r 3 contains the minimum associated with isr in r 1 transitions to the basin of attraction of the rest point are not observed until a small critical value of c 1 is reached at the beginning of r 2 the sudden decline in firing rate when is just greater than c 1 implies that there is only a small range of noise levels 0 c 1 where repetitive spiking is safe from annihilation by noise the firing rate remains small throughout r 3 at a larger critical value c 2 which signals the beginning of r 4 the probability of transitions from the basin of attraction of the equilibrium point to that of the limit cycle apparently becomes greater than zero and the spike rate thereafter increases with increasing the quantitative scheme underlying the isr curve is outlined in terms of the properties of exit time random variables in the final subsection several statistical properties of the main random variables associated with long term spiking activity are given including distributions of exit times from the two relevant basins of attraction and the interspike interval

hypoelliptic diffusions filtering and inference from complete and partial observations the statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications however because of the noise structure where the noise components of the different co ordinates of the multi dimensional process operate on different timescales standard inference tools are ill conditioned we propose to use a higher order scheme to approximate the likelihood such that the different timescales are appropriately accounted for we show consistency and asymptotic normality with non typical convergence rates when only partial observations are available we embed the approximation in a filtering algorithm for the unobserved co ordinates and use this as a building block in a stochastic approximation expectation maximization algorithm we illustrate on simulated data from three models the harmonic oscillator the fitzhugh nagumo model used to model membrane potential evolution in neuroscience and the synaptic inhibition and excitation model used for determination of neuronal synaptic input

cluster validity measure and merging system for hierarchical clustering considering outliers clustering algorithms have evolved to handle more and more complex structures however the measures that allow to qualify the quality of such clustering partitions are rare and have been developed only for specific algorithms in this work we propose a new cluster validity measure cvm to quantify the clustering performance of hierarchical algorithms that handle overlapping clusters of any shape and in the presence of outliers this work also introduces a cluster merging system cms to group clusters that share outliers when located in regions of cluster overlap these outliers may be issued by a mixture of nearby cores the proposed cvm and cms are applied to hierarchical extensions of the support vector and gaussian process clustering algorithms both in synthetic and real experiments these results show that the proposed metrics help to select the appropriate level of hierarchy and the appropriate hyperparameters highlightscluster validity measure for arbitrary shaped clusters with outliers cluster merging system grouping cluster cores based on the outliers structure truly hierarchical variants of support vector and gaussian process clustering benefits for unsupervised change detection applications are presented

analysis of data from continuous probability distributions given a set of points drawn from an unknown continuous probability distribution one often wishes to infer the underlying distribution this distribution can be estimated using a simple scalar field theory fluctuations around the estimate are characterized by a robust measure of goodness of fit analogous to the conventional ensuremath chi 2 whose distribution can also be calculated the resulting method of data analysis has some advantages over conventional approaches

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

dynamic pattern denoising method using multi basin system with kernels in this paper we propose a novel pattern denoising method that utilizes the topological property of a support that describes the distribution of normal patterns to denoise noisy patterns the method first trains a support function which captures the domain of normal patterns and then construct a so called multi basin system associated with the trained support function by moving noisy patterns along the trajectories of the multi basin system noise is removed while the pattern recovers its normality the denoised pattern is obtained when the noisy pattern arrives at the attracting manifold generated by a set of normal patterns and this is the most similar normal pattern with the noisy pattern in the topological sense through simulations on some toy dataset and real image datasets we show that the proposed framework effectively removes the noise while preserving the information contained in the noisy pattern

gaussian processes for classification mean field algorithms we derive a mean field algorithm for binary classification with gaussian processes that is based on the tap approach originally proposed in statistical physics of disordered systems the theory also yields an approximate leave one out estimator for the generalization error which is computed with no extra computational cost we show that from the tap approach it is possible to derive both a simpler naive mean field theory and support vector machines svms as limiting cases for both mean field algorithms and support vector machines simulation results for three small benchmark data sets are presented they show that one may get state of the art performance by using the leave one out estimator for model selection and the built in leave one out estimators are extremely precise when compared to the exact leave one out estimate the second result is taken as strong support for the internal consistency of the mean field approach

constructing sparse kernel machines using attractors in this brief a novel method that constructs a sparse kernel machine is proposed the proposed method generates attractors as sparse solutions from a built in kernel machine via a dynamical system framework by readjusting the corresponding coefficients and bias terms a sparse kernel machine that approximates a conventional kernel machine is constructed the simulation results show that the constructed sparse kernel machine improves the efficiency of testing phase while maintaining comparable test error

on the distribution of spacings between zeros of the zeta function etude numerique de la distribution des espacements des zeros de la fonction zeta de riemann observation de certains phenomenes inatendus

applications of cumulants to array processing ii non gaussian noise suppression the main motivation of using higher order statistics in signal processing applications has been their insensitivity to additive colored gaussian noise the main objection to those methods is their possible vulnerability to non gaussian noise the authors investigate the effects of non gaussian ambient noise on cumulant based direction finding systems using the interpretation for the information provided by cumulants for array processing applications described in dogan and mendek they first demonstrate the suppression of uncorrelated non gaussian noise that has spatially varying statistics then they indicate methods to suppress spatially colored non gaussian noise using cumulants and an additional sensor whose measurement noise component is independent of the noise components of the original array measurements they also indicate the noise suppression properties of the virtual esprit algorithm proposed in dogan and mendel in addition they propose a method that combines second and fourth order statistics together in order to suppress spatially colored non gaussian noise finally they also illustrate how to suppress spatially colored non gaussian noise when the additional sensor measurement is not available simulations are presented to verify the results

hierarchies of higher order kernels recent literature on functional estimation has shown the importance of kernels with vanishing moments although no general framework was given to build kernels of increasing order apart from some specific methods based on moment relationships the purpose of the present paper is to develop such a framework and to show how to build higher order kernels with nice properties and to solve optimization problems about kernels the proofs given here unlike standard variational arguments explain why some hierarchies of kernels do have optimality properties applications are given to functional estimation in a general context in the last section special attention is paid to density estimates based on kernels of order m r i e kernels of orderr for estimation of derivatives of orderm convergence theorems are easily derived from interpretation by means of projections inl2 spaces

estimation of the input parameters in the ornstein uhlenbeck neuronal model the stochastic ornstein uhlenbeck neuronal model is studied and estimators of the model input parameters depending on the firing regime of the process are derived closed expressions for the laplace transforms of the first two moments of the normalized first passage time through a constant boundary in the suprathreshold regime are derived which is used to define moment estimators in the subthreshold regime the exponentiality of the first passage time is utilized to characterize the input parameters in the threshold regime and for the wiener process approximation analytic expressions for the first passage time density are used to derive the maximum likelihood estimators of the parameters the methods are illustrated on simulated data under different conditions including misspecification of the intrinsic parameters of the model finally known approximations of the first passage time moments are improved

a novel kernel method for clustering kernel methods are algorithms that by replacing the inner product with an appropriate positive definite function implicitly perform a nonlinear mapping of the input data into a high dimensional feature space in this paper we present a kernel method for clustering inspired by the classical k means algorithm in which each cluster is iteratively refined using a one class support vector machine our method which can be easily implemented compares favorably with respect to popular clustering algorithms like k means neural gas and self organizing maps on a synthetic data set and three uci real data benchmarks iris data wisconsin breast cancer database spam database

direction finding algorithms based on high order statistics two direction finding algorithms are presented for nongaussian signals which are based on the fourth order cumulants of the data received by the array the first algorithm is similar to music while the second is asymptotically minimum variance in a certain sense the first algorithm requires singular value decomposition of the cumulant matrix while the second is based on nonlinear minimization of a certain cost function the performance of the minimum variance algorithm can be assessed by analytical means at least for the case of discrete probability distributions of the source signals and spatially uncorrelated gaussian noise the numerical experiments performed seem to confirm the insensitivity of these algorithms to the gaussian noise parameters

fast support based clustering method for large scale problems in many support vector based clustering algorithms a key computational bottleneck is the cluster labeling time of each data point which restricts the scalability of the method in this paper we review a general framework of support vector based clustering using dynamical system and propose a novel method to speed up labeling time which is log linear to the size of data we also give theoretical background of the proposed method various large scale benchmark results are provided to show the effectiveness and efficiency of the proposed method

self consistent method for density estimation the estimation of a density profile from experimental data points is a challenging problem usually tackled by plotting a histogram prior assumptions on the nature of the density from its smoothness to the specification of its form allow the design of more accurate estimation procedures such as maximum likelihood our aim is to construct a procedure that makes no explicit assumptions but still providing an accurate estimate of the density we introduce the self consistent estimate the power spectrum of a candidate density is given and an estimation procedure is constructed on the assumption to be released a posteriori that the candidate is correct the self consistent estimate is defined as a prior candidate density that precisely reproduces itself our main result is to derive the exact expression of the self consistent estimate for any given dataset and to study its properties applications of the method require neither priors on the form of the density nor the subjective choice of parameters a cutoff frequency akin to a bin size or a kernel bandwidth emerges naturally from the derivation we apply the self consistent estimate to artificial data generated from various distributions and show that it reaches the theoretical limit for the scaling of the square error with the dataset size

dynamic characterization of cluster structures for robust and inductive support vector clustering a topological and dynamical characterization of the cluster structures described by the support vector clustering is developed it is shown that each cluster can be decomposed into its constituent basin level cells and can be naturally extended to an enlarged clustered domain which serves as a basis for inductive clustering a simplified weighted graph preserving the topological structure of the clusters is also constructed and is employed to develop a robust and inductive clustering algorithm simulation results are given to illustrate the robustness and effectiveness of the proposed method

continuous probability distributions from finite data recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution this paper presents a more general form for the prior distribution that has a geometrical interpretation and can improve the specificity of likely solutions it is also demonstrated that a numerical sampling of the posterior probability distribution can be used as an alternative to a histogram for visualization and to make probabilistic inferences from the data

parameters of stochastic diffusion processes estimated from observations of first hitting times application to the leaky integrate and fire neuronal model a theoretical model has to stand the test against the real world to be of any practical use the first step is to identify parameters in the model estimated from experimental data in many applications where renewal point data are available models of first hitting times of underlying diffusion processes arise despite the seemingly simplicity of the model the problem of how to estimate parameters of the underlying stochastic process has resisted solution the few attempts have either been unreliable difficult to implement or only valid in subsets of the relevant parameter space here we present an estimation method that overcomes these difficulties is computationally easy and fast to implement and also works surprisingly well on small data sets the method is illustrated on simulated and experimental data two common neuronal models the ornstein uhlenbeck and feller models are investigated

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

variational gaussian process classifiers gaussian processes are a promising nonlinear regression tool but it is not straightforward to solve classification problems with them in the paper the variational methods of jaakkola and jordan 2000 are applied to gaussian processes to produce an efficient bayesian binary classifier

bayesian classification with gaussian processes we consider the problem of assigning an input vector to one of m classes by predicting p c x for c 1 m for a two class problem the probability of class one given x is estimated by spl sigma y x where spl sigma y 1 1 e sup y a gaussian process prior is placed on y x and is combined with the training data to obtain predictions for new x points we provide a bayesian treatment integrating over uncertainty in y and in the parameters that control the gaussian process prior the necessary integration over y is carried out using laplace s approximation the method is generalized to multiclass problems m 2 using the softmax function we demonstrate the effectiveness of the method on a number of datasets