spectral theory for the periodic sine gordon equation a concrete viewpoint a summary of the spectral theory for quasiperiodic sine and sinh gordon equations is given analogies with whole line solitons and scattering theory motivates the discussion the relation between the ingredients in the inverse spectral solution of the periodic sine gordon equation and physical characteristics of sine gordon waves is emphasized the explicit topics covered are summarized in the table of contents in the introduction

graph dual regularization non negative matrix factorization for co clustering low rank matrix factorization is one of the most useful tools in scientific computing data mining and computer vision among of its techniques non negative matrix factorization nmf has received considerable attention due to producing a parts based representation of the data recent research has shown that not only the observed data are found to lie on a nonlinear low dimensional manifold namely data manifold but also the features lie on a manifold namely feature manifold in this paper we propose a novel algorithm called graph dual regularization non negative matrix factorization dnmf which simultaneously considers the geometric structures of both the data manifold and the feature manifold we also present a graph dual regularization non negative matrix tri factorization algorithm dnmtf as an extension of dnmf moreover we develop two iterative updating optimization schemes for dnmf and dnmtf respectively and provide the convergence proofs of our two optimization schemes experimental results on uci benchmark data sets several image data sets and a radar hrrp data set demonstrate the effectiveness of both dnmf and dnmtf

robust adaptive embedded label propagation with weight learning for inductive classification we propose a robust inductive semi supervised label prediction model over the embedded representation termed adaptive embedded label propagation with weight learning aelp wl for classification aelp wl offers several properties first our method seamlessly integrates the robust adaptive embedded label propagation with adaptive weight learning into a unified framework by minimizing the reconstruction errors over embedded features and embedded soft labels jointly our aelp wl can explicitly ensure the learned weights to be joint optimal for representation and classification which differs from most existing lp models that perform weight learning separately by an independent step before label prediction second existing models usually precalculate the weights over the original samples that may contain unfavorable features and noise decreasing performance to this end our model adds a constraint that decomposes original data into a sparse component encoding embedded noise removed sparse representations of samples and a sparse error part fitting noise and then performs the adaptive weight learning over the embedded sparse representations third our aelp wl computes the projected soft labels by trading off the manifold smoothness and label fitness errors over the adaptive weights and the embedded representations for enhancing the label estimation power by including a regressive label approximation error for simultaneous minimization to correlate sample features with the embedded soft labels the out of sample issue is naturally solved by minimizing the reconstruction errors over features and embedded soft labels classification error and label approximation error jointly state of the art results are delivered

fir channel estimation through generalized cumulant slice weighting we study the problem of linear channel estimation with unknown channel input signals our work stems from the weighted slice algorithm in which cumulant slices of different orders are linearly combined to produce an estimate of a single input single output channel aiming to improve the reliability of estimation the new approach incorporates a certain matrix structure constraint into its weight computation criterion it provides more reliable results for channels with weak leading coefficients this generalized algorithm maintains the advantage of fonollosa and vidal s algorithm in handling the situation with channel order overestimation its natural extension to multiple input multiple output channel estimation is presented along with the channel identifiability conditions required

interaction of sine gordon kinks with defects the two bounce resonance a model of soliton defect interactions in the sine gordon equations is studied using singular perturbation theory melnikov theory is used to derive a critical velocity for strong interactions which is shown to be exponentially small for weak defects matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem which are then used to derive analytical formulas for the locations of the well known two and three bounce resonance windows as well as several other phenomena seen in numerical simulations

graphical krein signature theory and evans krein functions two concepts evidently very different in nature have proved to be useful in analytical and numerical studies of spectral stability in nonlinear wave theory i the krein signature of an eigenvalue a quantity usually defined in terms of the relative orientation of certain subspaces that is capable of detecting the structural instability of imaginary eigenvalues and hence their potential for moving into the right half plane leading to dynamical instability under perturbation of the system and ii the evans function an analytic function detecting the location of eigenvalues one might expect these two concepts to be related but unfortunately examples demonstrate that there is no way in general to deduce the krein signature of an eigenvalue from the evans function for example by studying derivatives of the latter the purpose of this paper is to recall and popularize a simple graphical interpretation of the krein signature well known in the spectral theory of polynomial operator pencils once esta

non gaussian multivariate adaptive ar estimation using the super exponential algorithm we formulate as a deconvolution problem the causal noncausal non gaussian multichannel autoregressive ar parameter estimation problem the super exponential algorithm presented in a paper by shalvi and weinstein 1993 is generalized to the vector case we present an adaptive implementation that is very attractive since it is higher order statistics hos based but does not present the high computational complexity of methods proposed up to now

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

performance limits of alphabet diversities for fir siso channel identification finite impulse responses fir of single input single output siso channels can be blindly identified from second order statistics of transformed data for instance when the channel is excited by binary phase shift keying bpsk minimum shift keying msk or quadrature phase shift keying qpsk inputs identifiability conditions are derived by considering that noncircularity induces diversity theoretical performance issues are addressed to evaluate the robustness of standard subspace based estimators with respect to these identifiability conditions then benchmarks such as asymptotically minimum variance amv bounds based on various statistics are presented some illustrative examples are eventually given where monte carlo experiments are compared to theoretical performances these comparisons allow to quantify limits to the use of the alphabet diversities for the identification of fir siso channels and to demonstrate the robustness of algorithms based on high order statistics

fourth order blind identification of underdetermined mixtures of sources fobium for about two decades numerous methods have been developed to blindly identify overdetermined p spl les n mixtures of p statistically independent narrowband nb sources received by an array of n sensors these methods exploit the information contained in the second order so the fourth order fo or both the so and fo statistics of the data however in practical situations the probability of receiving more sources than sensors increases with the reception bandwidth and the use of blind identification bi methods able to process underdetermined mixtures of sources for which p n may be required although such methods have been developed over the past few years they all present serious limitations in practical situations related to the radiocommunications context for this reason the purpose of this paper is to propose a new attractive bi method exploiting the information contained in the fo data statistics only that is able to process underdetermined mixtures of sources without the main limitations of the existing methods provided that the sources have different trispectrum and nonzero kurtosis with the same sign a new performance criterion that is able to quantify the identification quality of a given source and allowing the quantitative comparison of two bi methods for each source is also proposed in the paper finally an application of the proposed method is presented through the introduction of a powerful direction finding method built from the blindly identified mixture matrix

efficient closed form estimation of multivariate moving average processes using higher order statistics an improved algorithm is proposed for estimation of non gaussian nonminimum phase multivariate moving average ma processes using higher order cumulants this algorithm improves upon earlier results and contains development beyond existing algorithms it provides a closed form solution to estimating the ma parameter matrices up to a post multiplication by a permutation matrix and under certain assumptions eliminates the indeterminacy associated with scaling the algorithm is theoretically derived and tested via computer simulations in addition it is shown that this algorithm is computationally more efficient than the one proposed by tong inouye and liu see ibid vol 40 no 10 p 2547 2558 1992 finally the effect of imperfect input data on our algorithm is tested via simulations

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

identification of linear systems using input output cumulants a new identification method is proposed for estimating the parameters of a discrete time linear dynamic system excited by non gaussian inputs using kth order k 2 cumulants of input and output signals contaminated by additive possibly coloured gaussian noise the parameter estimates obtained by this method are proved to be consistent under weak conditions this method has an on line algorithm for computing the parameter estimates just like the least squares method a simulation example is included to demonstrate the effectiveness of this method

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

blind parafac receivers for ds cdma systems this paper links the direct sequence code division multiple access ds cdma multiuser separation equalization detection problem to the parallel factor parafac model which is an analysis tool rooted in psychometrics and chemometrics exploiting this link it derives a deterministic blind parafac ds cdma receiver with performance close to non blind minimum mean squared error mmse the proposed parafac receiver capitalizes on code spatial and temporal diversity combining thereby supporting small sample sizes more users than sensors and or less spreading than users interestingly parafac does not require knowledge of spreading codes the specifics of multipath interchip interference doa calibration information finite alphabet constant modulus or statistical independence whiteness to recover the information bearing signals instead parafac relies on a fundamental result regarding the uniqueness of low rank three way array decomposition due to kruskal 1977 1988 and generalized herein to the complex valued case that guarantees identifiability of all relevant signals and propagation parameters these and other issues are also demonstrated in pertinent simulation experiments

a universal separatrix map for weak interactions of solitary waves in generalized nonlinear schrodinger equations abstract it is known that weak interactions of two solitary waves in generalized nonlinear schrodinger nls equations exhibit fractal dependence on initial conditions and the dynamics of these interactions is governed by a universal two degree of freedom ode system y zhu j yang universal fractal structures in the weak interaction of solitary waves in generalized nonlinear schrodinger equations phys rev e 75 2007 036605 in this paper this ode system is analyzed comprehensively using asymptotic methods along separatrix orbits a simple second order map is derived this map does not have any free parameters after variable rescalings and thus is universal for all weak interactions of solitary waves in generalized nls equations comparison between this map s predictions and direct simulations of the ode system shows that the map can capture the fractal scattering phenomenon of the ode system very well both qualitatively and quantitatively

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

generalized re weighting local sampling mean discriminant analysis despite the general success in the pattern recognition community linear discriminant analysis lda has four intrinsic drawbacks in this paper we propose a new feature extraction algorithm namely local sampling mean discriminant analysis lsmda to make up for the first three drawbacks and a generalized re weighting grw framework to make up for the fourth drawback extensive experiments are conducted on both synthetic and real world datasets to evaluate the classification performance of our work the experimental results demonstrate the effectiveness of both lsmda and the grw framework in classifications

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

purely imaginary eigenvalues of zakharov shabat systems zakharov shabat systems with single hump and real but not necessarily symmetric potentials are shown to have purely imaginary eigenvalues only coupled with examples of double hump potentials with nonimaginary eigenvalues this establishes that confinement of zakharov shabat eigenvalues to the imaginary axis is a characteristic of potentials whose energy is concentrated in a single region of the time axis

blind mimo system identification based on cumulant subspace decomposition blind identification of multiple input multiple output mimo linear systems can be achieved by utilizing higher order statistics of the output signals we study the blind identification of mimo systems whose inputs are mutually independent temporally white non gaussian source signals based on sub space analysis we develop a new linear batch algorithm to identify mimo systems from the common nullspace of a set of fourth order cumulant matrices of the channel outputs given knowledge of the channel orders the identifiability conditions required by the proposed algorithm are properly established like most subspace based approaches this new algorithm remains sensitive to channel order overestimation simulation results illustrate its performance for various channel models

fast semi supervised clustering with enhanced spectral embedding in recent years semi supervised clustering ssc has aroused considerable interests from the machine learning and data mining communities in this paper we propose a novel ssc approach with enhanced spectral embedding ese which not only considers the geometric structure information contained in data sets but also can make use of the given side information such as pairwise constraints specially we first construct a symmetry favored k nn graph which is highly robust to noise and outliers and can reflect the underlying manifold structures of data sets then we learn the enhanced spectral embedding towards an ideal data representation as consistent with the given pairwise constraints as possible finally by using the regularization of spectral embedding we formulate learning the new data representation as a semidefinite quadratic linear programming sqlp problem which can be efficiently solved experimental results on a variety of synthetic and real world data sets show that our ese approach outperforms the state of the art ssc algorithms in terms of speed and quality on both vector based and graph based clustering

fast affinity propagation clustering a multilevel approach in this paper we propose a novel fast affinity propagation clustering approach fap fap simultaneously considers both local and global structure information contained in datasets and is a high quality multilevel graph partitioning method that can implement both vector based and graph based clustering first a new fast sampling algorithm fs is proposed to coarsen the input sparse graph and choose a small number of final representative exemplars then a density weighted spectral clustering method is presented to partition those exemplars on the global underlying structure of data manifold finally the cluster assignments of all data points can be achieved through their corresponding representative exemplars experimental results on two synthetic datasets and many real world datasets show that our algorithm outperforms the state of the art original affinity propagation and spectral clustering algorithms in terms of speed memory usage and quality on both vector based and graph based clustering

slow passage through the nonhyperbolic homoclinic orbit associated with a subcritical pitchfork bifurcation for hamiltonian systems and the change in action slowly varying conservative systems are analyzed in the case of a reverse subcritical pitchfork bifurcation in which two saddles and a center coalesce before the bifurcation there is a hyperbolic double homoclinic orbit connecting a linear saddle point at the bifurcation a double nonhyperbolic homoclinic orbit connects to a nonlinear saddle point strongly nonlinear oscillations obtained by the method of averaging are not valid near unperturbed homoclinic orbits in the case in which the solution slowly passes through the nonhyperbolic homoclinic orbit associated with the subcritical pitchfork bifurcation the solution consists of a large sequence of nonhyperbolic homoclinic orbits connecting autonomous nonlinear saddle approaches solutions are captured into the left and right well phase jumps and the boundaries of the basins of attraction are computed it is shown that the change in action in the slow passage through the nonhyperbolic homoclinic orbits is much larger than the known change in action f

ica based on asymmetry we build a new approach to ica which is based on the data asymmetry instead of densities with heavy tails we use asymmetric ones split gaussians we verified our approach on images sound and eeg data in the case of source signal reconstructing our approach gives better results independent component analysis ica one of the basic tools in data analysis aims to find a coordinate system in which the components of the data are independent most of existing methods are based on the minimization of the function of fourth order moment kurtosis skewness third order moment has received much less attention in this paper we present a competitive approach to ica based on the split gaussian distribution which is well adapted to asymmetric data consequently we obtain a method which works better than the classical approaches especially in the case when the underlying density is not symmetric which is a typical situation in the color distribution in images

krein signatures for the faddeev takhtajan eigenvalue problem one of the difficulties in analyzing eigenvalue problems that arise in connection with integrable systems is that they are frequently non self adjoint making it difficult to determine where the spectrum lies in this paper we consider the problem of locating and counting the discrete eigenvalues associated with the faddeev takhtajan eigenvalue problem for which the sine gordon equation is the isospectral flow in particular we show that for potentials having either zero topological charge or topological charge 1 and satisfying certain monotonicity conditions the point spectrum lies on the unit circle and is simple furthermore we give an exact count of the number of eigenvalues this result is an analog of that of klaus and shaw for the zakharov shabat eigenvalue problem we also relate our results as well as those of klaus and shaw to the krein stability theory for j unitary matrices in particular we show that the eigenvalue problem associated to the sine gordon equation has a j unitary structure and under the above conditions the point eigenvalues have a definite krein signature and are thus simple and lie on the unit circle

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

an asymptotic expression for the splitting of separatrices of the rapidly forced pendulum the measure of the splitting of the separatrices of the rapidly forced pendulum ddot x sin x mu sin frac t varepsilon is considered as a model problem that has been studied by different authors here e are small parameters e 0 but otherwise independent the following formula for the angle between separatrices is established alpha frac pi 2 varepsilon frac mu cosh frac pi 2 varepsilon left 1 o mu varepsilon 2 right

slow passage through homoclinic orbits for the unfolding of a saddle center bifurcation and the change in the adiabatic invariant slowly varying conservative one degree of freedom hamiltonian systems are analyzed in the case of a saddle center bifurcation at the bifurcation a homoclinic orbit connects to a nonhyperbolic saddle point using averaging for strongly nonlinear oscillations action is an adiabatic invariant before and after the slow passage of the homoclinic orbit the homoclinic orbit is assumed to be crossed near to its creation in the saddle center bifurcation a dynamic unfolding a large sequence of nearly homoclinic orbits with autonomous saddle approaches is matched to the strongly nonlinear oscillations valid before and after connection formulas are computed determining the change in the action due to the slow passage through the unfolding of the saddle center bifurcation if the energy in one specific saddle region is particularly small as occurs near the boundaries of the basin of attraction then the solution in only that saddle region satisfies the nonautonomous painleve i

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

on the orthogonal distance to class subspaces for high dimensional data classification the orthogonal distance from an instance to the subspace of a class is a key metric for pattern classification by the class subspace based methods there is a close relationship between the orthogonal distance and the residual standard deviation of a test instance from the class subspace in this paper we shall show that an established and widely used relationship between the residual standard deviation and the sum of squares of the residual pc scores is not precise and thus can lead to incorrect results for the inference of high dimensional data which nowadays are common in practice

cumulant based blind identification of linear multi input multi output systems driven by colored inputs the blind identification problem of a linear multi input multi output mimo system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation however such a problem is ill posed and has no unique solution therefore we can only find a solution of the problem within an equivalence class we address the blind identification problem of the linear mimo system driven by unobservable colored inputs using higher order statistics hos particularly the fourth order cumulants of the outputs where the unobservable inputs are mutually independent but temporally colored linear processes we first define the set which is denoted by s of stable scalar transfer functions and then define the notion of a generalized permutation matrix which is abbreviated by a g matrix over s then it is shown that the transfer function matrix of an unknown system is identified only up to post multiplication by a g matrix this result is applied to identifying fir systems for blind signal separation

coupling constant behavior of eigenvalues of zakharov shabat systems we consider the eigenvalues of the non self adjoint zakharov shabat systems as the coupling constant of the potential is varied in particular we are interested in eigenvalue collisions and eigenvalue trajectories in the complex plane we identify shape features in the potential that are responsible for the occurrence of collisions and we prove asymptotic formulas for large coupling constants that tell us where eigenvalues collide or where they emerge from the continuous spectrum some examples are provided which show that the asymptotic methods yield results that compare well with exact numerical computations

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

parameter identifiability of multichannel arma models of linear non gaussian signals via cumulant matching the problem of estimating the parameters of a vector stationary arma p q signal model driven by an i i d vector non gaussian sequence is considered the focus of the paper is the problem of parameter identifiability of multichannel arma models given the higher order cumulants of the signal on a finite set of lags the authors specify the finite lag set for general arma p q models the approach is to first derive the basic results via a diagonal canonical form and then to extend the parameter identifiability results to other more parsimonious canonical forms

blind identification of volterra hammerstein systems this paper is concerned with the blind identification of volterra hammerstein systems two identification scenarios are covered the first scenario assumes that although the input is not available the statistics of the input are a priori known this case appears in communication applications where the input statistics of the transmitter are known to the receiver the second scenario assumes that the input statistics are unknown in the case of known input statistics the input is stationary higher order white noise with arbitrary probability density function under the scenario of unknown input statistics the input is restricted to gaussian white process new cumulant based identification methods are described for the above scenarios the problem is converted into a linear multivariable form and the output cumulants are calculated using kronecker products first initial conditions are determined by a linear system of equations these correspond to the boundary values of the volterra kernels the remaining kernel coefficients can be determined under both identification schemes from a possibly overdetermined system of linear equations

the cross bicepstrum definition properties and application for simultaneous reconstruction of three nonminimum phase signals the recovery of three signals from their cross bispectrum or the identification of the impulse responses of three parallel linear time invariant lti systems from the cross bispectrum of their system outputs by computing the complex cepstrum of the cross bispectrum as long as the signals or impulse responses have no zeros on the unit circle is discussed it is shown that the three signals can be separated completely and approximately recovered in the cross bicepstrum domain except for their magnitude and linear phase factors the computation of the cross bicepstrum can be seen as a method for the simultaneous computation of the ordinary complex cepstra of three nonminimum phase signals without the need for phase unwrapping both least squares and fast fourier transform fft based methods for computing the bicepstral coefficients are presented simulation examples of signal reconstruction in gaussian white and nongaussian colored noise and of system identification are included the results are extended to nth order cross spectra and the factorization problem for these spectra is discussed

ground truth bias in external cluster validity indices external cluster validity indices cvis are used to quantify the quality of a clustering by comparing the similarity between the clustering and a ground truth partition however some external cvis show a biased behavior when selecting the most similar clustering users may consequently be misguided by such results recognizing and understanding the bias behavior of cvis is therefore crucial it has been noticed that some external cvis exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic directly or inversely in the number of clusters in candidate partitions this type of bias is caused by the functional form of the cvi model for example the popular rand index ri exhibits a monotone increasing ncinc bias while the jaccard index ji index suffers from a monotone decreasing ncdec bias this type of bias has been previously recognized in the literature in this work we identify a new type of bias arising from the distribution of the ground truth reference partition against which candidate partitions are compared we call this new type of bias ground truth gt bias this type of bias occurs if a change in the reference partition causes a change in the bias status e g ncinc ncdec of a cvi for example ncinc bias in the ri can be changed to ncdec bias by skewing the distribution of clusters in the ground truth partition it is important for users to be aware of this new type of biased behavior since it may affect the interpretations of cvi results the objective of this article is to study the empirical and theoretical implications of gt bias to the best of our knowledge this is the first extensive study of such a property for external cvis our computational experiments show that 5 of 26 pair counting based cvis studied in this paper which are all functions of the ri exhibit gt bias following the numerical examples we provide a theoretical analysis of gt bias based on the relationship between the ri and quadratic entropy specifically we prove that the quadratic entropy of the ground truth partition provides a computable test which predicts the nc bias status of the ri we identify the gt bias effect for external validation measures and explain its importance we test and discuss nc bias for 26 popular pair counting based validation measures we prove that the ri and related 4 indices suffer from gt bias we provide theoretical explanations for understanding why and when gt bias happens we present experimental results that support our analysis we present an empirical example to show that the ari also suffers from a modified gt bias

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

active selection of clustering constraints this paper examines active selection of clustering constraints which has become a topic of significant interest in constrained clustering active selection of clustering constraints which is known as minimizing the cost of acquiring constraints also includes quantifying utility of a given constraint set a sequential method is proposed in this paper to select the most beneficial set of constraints actively the proposed method uses information of boundary points and transition regions extracted by data description methods to introduce a utility measure for constraints since previously selected constraints affect the utility of remaining candidate constraints a method is proposed to update the utility of remaining constraints after selection of each constraint experiments carried out on synthetic and real datasets show that the proposed method improves the accuracy of clustering while reducing human interaction highlightsactive constraint selection as an open issue in constrained clustering is examined the method relies on the information of boundaries and transition regions of data a utility measure based on the description of data is proposed for constraints this utility measure considers the constraint utility dependencies constraints are selected in a sequential approach utilizing the utility measure

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

exact solutions of semiclassical non characteristic cauchy problems for the sine gordon equation abstract the use of the sine gordon equation as a model of magnetic flux propagation in josephson junctions motivates studying the initial value problem for this equation in the semiclassical limit in which the dispersion parameter e tends to zero assuming natural initial data having the profile of a moving 2 kink at time zero we analytically calculate the scattering data of this completely integrable cauchy problem for all e 0 sufficiently small and further we invert the scattering transform to calculate the solution for a sequence of arbitrarily small e this sequence of exact solutions is analogous to that of the well known n soliton or higher order soliton solutions of the focusing nonlinear schrodinger equation we then use plots obtained from a careful numerical implementation of the inverse scattering algorithm for reflectionless potentials to study the asymptotic behavior of solutions in the semiclassical limit in the limit e 0 one observes the appearance of nonlinear caustics i e curves in space time that are independent of e but vary with the initial data and that separate regions in which the solution is expected to have different numbers of nonlinear phases in the appendices we give a self contained account of the cauchy problem from the perspectives of both inverse scattering and classical analysis picard iteration specifically appendix a contains a complete formulation of the inverse scattering method for generic l 1 sobolev initial data and appendix b establishes the well posedness for l p sobolev initial data which in particular completely justifies the inverse scattering analysis in appendix a

general approach to blind source separation this paper identifies and studies two major issues in the blind source separation problem separability and separation principles we show that separability is an intrinsic property of the measured signals and can be described by the concept of m row decomposability introduced in this paper we also show that separation principles can be developed by using the structure characterization theory of random variables in particular we show that these principles can be derived concisely and intuitively by applying the darmois skitovich theorem which is well known in statistical inference theory and psychology some new insights are gained for designing blind source separation filters

critical velocity in kink defect interaction models rigorous results abstract in this work we study a model of interaction of kinks of the sine gordon equation with a weak defect we obtain rigorous results concerning the so called critical velocity derived in 7 by a geometric approach more specifically we prove that a heteroclinic orbit in the energy level 0 of a 2 dof hamiltonian h e is destroyed giving rise to heteroclinic connections between certain elements at infinity for exponentially small in e energy levels in this setting melnikov theory does not apply because there are exponentially small phenomena

kink antikink interactions in a modified sine gordon model we study numerically the interactions of a kink k and an antikink k in a parametrically modified sine gordon model with potential v 1 r 2 1 cos 1 r2 2rcos as the parameter r is varied from the pure sine gordon case r 0 to values for which the model is not completely integrable r 0 we find that a rich structure arises in the kk collisions for some regions of r 0 20 r 0 this structure is very similar to that observed in kk interactions in the 4 model and we show that the theory recently suggested for these collisions also applies quantitatively to the modified sine gordon model in other regions of r we observe new scattering phenomena which we present in detail numerically and discuss in a qualitative manner analytically

a cumulant based hankel approach to direction of arrival estimation a new cumulant based approach to doa estimation for independent nongaussian sources and a uniform linear array is presented the doas are obtained by finding the eigenvalues of a matrix made up from cumulants of the data as with other cumulant based methods the present method does not need the characteristics of the noise when the noise is gaussian this algorithm is developed using an approach that leads to a general relation between the cumulant functions and the parameters to be estimated this general relation gives a common framework for developing other algorithms for doa estimation computer simulation results show the effectiveness of this new method

complexity and regularity of vector soliton collisions in this paper we extensively investigate the collision of vector solitons in the coupled nonlinear schrodinger equations first we show that for collisions of orthogonally polarized and equal amplitude vector solitons when the cross phase modulational coefficientb is small a sequence of reflection windows similar to that in the f 4 model arises when b increases a fractal structure unlike f 4 s gradually emerges but when b is greater than one this fractal structure disappears analytically we explain these collision behaviors by a variational model that qualitatively reproduces the main features of these collisions this variational model helps to establish that these window sequences and fractal structures are caused entirely or partially by a resonance mechanism between the translational motion and width oscillations of vector solitons next we investigate collision dependence on initial polarizations of vector solitons we discovered a sequence of reflection windows that is phase induced rather than resonance induced analytically we have derived a simple formula for the locations of these phase induced windows and this formula agrees well with the numerical data last we discuss collision dependence on relative amplitudes of initial vector solitons we show that when vector solitons have different amplitudes the collision structure simplifies feasibility of experimental obser vation of these results is also discussed at the end of the paper