broad band detection based on two dimensional mixed autoregressive models two detectors for broadband plane waves in colored noise fields that use a linear array are described the signal spectrum arrival angle and noise field coloration are not known a priori using a two dimensional mixed autoregressive model a generalized likelihood ratio test and its weak signal equivalent the rao test are derived the performances of the proposed detectors are shown by computer simulations to be superior to those of conventional fourier based methods detection results for real data are presented

density based multiscale data condensation a problem gaining interest in pattern recognition applied to data mining is that of selecting a small representative subset from a very large data set in this article a nonparametric data reduction scheme is suggested it attempts to represent the density underlying the data the algorithm selects representative points in a multiscale fashion which is novel from existing density based approaches the accuracy of representation by the condensed set is measured in terms of the error in density estimates of the original and reduced sets experimental studies on several real life data sets show that the multiscale approach is superior to several related condensation methods both in terms of condensation ratio and estimation error the condensed set obtained was also experimentally shown to be effective for some important data mining tasks like classification clustering and rule generation on large data sets moreover it is empirically found that the algorithm is efficient in terms of sample complexity

on the limit products of a family of matrices in this paper we direct attention at bounded families of complex n n matrices in order to study their asymptotic behaviour we recall from linear algebra appl 322 2001 162 the concept of limit spectrum maximizing product and show that nondefective families always admit such limit products then we consider defective families in loc cite we proved that for finite families of 2 2 matrices defectivity is equivalent to the existence of defective such limit products this result led us to conjecture the validity of this property also for higher dimensions n 3 here instead by making use of the results obtained by bousch and mairesse j am math soc 15 2002 77 that disproved the well known finiteness conjecture we find some counterexamples to our conjecture in loc cite for all n 3 2002 elsevier science inc all rights reserved

on minimum class locality preserving variance support vector machine in this paper a so called minimum class locality preserving variance support machine mclpv svm algorithm is presented by introducing the basic idea of the locality preserving projections lpp which can be seen as a modified class of support machine svm and or minimum class variance support machine mcvsvm mclpv svm in contrast to svm and mcvsvm takes the intrinsic manifold structure of the data space into full consideration and inherits the characteristics of svm and mcvsvm we discuss in the paper the linear case the small sample size case and the nonlinear case of the mclpv svm similar to mcvsvm the mclpv svm optimization problem in the small sample size case is solved by using dimensionality reduction through principal component analysis pca and one in the nonlinear case is transformed into an equivalent linear mclpv svm problem under kernel pca kpca experimental results on real datasets indicate the effectiveness of the mclpv svm by comparing it with svm and mcvsvm

parametric glrt for multichannel adaptive signal detection this paper considers the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance a parametric generalized likelihood ratio test glrt is developed by modeling the disturbance as a multichannel autoregressive ar process maximum likelihood ml parameter estimation underlying the parametric glrt is examined it is shown that the ml estimator for the alternative hypothesis is nonlinear and there exists no closed form expression to address this issue an asymptotic ml aml estimator is presented which yields asymptotically optimum parameter estimates at reduced complexity the performance of the parametric glrt is studied by considering challenging cases with limited or no training signals for parameter estimation such cases especially when training is unavailable are of great interest in detecting signals in heterogeneous fast changing or dense target environments but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level compared with the recently introduced parametric adaptive matched filter pamf and parametric rao detectors the parametric glrt achieves higher data efficiency offering improved detection performance in general

harmonic retrieval using higher order statistics a deterministic formulation given a single record the authors consider the problem of estimating the parameters of a harmonic signal buried in noise the observed data are modeled as a sinusoidal signal plus additive gaussian noise of unknown covariance the authors define novel higher order statistics referred to as mixed cumulants that can be consistently estimated using a single record and are insensitive to colored gaussian noise employing fourth order mixed cumulants they estimate the sinusoid parameters using a consistent nonlinear matching approach the algorithm requires an initial estimate that is obtained from a consistent linear estimator finally the authors examine the performance of the proposed method via simulations

scalable tsk fuzzy modeling for very large datasets using minimal enclosing ball approximation in order to overcome the difficulty in takagi sugeno kang tsk fuzzy modeling for large datasets scalable tsk stsk fuzzy model training is investigated in this study based on the core set based minimal enclosing ball meb approximation technique the specified l2 norm penalty based insensitive criterion is first proposed for tsk model training and it is found that such tsk fuzzy model training can be equivalently expressed as a center constrained meb problem with this finding an stsk fuzzy model training algorithm which is called stsk for large or very large datasets is then proposed by using the core set based meb approximation technique the proposed algorithm has two distinctive advantages over classical tsk fuzzy model training algorithms the maximum space complexity for training is not reliant on the size of the training dataset and the maximum time complexity for training is linear with the size of the training dataset as confirmed by extensive experiments on both synthetic and real world regression datasets

parameter estimation of exponentially damped sinusoids using higher order statistics a new approach for the estimation of the parameters of exponentially damped sinusoids is introduced based on third or fourth order statistics of the observation signal the method may be seen as an extension of the minimum norm principal eigenvectors method to higher order statistics domains the strong points and limitations of the method are discussed as well as sufficient conditions for the existence of the solution the utilization of the method in the case of finite length signals in the presence of additive gaussian noise white or colored is addressed monte carlo simulations demonstrate the effectiveness of the new method when the additive noise is colored gaussian with unknown autocorrelation sequence for different signal to noise ratios and a single data record the case of an ensemble of data records is studied when the exponentially damped sinusoids are assumed to have random phase

fast parzen density estimation using clustering based branch and bound this correspondence proposes a fast parzen density estimation algorithm that would be especially useful in nonparametric discriminant analysis problems by preclustering the data and applying a simple branch and bound procedure to the clusters significant numbers of data samples that would contribute little to the density estimate can be excluded without detriment to actual evaluation via the kernel functions this technique is especially helpful in the multivariant case and does not require a uniform sampling grid the proposed algorithm may also be used in conjunction with the data reduction technique of fukunaga and hayes 1989 to further reduce the computational load experimental results are presented to verify the effectiveness of this algorithm

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

estimation of close sinusoids in colored noise and model discrimination this paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown earlier attempts have assumed the additive noise to be independent next we develop decision rules for checking whether the observed signal has only one sinusoid or two close sinusoids all of the earlier studies assumed that there are two close sinusoids in the signal another model discrimination problem considered is the determination of the causal structure of the observed periodicity a rule is given to test whether the observation comes from a sinusoid plus additive noise possible colored or the observation comes from a stationary autoregressive model we also present a numerical study showing the efficacy of the robust estimation procedure for estimating the two frequencies and the decision rules for checking the number of dominant frequencies and the causal mechanism finally we compare the proposed method to well known methods used for two close sinusoids in white noise

density estimation by wavelet thresholding density estimation is a commonly used test case for nonparametric estimation methods we explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients minimax rates of convergence are studied over a large range of besov function classes b pq and for a range of global l p error measures 1 p p some form of nonlinearity is essential since the minimax linear estimators are suboptimal by polynomial powers of n a second approach using an approximation of a gaussian white noise model in a mallows metric is used to attain exactly optimal rates of convergence for quadratic error p 2

a compact cramer rao bound expression for parametric estimation of superimposed signals the problem of parameter estimation of superimposed signals in white gaussian noise is considered closed form expressions of the cramer rao bound for real or complex signals with vector parameters are derived extending recent results by p stoica and a nehorai 1989

on the asymptotic properties of a family of matrices in this paper we consider bounded families f of complex n n matrices after introducing the concept of asymptotic order we investigate how the norm of products of matrices behaves as the number of factors goes to infinity in the case of defective families f u sing the asymptotic order allows us to get a deeper knowledge of the asymptotic behaviour than just considering the so called generalized spectral radius with reference to the well known finiteness conjecture for finite families we also introduce the concepts of spectrum maximizing product and limit spectrum maximizing product showing that for finite families of 2 2matrices defectivity is equivalent to the existence of defective such limit products 2001 elsevier science inc all rights reserved

parameter estimation and glrt detection in colored non gaussian autoregressive processes the problem of estimating signal and noise parameters from a mixture of nongaussian autoregressive noise with partially known deterministic signal is discussed two models are considered in order to examine different kinds of additive mixing the cramer rao bounds to the joint estimation of the signal amplitude and the noise parameters are presented a computationally simple estimator which was previously proposed for estimation in the absence of signal is extended for the two models under consideration the proposed method essentially consists of two stages of least squares estimation which is motivated by the maximum likelihood estimation the technique is applied to the problem of detecting a signal known except for amplitude in colored nongaussian noise two slightly different mixing models are used and a generalized likelihood ratio test glrt coupled with the proposed estimation scheme is used to solve the problems the results of computer simulations are presented as evidence of the validity of the theoretical productions of performance

maximum likelihood parameter estimation of discrete homogeneous random fields with mixed spectral distributions this paper presents a maximum likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a real valued 2 d homogeneous random field with mixed spectral distribution on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent the proposed algorithm provides a complete solution to the joint estimation problem of the random field components by introducing appropriate parameter transformations the highly nonlinear least squares problem that results from the maximization of the likelihood function is transformed into a separable least squares problem in this new problem the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares solution of the transformation equations provides a complete solution of the field model parameter estimation problem

asymptotically optimal detection in unknown colored noise via autoregressive modeling the problem of detecting a known signal in colored gaussian noise of unknown covariance is addressed the noise is modeled as an autoregressive process of known order but unknown coefficients by employing the theory of generalized likelihood ratio testing a detector structure is derived and then analyzed for performance it is proven that for large data records the detection performance is identical to that of an optimal prewhitener and matched filter and therefore the detector itself is optimal simulation results indicate that the data record length necessary for the asymptotic results to apply can be quite small thus the proposed detector is well suited for practical applications

enhancement of sinusoids in colored noise and the whitening performance of exact least squares predictors the extraction of sinusoids in white noise using least squares predictors has attracted a lot of attention in the past mainly in the context of the adaptive line enhancer ale however very few results exist for the practical colored noise case or for the whitening performance of the predictors we use a matrix formulation to derive the optimal least squares coefficients and frequency response of the d step predictor or ale for sinusoids real or complex in additive colored noise several cases are considered and in particular new formulas for the amplitude gain are obtained in low pass background noise the amplitude gain of the sinusoids becomes essentially a monotonically increasing function of their frequency and a decreasing function for high pass noise for the whitening application signal to noise ratio snr bounds of the output are derived when the input is a white signal plus a sinusoidal interference we also give a state space model and stochastic interpretations of our analysis of the d step predictor providing connections to other related areas to enable filtering of nonstationary complex inputs as well as multichannel and multiexperiment data a complex vector version of the ladder algorithm is presented that can be used to implement the ale noise cancelling and noise inversion for narrow band interference rejection

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

on the accuracy of estimating the parameters of a regular stationary process any regular stationary random processes can be represented as the sum of a purely indeterministic process and a deterministic one this paper considers the achievable accuracy in the joint estimation of the parameters of these two components from a single observed realization of the process an exact form of the cramer rao bound crb is derived as well as a conditional crb the relationships between these bounds and their relations to the previously derived asymptotic bound are explored by analysis and numerical examples

detection in incompletely characterized colored non gaussian noise via parametric modeling the problem of detecting a weak signal known except for amplitude in incompletely characterized colored non gaussian noise is addressed the problem is formulated as a test of composite hypotheses using parameteric models for the statistical behavior of the noise a generalized likelihood ratio test glrt is employed it is shown that for a symmetric noise probability density function the detection performance is asymptotically equivalent to that obtained for a similar detector designed with a priori knowledge of the noise parameters non gaussian distributions are found to be more favorable for the purpose of detection than the gaussian distribution the computational burden of the glrt may be partially reduced by employing a rao efficient score test which shares all the nice asymptotic properties of the glrt for small signal amplitudes computer simulations of the performance of the rao detector support the theoretical results

asymptotically optimal detection for additive watermarking in the dct and dwt domains most of the watermarking schemes that have been proposed until now employ a correlation detector matched filter the current paper proposes a new detector scheme that can be applied in the case of additive watermarking in the dct discrete cosine transform or dwt discrete wavelet transform domain certain properties of the probability density function of the coefficients in these domains are exploited thus an asymptotically optimal detector is constructed based on well known results of the detection theory experimental results prove the superiority of the proposed detector over the correlation detector

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

efficient mixed spectrum estimation with applications to target feature extraction we present a decoupled parameter estimation dpe algorithm for estimating sinusoidal parameters from both 1 d and 2 d data sequences corrupted by autoregressive ar noise in the first step of the dpe algorithm we use a relaxation relax algorithm that requires simple fast fourier transforms ffts to obtain the estimates of the sinusoidal parameters we describe how the relax algorithm may be used to extract radar target features from both 1 d and 2 d data sequences in the second step of the dpe algorithm a linear least squares approach is used to estimate the ar noise parameters the dpe algorithm is both conceptually and computationally simple the algorithm not only provides excellent estimation performance under the model assumptions in which case the estimates obtained with the dpe algorithm are asymptotically statistically efficient but is also robust to mismodeling errors

on frequency estimation with the iqml algorithm a popular implementation of the kiss iqml algorithm for frequency estimation applies an inappropriate constraint to the parameter vector this results in high thresholds for certain frequency configurations by applying a consistent constraint a better estimator can be obtained

lightweight detection of additive watermarking in the dwt domain this article aims at lightweight blind detection of additive spread spectrum watermarks in the dwt domain we focus on two host signal noise models and two types of hypothesis tests for watermark detection as a crucial point of our work we take a closer look at the computational requirements of watermark detectors this involves the computation of the detection response parameter estimation and threshold selection we show that by switching to approximate host signal parameter estimates or even fixed parameter settings we achieve a remarkable improvement in runtime performance without sacrificing detection performance our experimental results on a large number of images confirm the assumption that there is not necessarily a tradeoff between computation time and detection performance

spectral analysis based on the canonical autoregressive decomposition statistical inference for mixed spectral problems based on a parametric time series model is studied the model used is based on the canonical autoregressive decomposition card and represents the underlying random process as the sum of an autoregressive process and sinusoids maximum likelihood estimation of the unknown parameters in the model is considered the entire estimation problem can be shown to require a numerical maximization with respect to only the sinusoidal frequencies an iterative algorithm to efficiently implement this maximization is presented this enables us to examine a host of issues associated with a practical implementation of inferential procedures for mixed spectral problems some of the topics are accuracy of parameter estimates selection of model orders and sensitivity and robustness of the spectral estimates to modeling inaccuracies the modeling approach together with the inferential procedures overcome many of the difficulties encountered in current spectral estimation techniques

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

fast computation of the exact fim for deterministic signals in colored noise a fast algorithm for computing the exact finite sample fisher information matrix fim for the parameters of a deterministic signal observed in gaussian ar noise is derived in the case of a harmonic signal with random phases closed form expressions for the finite sample posterior cramer rao bound pcrb are established it is shown that the fast algorithm is also useful for computing the conditional crb when the additive noise is a non gaussian ar process it is seen that the asymptotic crb may deviate significantly from the exact crb even when the data length is moderate whereas the pcrb which is easy to compute provides a better approximation theoretical results are illustrated via numerical evaluation of the different lower bounds

bayesian detection and estimation of cisoids in colored noise the problem of estimating the number of cisoids in colored noise is addressed it is assumed that the noise can be modeled by an autoregression whose order has also to be estimated a new criterion is proposed for estimating the number of cisoids and the autoregressive model order as well as a new algorithm for estimating the cisoidal frequencies in the derivation a bayesian methodology and subspace decomposition are employed the proposed criterion significantly outperforms the popular mdl and aic as applied in a paper by nagesha and kay in addition an algorithm that reduces the computational complexity of the solution is developed computer simulations that demonstrate the performance of the criterion are included

maximum likelihood estimation of multiple frequencies with constraints to guarantee unit circle roots an approximate maximum likelihood estimator mle of multiple exponentials converts the frequency estimation problem into a problem of estimating the coefficients of a z polynomial with roots at the desired frequencies theoretically the roots of the estimated polynomial should fall on the unit circle but mle as originally proposed does not guarantee unit circle roots this drawback sometimes causes merged frequency estimates especially at low snr if all the sufficient conditions for the z polynomial to have unit circle roots are incorporated the optimization problem becomes too nonlinear and it loses the desirable weighted quadratic structure of mle in the present paper the exact constraints are imposed on each of the first order factors corresponding to individual frequencies for ensuring unit circle roots the constraints are applied during optimization alternately for each frequency in the absence of any merged frequency estimates the rms values more closely approach the theoretical cramer rao cr bound at low snr levels

robust estimation of sinusoidal signals with colored noise using decentralized processing a technique is developed for the estimation of the number of signals and their central frequencies using decentralized processing when it is known a priori that the observations consist of a finite number of sinusoidal signals corrupted by an additive colored random noise process with unknown correlations such a noise sequence may be caused by jamming from a hostile agent the authors decentralized processing scheme is one in which each sensor estimates the frequencies and their covariance matrix and sends the results to the fusion center at the fusion center since the estimates from the sensors have a mixture density that is possibly not gaussian a robust technique is utilized to combine the estimates even when the numbers of frequencies transmitted by the various sensors are identical determining corresponding frequencies from each sensor is not a straightforward task also outliers caused by line splitting or by spurious frequencies are hard to detect these problems can be resolved by two methods the so called refitting method and the ranking method algorithms for both are presented in detail

a robust approach for high resolution frequency estimation a robust estimation method for frequencies of received signals is considered the influence function of a robust estimate is derived for the sinusoidal signals the variance of the robust estimate is also derived using the influence function it is found that the robust estimate attains the cramer rao lower bound crlb for the contaminated gaussian distribution it is of order o n sup 3 and is close to the crlb for the perfect gaussian distribution the authors introduce some basic definitions for the high resolution frequency estimation method and prove that the robust estimate has the high resolution property this property is also confirmed by numerical simulations

direction finding in the presence of colored noise by candidate identification a method is developed for identifying correct angles of arrivals from a set of candidate angles that contains spurious angles and the true ones under the assumption that the colored noise is an autoregressive process and that a uniform linear array of sensors is used the procedure is based on a relation derived for the higher order reflection coefficients corresponding to the autocorrelation sequence of the signal plus noise it is shown that the higher order reflection coefficients of a set of plane waves impinging on a uniform linear array of sensors in the presence of an unknown spatially autoregressive colored noise process are equal to an order independent linear combination of the values of the fourier transform of the corresponding optimal linear least squares normalized prediction error filter at the electric phase angles of the plane waves the magnitudes of the coefficients are then used to decide whether a given candidate direction of arrival corresponds to an actual plane wave or not the estimation of candidate angles is also briefly discussed

frsde fast reduced set density estimator using minimal enclosing ball approximation reduced set density estimator rsde is an important technique that can be used to replace the classical parzen window estimator pw for saving the computational cost though rsde demonstrates a nicer performance in the density accuracy and the computational time compared with several existing methods it still faces the critical challenge for practical applications because of its high time complexity no less than o n 2 and space complexity o n 2 in training the model weighting coefficients on large data sets in order to overcome this shortcoming a fast reduced set density estimator algorithm frsde is proposed in this study first the relationship between rsde and the minimal enclosing ball problems meb in computational geometry is revealed then the finding that rsde is equivalent to a special meb problem is derived with this finding the fast core set based meb approximation algorithm is introduced to develop the proposed algorithm frsde compared with rsde frsde has the following distinctive advantage it can guarantee that the upper bound of the time complexity is linear with the size n of a large data set and the upper bound of the space complexity is independent of n our experimental results show that the proposed frsde has a competitive performance in the density accuracy and an overwhelming advantage over rsde for large data sets in the data condensation rate and the training time for the weighting coefficients

detection of weak signals in non gaussian noise a locally optimum detector structure is derived for the detection of weak signals in non gaussian environments optimum performance is obtained by employing a zero memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise gaussian the asymptotic detection performance of the locally optimum detector under non gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in gaussian noise numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest

a dynamic programming algorithm for the maximum likelihood localization of multiple sources a dynamic programming algorithm is presented for simultaneously computing the maximum likelihood ml estimator of the number of multiple sources and their directions of arrival doa in sensor array processing based on the projection matrix decomposition technique the multivariate log likelihood maximization problem is transformed into a multistage one dimensional maximization problem the estimation procedure is obtained with relatively light computational load in addition the estimator gives satisfactory performance in the case of both coherent and incoherent sources the simulation results also show that when the element snr is low and or the number of snapshots is small the dp ml algorithm is much superior to music

bounds for estimation of complex exponentials in unknown colored noise we consider the problem of estimating the parameters of complex exponentials in the presence of complex additive gaussian noise with unknown covariance bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise we first present an exact cramer rao bound crb for this problem and specialize it for the cases of circular gaussian processes and autoregressive processes we also derive an approximate expression for the crb which is related to the conditional likelihood function numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy

singular value decomposition and improved frequency estimation using linear prediction linear prediction based lp methods for fitting multiple sinusoid signal models to observed data such as the forward backward fblp method of nuttall 5 and ulrych and clayton 6 are very ill conditioned the locations of estimated spectral peaks can be greatly affected by a small amount of noise because of the appearance of outliers lp estimation of frequencies can be greatly improved at low snr by singular value decomposition svd of the lp data matrix the improved performance at low snr is also better than that obtained by using the eigenvector corresponding to the minimum eigenvalue of the correlation matrix as is done in pisarenko s method and its variants

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

an algorithm for finding extremal polytope norms of matrix families in this paper the problem of the computation of the joint spectral radius of a finite set of matrices is considered we present an algorithm which under some suitable assumptions is able to check if a certain product in the multiplicative semigroup is spectrum maximizing the algorithm proceeds by attempting to construct a suitable extremal norm for the family namely a complex polytope norm as examples for testing our technique we first consider the set of two 2 dimensional matrices recently analyzed by blondel nesterov and theys to disprove the finiteness conjecture and then a set of 3 dimensional matrices arising in the zero stability analysis of the 4 step bdf formula for ordinary differential equations

broadband doa estimation using spatial only modeling of array data most of the existing techniques for doa estimation of broadband sources use both spatial and temporal modeling this may lead to increased complexity besides a large algorithmic delay we propose a technique that employs only spatial information in the form of a single spatial array covariance matrix assuming the source to have an ideal bandpass power spectral density we formulate two subspace based search functions for the estimation of the doas of broadband sources one of these employs a multidimensional search in the parameter space whereas the other requires a music like one dimensional 1 d search the multidimensional cost function is shown to be consistent yields performance close to the cramer rao cr bound and is insensitive to correlation between sources both the proposed methods are shown to be robust to deviations from the assumption of ideal bandpass power spectral density used in their formulation

image segmentation based on adaptive cluster prototype estimation an image segmentation algorithm based on adaptive fuzzy c means fcm clustering is presented in this paper in the conventional fcm clustering algorithm cluster assignment is based solely on the distribution of pixel attributes in the feature space and does not take into consideration the spatial distribution of pixels in an image by introducing a novel dissimilarity index in the modified fcm objective function the new adaptive fuzzy clustering algorithm is capable of utilizing local contextual information to impose local spatial continuity thus exploiting the high inter pixel correlation inherent in most real world images the incorporation of local spatial continuity allows the suppression of noise and helps to resolve classification ambiguity to account for smooth intensity variation within each homogenous region in an image a multiplicative field is introduced to each of the fixed fcm cluster prototype the multiplicative field effectively makes the fixed cluster prototype adaptive to slow smooth within cluster intensity variation and allows homogenous regions with slow smooth intensity variation to be segmented as a whole experimental results with synthetic and real color images have shown the effectiveness of the proposed algorithm

maximum likelihood estimation of signals in autoregressive noise time series modeling as the sum of a deterministic signal and an autoregressive ar process is studied maximum likelihood estimation of the signal amplitudes and ar parameters is seen to result in a nonlinear estimation problem however it is shown that for a given class of signals the use of a parameter transformation can reduce the problem to a linear least squares one for unknown signal parameters in addition to the signal amplitudes the maximization can be reduced to one over the additional signal parameters the general class of signals for which such parameter transformations are applicable thereby reducing estimator complexity drastically is derived this class includes sinusoids as well as polynomials and polynomial times exponential signals the ideas are based on the theory of invariant subspaces for linear operators the results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems the authors briefly discuss some applications such as spectral analysis broadband transient detection using line array data and fundamental frequency estimation for periodic signals

covariance sequence approximation for parametric spectrum modeling parametric methods of spectrum analysis are founded on finite dimensional models for covariance sequences rational spectrum approximants for continuous spectra are based on autoregressive ar moving average ma or autoregressive moving average arma models for covariance sequences line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences in this paper we make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes frequencies and damping factors the associated modal decomposition is appropriate for both continuous and discrete components of the spectrum the domain of attraction for the decomposition includes arma sequences harmonically or nonharmonically related sinusoids damped sinusoids white noise and linear combinations of these the parametric spectrum analysis problem now becomes one of identifying mode parameters this we achieve by solving two modified least squares problems numerical results are presented to illustrate the identification of mode parameters and corresponding spectra from finite records of perfect and estimated covariance sequences the results for sinusoids and sinusoids in white noise are interpreted in terms of in phase and quadrature effects attributable to the finite record length

probability density estimation from optimally condensed data samples the requirement to reduce the computational cost of evaluating a point probability density estimate when employing a parzen window estimator is a well known problem this paper presents the reduced set density estimator that provides a kernel based density estimator which employs a small percentage of the available data sample and is optimal in the l sub 2 sense while only requiring spl oscr n sup 2 optimization routines to estimate the required kernel weighting coefficients the proposed method provides similar levels of performance accuracy and sparseness of representation as support vector machine density estimation which requires spl oscr n sup 3 optimization routines and which has previously been shown to consistently outperform gaussian mixture models it is also demonstrated that the proposed density estimator consistently provides superior density estimates for similar levels of data reduction to that provided by the recently proposed density based multiscale data condensation algorithm and in addition has comparable computational scaling the additional advantage of the proposed method is that no extra free parameters are introduced such as regularization bin width or condensation ratios making this method a very simple and straightforward approach to providing a reduced set density estimator with comparable accuracy to that of the full sample parzen density estimator

estimation and detection in non gaussian noise using higher order statistics one of the primary applications of higher order statistics has been for detection and estimation of nongaussian signals in gaussian noise of unknown covariance this is motivated by the fact that higher order cumulants of gaussian processes vanish we study the opposite problem namely detection and estimation in nongaussian noise we estimate cumulants of nongaussian processes in the presence of unknown deterministic and or gaussian signals which allows either parametric or nonparametric estimation of the covariance of the nongaussian noise our approach is to augment existing second order detection methods using cumulants we propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants where the resulting solutions are valid under either detection hypotheses this allows for single record detection and obviates the need for noise only training records the problem of estimating signal strength in the presence of nongaussian noise of unknown covariance is also considered and a cumulant based solution is proposed which uses a single data record examples are used throughout to illustrate our proposed methods

signal detection in complex structured para normal noise in this paper we address target detection in correlated non gaussian noise we introduce a new class of multivariate complex valued distributions that allows us to specify flexible non gaussian marginals as well as correlation between the variables while preserving circular symmetry for noise belonging to this class we study the fundamental problem of signal detection under different settings and develop the needed generalized likelihood ratio tests we also consider estimation of the noise parameters and derive the maximum likelihood formulations we evaluate the merit of our approach using numerical simulations on synthetic and real data and clearly demonstrate the advantage of using both correlations and non gaussianity

wideband source location through frequency dependent modeling this paper describes a method for locating multiple wideband sources using the signals received by an array of sensors in the present approach the problem of source location is treated as a frequency dependent estimation problem each wideband source is received by the array as a vector signal the spatial spectrum of this signal has a linear frequency modulation with respect to the usual frequency which is characteristic of the source location the frequency modulation may be recovered by frequency dependent modeling over the entire frequency band the models are estimated by a technique of model expansion which consists in the replacement of the data by their projections on a basis of functions of frequency an invariant expanded model is fitted to these projections it expresses the evolution of a spatial model with respect to frequency an estimator based upon an eigen decomposition of a covariance matrix built from the observations is discussed this estimator leads to wideband versions of the high resolution estimators minimum norm solution and music simulations will conclude the paper and compare this estimator with the coherent signal subspace method

cisoid parameter estimation in the colored noise case asymptotic cramer rao bound maximum likelihood and nonlinear least squares the problem of estimating the parameters of complex valued sinusoidal signals cisoids for short from data corrupted by colored noise occurs in many signal processing applications we present a simple formula for the asymptotic large sample cramer rao bound crb matrix associated with this problem the maximum likelihood method mlm which estimates both the signal and noise parameters attains the performance corresponding to the asymptotic crb as the sample length increases more interestingly we show that a computationally much simpler nonlinear least squares method nlsm which estimates the signal parameters only achieves the same performance in large samples

weighted parzen windows for pattern classification this paper introduces the weighted parzen window classifier the proposed technique uses a clustering procedure to find a set of reference vectors and weights which are used to approximate the parzen window kernel estimator classifier the weighted parzen window classifier requires less computation and storage than the full parzen window classifier experimental results showed that significant savings could be achieved with only minimal if any error rate degradation for synthetic and real data sets

the finiteness conjecture for the generalized spectral radius of a set of matrices the generalized spectral radius g9 of a set of n n matrices is g9 lim supk g9k 1k where g9k sup a1a2 ak each ai the joint spectral radius g9 is g9 lim supk g9k 1k where g9k sup a1 ak each ai it is known that g9 g9 holds for any finite set of n n matrices the finiteness conjecture asserts that for any finite set of real n n matrices there exists a finite k such that g9 g9 g9k 1k the normed finiteness conjecture for a given operator norm asserts that for any finite set a1 am having all ai op 1 either g9 1 or g9 g9 g9k 1k 1 for some finite k it is shown that the finiteness conjecture is true if and only if the normed finiteness conjecture is true for all operator norms the normed finiteness conjecture is proved for a large class of operator norms extending results of gurvits in particular for polytope norms and for the euclidean norm explicit upper bounds are given for the least k having g9 g9k 1k these results imply upper bounds for generalized critical exponents for these norms

generalized core vector machines kernel methods such as the support vector machine svm are often formulated as quadratic programming qp problems however given m training patterns a naive implementation of the qp solver takes o m 3 training time and at least o m2 space hence scaling up these qps is a major stumbling block in applying kernel methods on very large data sets and a replacement of the naive method for finding the qp solutions is highly desirable recently by using approximation algorithms for the minimum enclosing ball meb problem we proposed the core vector machine cvm algorithm that is much faster and can handle much larger data sets than existing svm implementations however the cvm can only be used with certain kernel functions and kernel methods for example the very popular support vector regression svr cannot be used with the cvm in this paper we introduce the center constrained meb problem and subsequently extend the cvm algorithm the generalized cvm algorithm can now be used with any linear nonlinear kernel and can also be applied to kernel methods such as svr and the ranking svm moreover like the original cvm its asymptotic time complexity is again linear in m and its space complexity is independent of m experiments show that the generalized cvm has comparable performance with state of the art svm and svr implementations but is faster and produces fewer support vectors on very large data sets

detection of broadband planewaves in the presence of gaussian noise of unknown covariance asymptotically optimum tests using the 2 d autoregressive noise model this paper addresses the problem of detecting a broadband planewave in noise of unknown spatial and temporal covariance at a linear array of sensors results of asymptotic detection theory are applied to derive detectors that approach optimal performance for large data records a parametric approach is used to model the statistics of the data a 2 d autoregressive 2dar model is chosen to model the noise process two broadband planewave signal models are considered both models represent the signal as a sum of monochromatic planewaves in the gaussian model the amplitudes are assumed to be gaussian with a single variance parameter whereas in the deterministic assumption they are individual unknown parameters detectors based on asymptotic theory are derived for both models as part of the development of the asymptotically as optimum detector the fisher information matrix fim is derived a proof of the locally asymptotic normal lan property is provided for the gaussian model probability density function pdf both detectors however are as equivalent to the generalized likelihood ratio test glrt are as of constant false alarm rate cfar and perform as as well as the glrt constructed with full knowledge of the noise statistics the performance of both detectors are compared with each other and to a standard spatially normalized beamformer in a computer simulation

two dimensional modal analysis based on maximum likelihood the authors present a method for estimating the parameters of 2 d damped harmonic modal signals in additive gaussian noise this method applies in the cases of single or multiexperiment data and incoherent or coherent signals both synthesis and analysis models for the data are developed central to these models are the signal and orthogonal subspaces under the assumption of distinct modes in one of the two dimensions there exists an invertible function between the parameters of these two subspaces this function can be used to express the optimization problem given by maximum likelihood in terms of the orthogonal subspace the resulting problem can be solved by any of several methods including total least squares and iterative quadratic maximum likelihood iqml

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

the potential performance gain in using spectral information in passive detection localization of wideband sources we address the problem of detecting the presence of wideband point sources and or estimating their location using data collected by an array of sensors this passive localization problem is typical to applications where the radiated signals do not carry information and are of no interest however knowledge of their waveshape or their cross spectral matrix is essential for applying optimal sub optimal detection localization algorithms in this paper we present results of a study in which we compare the optimal procedures for detection localization and their performance to suboptimal procedures that use no spectral information or only partial spectral information we show that if the number of sensors in the array is larger than the number of sources to be localized or detected then the performance gain of the optimal procedures is potentially significant mainly in conditions of small separation and or high correlation between sources the performance gain is also a function of the spectrum it is potentially higher if the sources are known to be correlated and if their spectra is not smooth if however the number of sources is smaller than the number of sensors then the role of the spectral information in improving detection localization performance becomes major only the use of spectral prior enables reliable localization of more sources than sensors

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

estimating two dimensional frequencies by matrix enhancement and matrix pencil a new method called the matrix enhancement and matrix pencil memp method is presented for estimating two dimensional 2 d frequencies in the memp method an enhanced matrix is constructed from the data samples and then the matrix pencil approach is used to extract out the 2 d sinusoids from the principal eigenvectors of the enhanced matrix the memp method yields the estimates of the 2 d frequencies efficiently without solving the roots of a 2 d polynomial or searching in a 2 d space it is shown that the memp method can be faster than a 2 d fft method if the number of the 2 d sinusoids is much smaller than the data set simulation results are provided to show that the accuracy of the memp method can be very close to the cramer rao lower bound

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

a hybrid approach to harmonic retrieval in non gaussian arma noise addresses the harmonic retrieval problem in colored noise as contrasted to the reported studies in which gaussian noise was assumed this paper focuses on additive non gaussian arma noise our approach is hybrid in the sense that third order cumulants are first used to identify the ar part of the non gaussian noise process and then correlation based high resolution methods are used for the filtered process to estimate the number of harmonics and their frequencies simulation examples are presented to demonstrate the high resolution of this approach

semi supervised classification method through oversampling and common hidden space semi supervised classification methods attempt to improve classification performance based on a small amount of labeled data through full use of abundant unlabeled data although existing semi supervised classification methods have exhibited promising results in many applications they still have drawbacks including performance degeneration due to the introduction of unlabeled data and partially false labels in a small amount of labeled data to circumvent such drawbacks a new semi supervised classification method ochs ssc through oversampling and a common hidden space is proposed in the paper the primary characteristics of the proposed method include two aspects one is that unlabeled data are only used to generate new synthetic data to extend the minimal amount of labeled data the other is that the final classifier is learned in the extended feature space which is composed of the original feature space and the common hidden space found between labeled data and the synthetic data instead of the original feature space extensive experiments on 23 datasets indicate the effectiveness of the proposed method

modal decomposition signal subspace algorithms a new method of estimating the locations of multiple wide band emitters arriving at an array of sensors is presented in this paper the wide band emitter location problem is treated as a separable multidimensional spectrum estimation problem by modal decomposition of the estimated spectral factor or spectral density matrix at the poles of the emitters this modal decomposition method extends conventional sinusoidal separation approaches to wide band emitters several methods of modal decomposition are presented and the signal subspace approach of schmidt 2 and su and morf 3 4 is extended and applied to the decomposed spectral residues for determination of emitter locations the method is asymptotically exact and provides the capability to resolve correlated or even coherent emitters

a note on marginal stability of switched systems in this note we present criteria for marginal stability and marginal instability of switched systems for switched nonlinear systems we prove that uniform stability is equivalent to the existence of a common weak lyapunov function cwlf that is generally not continuous for switched linear systems we present a unified treatment for marginal stability and marginal instability for both continuous time and discrete time switched systems in particular we prove that any marginally stable system admits a norm as a cwlf by exploiting the largest invariant set contained in a polyhedron several insightful algebraic characteristics are revealed for marginal stability and marginal instability

generalized likelihood ratios for testing the properness of quaternion gaussian vectors in a recent paper the second order statistical analysis of quaternion random vectors has shown that there exist two different kinds of quaternion widely linear processing which are associated with the two main types of quaternion properness in this paper we consider the problem of determining from a finite number of independent vector observations whether a quaternion gaussian vector is proper or not specifically we derive three generalized likelihood ratio tests glrts for testing the two main kinds of quaternion properness and show that the glrts reduce to the estimation of three previously proposed quaternion improperness measures interestingly the three glrt statistics improperness measures can be interpreted as an estimate of the entropy loss due to the quaternion improperness additionally we analyze the case in which the orthogonal basis for the representation of the quaternion vector is unknown which results in the problem of estimating the principal bbc properness direction i e the pure unit quaternion minimizing the bbc improperness measure although this estimation problem is not convex we propose a technique based on successive convex approximations which can be solved in closed form finally some simulation examples illustrate the performance and practical application of the proposed tests

multivariate online kernel density estimation with gaussian kernels we propose a novel approach to online estimation of probability density functions which is based on kernel density estimation kde the method maintains and updates a non parametric model of the observed data from which the kde can be calculated we propose an online bandwidth estimation approach and a compression revitalization scheme which maintains the kde s complexity low we compare the proposed online kde to the state of the art approaches on examples of estimating stationary and non stationary distributions and on examples of classification the results show that the online kde outperforms or achieves a comparable performance to the state of the art and produces models with a significantly lower complexity while allowing online adaptation

doa estimation of wideband sources using a harmonic source model and uniform linear array we consider the problem of estimation of the doas of multiple wideband sources incident on a uniform linear array ula in the presence of spatially and temporally white gaussian noise wgn the approach presented builds up on the iqml algorithm suggested by bresler and macovski 1986 for the case of narrowband doa estimation it is shown that the concept of an arma model for the observed data vector for the narrowband case can be generalized to model an appropriately stacked space time data vector obtained by combining the space time samples the coefficients of the corresponding 2 d predictor polynomial can be used to represent the null subspace of the wideband array steering matrix and rooting of the polynomial at each frequency separately gives the doa estimates these separate estimates at multiple frequencies are combined into a single doa estimate in a least squares sense this leads to the formulation of an iqml like procedure for the spatial parameter estimation of wideband sources like its narrowband counterpart the proposed approach is applicable to both noncoherent and coherent sources the performance of the proposed method is studied via extensive computer simulations and by comparison with the cramer rao bounds

asymptotically optimal detection in incompletely characterized non gaussian noise the problem of detecting a signal known except for amplitude in non gaussian noise is addressed the noise samples are assumed to be independent and identically distributed with a probability density function known except for a few parameters using a generalized likelihood ratio test it is proven that for a symmetric noise probability density function the detection performance is asymptotically equivalent to that obtained for a detector designed with a priori knowledge of the noise parameters a computationally more efficient but equivalent test is proposed and a computer simulation performed to illustrate the theory is described

robust relief feature weighting margin maximization and fuzzy optimization a latest advance in relief feature weighting techniques is that the iterative procedure of relief can be approximately expressed as a margin maximization problem and therefore its distinctive properties can be investigated with the help of optimization theory being motivated by this advance the relief feature weighting algorithm is investigated for the first time within a fuzzy optimization framework a new margin based objective function that incorporates three fuzzy concepts namely fuzzy difference measure fuzzy feature weighting and fuzzy instance force coefficient is introduced by the application of fuzzy optimization to this new margin based objective function several useful theoretical results are derived based upon which a set of robust relief feature weighting algorithms are proposed for two class data multiclass data and then online data as demonstrated by extensive experiments in synthetic datasets the university of california at irvine uci benchmark datasets cancer gene expression datasets and face image datasets the proposed algorithms were found to be competitive with the state of the art algorithms and robust for datasets with noise and or outliers

t2fela type 2 fuzzy extreme learning algorithm for fast training of interval type 2 tsk fuzzy logic system a challenge in modeling type 2 fuzzy logic systems is the development of efficient learning algorithms to cope with the ever increasing size of real world data sets in this paper the extreme learning strategy is introduced to develop a fast training algorithm for interval type 2 takagi sugeno kang fuzzy logic systems the proposed algorithm called type 2 fuzzy extreme learning algorithm t2fela has two distinctive characteristics first the parameters of the antecedents are randomly generated and parameters of the consequents are obtained by a fast learning method according to the extreme learning mechanism in addition because the obtained parameters are optimal in the sense of minimizing the norm the resulting fuzzy systems exhibit better generalization performance the experimental results clearly demonstrate that the training speed of the proposed t2fela algorithm is superior to that of the existing state of the art algorithms the proposed algorithm also shows competitive performance in generalization abilities

classification of digital amplitude phase modulated signals in time correlated non gaussian channels in this paper a new algorithm is proposed for the classification of digital amplitude phase modulated signals in flat fading channels with time correlated non gaussian noise the first order statistics of the additive noise is modeled by a gaussian mixture distribution and an autoregressive ar process is used to model the time correlation the proposed classifier involves the use of a whitening filter necessary to reduce the complexity of the classification process and maximum likelihood classification for the estimation of the whitening filter coefficients a new blind technique that is based on the use of a robust h filter is developed after whitening the received signal following a composite hypothesis testing approach the unknown fading and noise distribution parameters are estimated results are presented which show that when the noise process is time correlated non gaussian the proposed classifier outperforms maximum likelihood classifiers developed under the assumption that the noise process is either white non gaussian or white gaussian it is also shown that when the noise process is white gaussian the proposed classifier s performance closely approaches that of the maximum likelihood classifier developed for white gaussian noise channels

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

optimal norms and the computation of joint spectral radius of matrices the notion of spectral radius of a set of matrices is a natural extension of spectral radius of a single matrix the finiteness conjecture fc claims that among the infinite products made from the elements of a given finite set of matrices there is a certain periodic product made from the repetition of the optimal product whose rate of growth is maximal fc has been disproved in this paper it is conjectured that fc is almost always true and an algorithm is presented to verify the optimality of a given product the algorithm uses optimal norms as a special subset of extremal norms several conjectures related to optimal norms and non decomposable sets of matrices are presented the algorithm has successfully calculated the spectral radius of several parametric families of pairs of matrices associated with compactly supported multi resolution analyses and wavelets the results of related numerical experiments are presented

asymptotic stability and generalized gelfand spectral radius formula let be a set of n n complex matrices for m 1 2 let m be the set of all products of matrices in of length m denote by the multiplicative semigroup generated by is said to be asymptotically stable in the sense of dynamical systems if there is 0 1 such that there are bounded neighborhoods u v cn of the origin for which av mu for all a m m 1 2 for a bounded set of n n complex matrices it is shown that the following conditions are mutually equivalent i is asymptotically stable ii g9 lim supm supa m a 1 m 1 iii lim supm supa m a 1 m 1 where a stands for the spectral radius of a and iv there exists a positive number such that a 1 for all a this fact answers an open question raised by brayton and tong the generalized gelfand spectral radius formula that is g9 conjectured by daubechies and lagarias and proved by berger and wang using advanced tools from ring theory and then by elsner using analytic geometric tools follows immediately form the above asymptotic stability theorem

asymptotic height optimization for topical ifs tetris heaps and the finiteness conjecture given an iterated function system ifs of topical maps verifying some conditions we prove that the asymptotic height optimization problems are equivalent to finding the extrema of a continuous functional the average height on some compact space of measures we give general results to determine these extrema and then apply them to two concrete problems first we give a new proof of the theorem that the densest heaps of two tetris pieces are sturmian second we construct an explicit counterexample to the lagarias wang finiteness conjecture

core vector machines fast svm training on very large data sets standard svm training has o m3 time and o m2 space complexities where m is the training set size it is thus computationally infeasible on very large data sets by observing that practical svm implementations only approximate the optimal solution by an iterative strategy we scale up kernel methods by exploiting such approximateness in this paper we first show that many kernel methods can be equivalently formulated as minimum enclosing ball meb problems in computational geometry then by adopting an efficient approximate meb algorithm we obtain provably approximately optimal solutions with the idea of core sets our proposed core vector machine cvm algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m experiments on large toy and real world data sets demonstrate that the cvm is as accurate as existing svm implementations but is much faster and can handle much larger data sets than existing scale up methods for example cvm with the gaussian kernel produces superior results on the kddcup 99 intrusion detection data which has about five million training patterns in only 1 4 seconds on a 3 2ghz pentium 4 pc