algebraic signal processing theory cooley tukey type algorithms for dcts and dsts in this paper we systematically derive a large class of fast general radix algorithms for various types of real discrete fourier transforms real dfts including the discrete hartley transform dht based on the algebraic signal processing theory this means that instead of manipulating the transform definition we derive algorithms by manipulating the polynomial algebras underlying the transforms using one general method the same method yields the well known cooley tukey fast fourier transform fft as well as general radix discrete cosine and sine transform algorithms the algebraic approach makes the derivation concise unifies and classifies many existing algorithms yields new variants enables structural optimization and naturally produces a human readable structural algorithm representation based on the kronecker product formalism we show for the first time that the general radix cooley tukey and the lesser known bruun algorithms are instances of the same generic algorithm further we show that this generic algorithm can be instantiated for all four types of the real dft and the dht

statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

oversampled graph laplacian matrix for graph filter banks we describe a method of oversampling signals defined on a weighted graph by using an oversampled graph laplacian matrix the conventional method of using critically sampled graph filter banks has to decompose the original graph into bipartite subgraphs and a transform has to be performed on each subgraph because of the spectral folding phenomenon caused by downsampling of graph signals therefore the conventional method cannot always utilize all edges of the original graph in a single stage transformation our method is based on oversampling of the underlying graph itself and it can append nodes and edges to the graph somewhat arbitrarily we use this approach to make one oversampled bipartite graph that includes all edges of the original non bipartite graph we apply the oversampled graph with the critically sampled graph filter bank or the oversampled one for decomposing graph signals and show the performances on some experiments

combined source channel vector quantization using deterministic annealing the authors present a new approach to combined source channel vector quantization the method derived within information theory and probability theory utilizes deterministic annealing to avoid some local minima that trap conventional descent algorithms such as the generalized lloyd algorithm the resulting vector quantizers satisfy the necessary conditions for local optimality for the noisy channel case they tested the method against several versions of the noisy channel generalized lloyd algorithm on stationary first order gauss markov sources with a binary symmetric channel the method outperformed other methods under all test conditions with the gains over noisy channel gla growing with the codebook size the quantizers designed using deterministic annealing are also shown to behave robustly under channel mismatch conditions as a comparison with a separate source channel system over a large range of test channel conditions the method outperformed a bandwidth equivalent system incorporating a hamming code also for severe channel conditions the method produces solutions with explicit error control coding

multivariate return period calculation via survival functions 1 the concept of return period is fundamental for the design and the assessment of many engineering works in a multivariate framework several approaches are available to its definition each one yielding different solutions in this paper we outline a theoretical framework for the calculation of return periods in a multidimensional environment based on survival copulas and the corresponding survival kendall s measures the present approach solves the problems raised in previous publications concerning the coherent foundation of the notion of return period in a multivariate setting as an illustration a practical hydrological application is presented

learning graphs with monotone topology properties and multiple connected components recent papers have formulated the problem of learning graphs from data as an inverse covariance estimation problem with graph laplacian constraints while such problems are convex existing methods cannot guarantee that solutions will have specific graph topology properties e g being a tree which are desirable for some applications the problem of learning a graph with topology properties is in general non convex in this paper we propose an approach to solve these problems by decomposing them into two sub problems for which efficient solutions are known specifically a graph topology inference gti step is employed to select a feasible graph topology then a graph weight estimation gwe step is performed by solving a generalized graph laplacian estimation problem where edges are constrained by the topology found in the gti step our main result is a bound on the error of the gwe step as a function of the error in the gti step this error bound indicates that the gti step should be solved using an algorithm that approximates the data similarity matrix by another matrix whose entries have been thresholded to zero to have the desired type of graph topology the gti stage can leverage existing methods which are typically based on minimizing the total weight of removed edges since the gwe stage is an inverse covariance estimation problem with linear constraints it can be solved using existing convex optimization methods we demonstrate that our approach can achieve good results for both synthetic and texture image data

ergodicity in stationary graph processes a weak law of large numbers for stationary signals in time the weak law of large numbers wlln states that ensemble and realization averages are within epsilon of each other with a probability of order mathcal o 1 n epsilon 2 when considering n signal components the graph wlln introduced in this paper shows that the same is essentially true for signals supported on graphs however the notions of stationarity ensemble mean and realization mean are different recent papers have defined graph stationary signals as those that satisfy a form of invariance with respect to graph diffusion the ensemble mean of a graph stationary signal is not a constant but a node varying signal whose structure depends on the spectral properties of the graph the realization average of a graph signal is defined here as an average of successive weighted averages of local signal values with signal values of neighboring nodes the graph wlln shows that these two node varying signals are within epsilon of each other with probability of order mathcal o 1 n epsilon 2 in at least some nodes in stationary time signals the realization average is not only a consistent estimator of the ensemble mean but also optimal in terms of mean squared error mse this is not true for graph signals optimal mse graph filter designs are also presented an example problem concerning the estimation of the mean of a gaussian random field is presented

the algebraic approach to the discrete cosine and sine transforms and their fast algorithms it is known that the discrete fourier transform dft used in digital signal processing can be characterized in the framework of the representation theory of algebras namely as the decomposition matrix for the regular module mathbb c z n mathbb c x x n 1 this characterization provides deep insight into the dft and can be used to derive and understand the structure of its fast algorithms in this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of chebyshev polynomials then we derive most of their known algorithms by pure algebraic means we identify the mathematical principle behind each algorithm and give insight into its structure our results show that the connection between algebra and digital signal processing is stronger than previously understood

discrete signal processing on graphs frequency analysis signals and datasets that arise in physical and engineering applications as well as social genetics biomolecular and many other domains are becoming increasingly larger and more complex in contrast to traditional time and image signals data in these domains are supported by arbitrary graphs signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs this paper studies the concepts of low and high frequencies on graphs and low high and band pass graph signals and graph filters in traditional signal processing these concepts are easily defined because of a natural frequency ordering that has a physical interpretation for signals residing on graphs in general there is no obvious frequency ordering we propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low high and band pass graph signals and filters we study the design of graph filters with specified frequency response and illustrate our approach with applications to sensor malfunction detection and data classification

compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs this paper extends previous results on wavelet filterbanks for data defined on graphs from the case of orthogonal transforms to more general and flexible biorthogonal transforms as in the recent work the construction proceeds in two steps first we design one dimensional two channel filterbanks on bipartite graphs and then extend them to multi dimensional separable two channel filterbanks for arbitrary graphs via a bipartite subgraph decomposition we specifically design wavelet filters based on the spectral decomposition of the graph and state sufficient conditions for the filterbanks to be perfect reconstruction and orthogonal while our previous designs referred to as graph qmf filterbanks are perfect reconstruction and orthogonal they are not exactly k hop localized i e the computation at each node is not localized to a small k hop neighborhood around the node in this paper we relax the condition of orthogonality to design a biorthogonal pair of graph wavelets that are k hop localized with compact spectral spread and still satisfy the perfect reconstruction conditions the design is analogous to the standard cohen daubechies feauveau s cdf construction of factorizing a maximally flat daubechies half band filter preliminary results demonstrate that the proposed filterbanks can be useful for both standard signal processing applications as well as for signals defined on arbitrary graphs

optimal quantizer design for noisy channels an approach to combined source channel coding we present an analysis of the zero memory quantization of memoryless sources when the quantizer output is to be encoded and transmitted across a noisy channel necessary conditions for the joint optimization of the quantizer and the encoder decoder pair are presented and an iterative algorithm for obtaining a locally optimum system is developed the performance of this locally optimal system obtained for the class of generalized gaussian distributions and the binary symmetric channel is compared against the optimum performance theoretically attainable using rate distortion theoretic arguments as well as against the performance of lloyd max quantizers encoded using the natural binary code and the folded binary code it is shown that this optimal design could result in substantial performance improvements the performance improvements are more noticeable at high bit rates and for broad tailed densities

on the joint source channel coding error exponent for discrete memoryless systems we investigate the computation of csisza spl acute r s bounds for the joint source channel coding jscc error exponent e sub j of a communication system consisting of a discrete memoryless source and a discrete memoryless channel we provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained these equivalent representations can be readily computed for arbitrary source channel pairs via arimoto s algorithm when the channel s distribution satisfies a symmetry property the bounds admit closed form parametric expressions we then use our results to provide a systematic comparison between the jscc error exponent e sub j and the tandem coding error exponent e sub t which applies if the source and channel are separately coded it is shown that e sub t spl les e sub j spl les 2e sub t we establish conditions for which e sub j e sub t and for which e sub j 2e sub t numerical examples indicate that e sub j is close to 2e sub t for many source channel pairs this gain translates into a power saving larger than 2 db for a binary source transmitted over additive white gaussian noise awgn channels and rayleigh fading channels with finite output quantization finally we study the computation of the lossy jscc error exponent under the hamming distortion measure

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

comment on bivariate extreme value distributions an application of the gibbs sampler to the analysis of floods by p t adamson a v metcalfe and b parmentier

algebraic signal processing theory 1 d space in our paper titled ldquoalgebraic signal processing theory foundation and 1 d timerdquo appearing in this issue of the ieee transactions on signal processing we presented the algebraic signal processing theory an axiomatic and general framework for linear signal processing the basic concept in this theory is the signal model defined as the triple a m phi where a is a chosen algebra of filters m an associated a module of signals and phi is a generalization of the z transform each signal model has its own associated set of basic sp concepts including filtering spectrum and fourier transform examples include infinite and finite discrete time where these notions take their well known forms in this paper we use the algebraic theory to develop infinite and finite space signal models these models are based on a symmetric space shift operator which is distinct from the standard time shift we present the space signal processing concepts of filtering or convolution ldquoz transform rdquo spectrum and fourier transform for finite length space signals we obtain 16 variants of space models which have the 16 discrete cosine and sine transforms dcts dsts as fourier transforms using this novel derivation we provide missing signal processing concepts associated with the dcts dsts establish them as precise analogs to the dft get deep insight into their origin and enable the easy derivation of many of their properties including their fast algorithms

multivariate copula analysis toolbox mvcat describing dependence and underlying uncertainty using a bayesian framework we present a newly developed multivariate copula analysis toolbox mvcat which includes a wide range of copula families with different levels of complexity mvcat employs a bayesian framework with a residual based gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties the contribution of this paper is threefold a providing a bayesian framework to approximate the predictive uncertainties of fitted copulas b introducing a hybrid evolution markov chain monte carlo mcmc approach designed for numerical estimation of the posterior distribution of copula parameters and c enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties we show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima the proposed method however addresses this limitation and improves describing the dependence structure mvcat also enables evaluation of uncertainties relative to the length of record which is fundamental to a wide range of applications such as multivariate frequency analysis

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

algebraic signal processing theory foundation and 1 d time this paper introduces a general and axiomatic approach to linear signal processing sp that we refer to as the algebraic signal processing theory asp basic to asp is the linear signal model defined as a triple a m phi where familiar concepts like the filter space and the signal space are cast as an algebra a and a module m respectively the mapping phi generalizes the concept of a z transform to bijective linear mappings from a vector space of signal samples into the module m common concepts like filtering spectrum or fourier transform have their equivalent counterparts in asp once these concepts and their properties are defined and understood in the context of asp they remain true and apply to specific instantiations of the asp signal model for example to develop signal processing theories for infinite and finite discrete time signals for infinite or finite discrete space signals or for multidimensional signals we need only to instantiate the signal model to one that makes sense for that specific class of signals filtering spectrum fourier transform and other notions follow then from the corresponding asp concepts similarly common assumptions in sp translate into requirements on the asp signal model for example shift invariance is equivalent to a being commutative for finite duration signals shift invariance then restricts a to polynomial algebras we explain how to design signal models from the specification of a special filter the shift the paper illustrates the general asp theory with the standard time shift presenting a unique signal model for infinite time and several signal models for finite time the latter models illustrate the role played by boundary conditions and recover the discrete fourier transform dft and its variants as associated fourier transforms finally asp provides a systematic methodology to derive fast algorithms for linear transforms this topic and the application of asp to space dependent signals and to multidimensional signals are pursued in companion papers

k sample anderson darling tests abstract two k sample versions of an anderson darling rank statistic are proposed for testing the homogeneity of samples their asymptotic null distributions are derived for the continuous as well as the discrete case in the continuous case the asymptotic distributions coincide with the k 1 fold convolution of the asymptotic distribution for the anderson darling one sample statistic the quality of this large sample approximation is investigated for small samples through monte carlo simulation this is done for both versions of the statistic under various degrees of data rounding and sample size imbalances tables for carrying out these tests are provided and their usage in combining independent one or k sample anderson darling tests is pointed out the test statistics are essentially based on a doubly weighted sum of integrated squared differences between the empirical distribution functions of the individual samples and that of the pooled sample one weighting adjusts for the possibly different s

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

m channel perfect recovery of coarsened graphs and graph signals with spectral invariance and topological preservation in this paper an m channel perfect reconstruction filter bank based on a coarsening algorithm is proposed compared with most of the designs of graph filter banks that do not consider the graph reconstruction our proposed design can provide the perfect graph reconstruction as well as perfect graph signal reconstruction in the analysis part the proposed filter bank provides a coarse version of the input graph as well as coarsened graph signal spectral invariant to the input signal in the synthesis part the filter bank perfectly reconstructs the input graph as well as input signal from their coarse version the spirit of the proposed design is to partition the spectral information of the input graph and input graph signal into every channel the partition method is adjustable and can be nonuniform two intuitive schemes named sort by eigenvalue and sort by intensity for uniform partition are introduced in the proposed design the coarsening operators are obtained through an existing coarsening algorithm while the recovery operators are defined by taking the conjugate transpose of the coarsening operators besides we address the relation between the proposed design and a framework of sampling graph signals based on the discrete sampling theory it is shown that the coarsening operator in the proposed design is actually a special case of the sampling operator in the framework based on the discrete sampling theory experimental results are presented to demonstrate the effectiveness of the proposed design of filter banks

algebraic signal processing theory 1 d nearest neighbor models we present a signal processing framework for the analysis of discrete signals represented as linear combinations of orthogonal polynomials we demonstrate that this representation implicitly changes the associated shift operation from the standard time shift to the nearest neighbor shift introduced in this paper using the algebraic signal processing theory we construct signal models based on this shift and derive their corresponding signal processing concepts including the proper notions of signal and filter spaces z transform convolution spectrum and fourier transform the presented results extend the algebraic signal processing theory and provide a general theoretical framework for signal analysis using orthogonal polynomials

downsampling of signals on graphs via maximum spanning trees downsampling of signals living on a general weighted graph is not as trivial as of regular signals where we can simply keep every other samples in this paper we propose a simple yet effective downsampling scheme in which the underlying graph is approximated by a maximum spanning tree mst that naturally defines a graph multiresolution this mst based method significantly outperforms the two previous downsampling schemes coloring based and svd based on both random and specific graphs in terms of computations and partition efficiency quantified by the graph cuts the benefit of using mst based downsampling for recently developed critical sampling graph wavelet transforms in compression of graph signals is demonstrated

coauthorship networks and patterns of scientific collaboration by using data from three bibliographic databases in biology physics and mathematics respectively networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper we use these networks to answer a broad variety of questions about collaboration patterns such as the numbers of papers authors write how many people they write them with what the typical distance between scientists is through the network and how patterns of collaboration vary between subjects and over time we also summarize a number of recent results by other authors on coauthorship patterns

estimation of copula based semiparametric time series models this paper studies the estimation of a class of copula based semiparametric stationary markov models these models are characterized by nonparametric marginal distributions and parametric copula functions while the copulas capture all the scale free temporal dependence of the processes simple estimators of the marginal distribution and the copula parameter are provided and their asymptotic properties are established under easily verifiable conditions these results are used to obtain root n consistent and asymptotically normal estimators of important features of the transition distribution such as the nonlinear conditional moments and conditional quantiles the semiparametric conditional quantile estimators are automatically monotonic across quantiles which is attractive for portfolio conditional value at risk calculations

chi plots for assessing dependence summary this paper presents a graphical method to be used in conjunction with a scatterplot to investigate possible association of two variates as manifested in a sample of bivariate measurements the method is designed so that the plot is approximately horizontal under independence and under various forms of association it produces corresponding characteristic patterns examples given include application to study of regression residuals dependence of two spatial point processes serial association of time series and comparison of two time series

the design of joint source and channel trellis waveform coders the generalized lloyd algorithm is applied to the design of joint source and channel trellis waveform coders to encode discrete time continuous amplitude stationary and ergodic sources operating over discrete memoryless noisy channels experimental results are provided for independent and autoregressive gaussian sources binary symmetric channels and absolute error and squared error distortion measures performance of the joint codes is compared with the tandem combination of a trellis source code and a trellis channel code on the independent gaussian source using the squared error distortion measure operating over an additive white gaussian noise channel it is observed that the jointly optimized codes achieve performance close to or better than that of separately optimized tandem codes of the same constraint length performance improvement via a predictive joint source and channel trellis code is demonstrated for the autoregressive gaussian source using the squared error distortion measure

blind identification of graph filters network processes are often represented as signals defined on the vertices of a graph to untangle the latent structure of such signals one can view them as outputs of linear graph filters modeling underlying network dynamics this paper deals with the problem of joint identification of a graph filter and its input signal thus broadening the scope of classical blind deconvolution of temporal and spatial signals to the less structured graph domain given a graph signal mathbf y modeled as the output of a graph filter the goal is to recover the vector of filter coefficients mathbf h and the input signal mathbf x which is assumed to be sparse while mathbf y is a bilinear function of mathbf x and mathbf h the filtered graph signal is also a linear combination of the entries of the lifted rank one row sparse matrix mathbf x mathbf h t the blind graph filter identification problem can thus be tackled via rank and sparsity minimization subject to linear constraints an inverse problem amenable to convex relaxations offering provable recovery guarantees under simplifying assumptions numerical tests using both synthetic and real world networks illustrate the merits of the proposed algorithms as well as the benefits of leveraging multiple signals to aid the blind identification task

copulas diagonals and tail dependence we present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence moreover we present the tail concentration function which depends on the diagonal section of a copula as a tool to give a description of tail dependence at finite scale the tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space moreover it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior

bivariate extreme value theory models and estimation summary bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima no natural parametric family exists for the dependence between the marginal distributions but there are considerable restrictions on the dependence structure we consider modelling the dependence function with parametric models for which two new models are presented tests for independence and discriminating between models are also given the estimation procedure and the flexibility of the new models are illustrated with an application to sea level data extreme value theory has recently been an area of much theoretical and practical work univariate theory is a well documented area whereas bivariate multivariate extreme value theory has until recently received surprisingly little attention in the multivariate case no natural parametric family exists for the dependence structure so this must be modelled in some way in the analysis of environmental extreme value data there is a need for models of dependence between extremes from different sources for example at various sea ports or at various points of a river in this paper we consider bivariate extreme value distributions we assume without loss of generality that we have exponential marginal distributions with unit means the class of bivariate exponential distributions in which we are interested satisfy a strong stability relation exponential variables x y satisfy the stability relation if and only if w min ax by is also exponentially distributed for all a b 0 pickands 1981 therefore the models we will consider have particular application in reliability and survival analysis one approach to modelling the dependence structure is via parametric models this requires a flexible family of models which satisfy certain constraints models are of two kinds either differentiable or nondifferentiable all nondifferentiable models give distri butions which are singular with nonzero probability concentrated on a certain subspace the differentiable models have densities but the existing models are symmetric which leads to the variables being exchangeable here we present two new asymmetric differenti able models which have increased flexibility properties of the differentiable models are examined estimation of the parametric models has previously been by ad hoc methods because there is a nonregular estimation problem when the margins are independent for the

multivariate assessment of droughts frequency analysis and dynamic return period 1 droughts like floods are extreme expressions of the river flow dynamics here droughts are intended as episodes during which the streamflow is below a given threshold and are described as multivariate events characterized by two variables average intensity and duration in this work we introduce the new concept of dynamic return period formulated using the theory of copulas and calculated via a survival kendall s approach we show how it can be used i to monitor the temporal evolution of a drought event and ii to perform real time assessment in addition a randomization strategy is introduced in order to get rid of repeated measurements which may adversely affect the statistical analysis of the available data as well as the calculation of the return periods of interest a practical example is shown involving the fit of the drought duration distribution the case study of the po river basin northern italy is used as an illustration

random walk graph laplacian based smoothness prior for soft decoding of jpeg images given the prevalence of joint photographic experts group jpeg compressed images optimizing image reconstruction from the compressed format remains an important problem instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform dct coefficient quantization bins hard decoding soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors the challenge thus lies in how to define suitable priors and apply them effectively in this paper we combine three image priors laplacian prior for dct coefficients sparsity prior and graph signal smoothness prior for image patches to construct an efficient jpeg soft decoding algorithm specifically we first use the laplacian prior to compute a minimum mean square error initial solution for each code block next we show that while the sparsity prior can reduce block artifacts limiting the size of the overcomplete dictionary to lower computation would lead to poor recovery of high dct frequencies to alleviate this problem we design a new graph signal smoothness prior desired signal has mainly low graph frequencies based on the left eigenvectors of the random walk graph laplacian matrix lerag compared with the previous graph signal smoothness priors lerag has desirable image filtering properties with low computation overhead we demonstrate how lerag can facilitate recovery of high dct frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering finally we construct a soft decoding algorithm using the three signal priors with appropriate prior weights experimental results show that our proposal outperforms the state of the art soft decoding algorithms in both objective and subjective evaluations noticeably

vector quantization by deterministic annealing a deterministic annealing approach is suggested to search for the optimal vector quantizer given a set of training data the problem is reformulated within a probabilistic framework no prior knowledge is assumed on the source density and the principle of maximum entropy is used to obtain the association probabilities at a given average distortion the corresponding lagrange multiplier is inversely related to the temperature and is used to control the annealing process in this process as the temperature is lowered the system undergoes a sequence of phase transitions when existing clusters split naturally without use of heuristics the resulting codebook is independent of the codebook used to initialize the iterations

high rate vector quantization for noisy channels with applications to wideband speech spectrum compression this paper considers the high rate performance of source coding for noisy discrete symmetric channels with random index assignment ia accurate analytical models are developed to characterize the expected distortion performance of vector quantization vq for a large class of distortion measures it is shown that when the point density is continuous the distortion can be approximated as the sum of the source quantization distortion and the channel error induced distortion expressions are also derived for the continuous point density that minimizes the expected distortion next for the case of mean squared error distortion a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component the extent of the singularity is also characterized these results provide analytical models for the expected distortion performance of both conventional vq as well as for channel optimized vq as a practical example compression of the linear predictive coding parameters in the wideband speech spectrum is considered with the log spectral distortion as performance metric the theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion

on the performance and complexity of channel optimized vector quantizers the performance and complexity of channel optimized vector quantizers are studied for the gauss markov source observations on the geometric structure of these quantizers are made which have an important implication on the encoding complexity for the squared error distortion measure it is shown that an operation equivalent to a euclidean distance measurement with respect to an appropriately defined set of points used to identify the encoding regions can be used to perform the encoding this implies that the encoding complexity is proportional to the number of encoding regions it is then demonstrated that for very noisy channels and a heavily correlated source when the codebook size is large the number of encoding regions is considerably smaller than the codebook size implying a reduction in encoding complexity

reconstruction of graph signals through percolation from seeding nodes new schemes to recover signals defined in the nodes of a graph are proposed our focus is on reconstructing bandlimited graph signals which are signals that admit a sparse representation in a frequency domain related to the structure of the graph most existing formulations focus on estimating an unknown graph signal by observing its value on a subset of nodes by contrast in this paper we study the problem of inducing a known graph signal using as input a graph signal that is nonzero only for a small subset of nodes the sparse signal is then percolated interpolated across the graph using a graph filter alternatively one can interpret graph signals as network states and study graph signal reconstruction as a network control problem where the target class of states is represented by bandlimited signals three setups are investigated in the first one a single simultaneous injection takes place on several nodes in the graph in the second one successive value injections take place on a single node the third one is a generalization where multiple nodes inject multiple signal values for noiseless settings conditions under which perfect reconstruction is feasible are given and the corresponding schemes to recover the desired signal are specified scenarios leading to imperfect reconstruction either due to insufficient or noisy signal value injections are also analyzed moreover connections with classical interpolation in the time domain are discussed specifically for time varying signals where the ideal interpolator after uniform sampling is a low pass filter our proposed approach and the reconstruction of a sampled signal coincide nevertheless for general graph signals we show that these two approaches differ the last part of the paper presents numerical experiments that illustrate the results developed through synthetic and real world signal reconstruction problems

discrete signal processing on graphs sampling theory we propose a sampling theory for signals that are supported on either directed or undirected graphs the theory follows the same paradigm as classical sampling theory we show that perfect recovery is possible for graph signals bandlimited under the graph fourier transform the sampled signal coefficients form a new graph signal whose corresponding graph structure preserves the first order difference of the original graph signal for general graphs an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise for graphs whose graph fourier transforms are frames with maximal robustness to erasures as well as for erd s renyi graphs random sampling leads to perfect recovery with high probability we further establish the connection to the sampling theory of finite discrete time signal processing and previous work on signal recovery on graphs to handle full band graph signals we propose a graph filter bank based on sampling theory on graphs finally we apply the proposed sampling theory to semi supervised classification of online blogs and digit images where we achieve similar or better performance with fewer labeled samples compared to previous work

channel optimized soft trellis waveform coding we provide a new fuzzy relaxation trellis codebook search algorithm over noisy channels the new algorithm solves the problems associated with the lbg algorithm in the sense of delivering relatively lower distortion configurations using short training sequences furthermore the new approach is significantly less sensitive to the initialization process the algorithm minimizes a weighted distortion measure averaged over both the source and the channel statistics the weights are soft distortion related reliability information which are delivered by a soft trellis vector quantization algorithm stvq the concept of soft compression is introduced by haddad and yongacoglu see proc globecom rio de janeiro brazil dec 1999 in another paper using the forward backward symbol map algorithm the work introduced in this paper is an extension of the work established for the noiseless channel case by haddad and yongacoglu see proc ieee icassp istanbul turkey june 2000 in yet another paper testing is performed using first and second order gauss markov sources over several trellis structures vector dimensions and compression rates moreover the robustness of the optimal configurations is tested under channel mismatch conditions and compared with tandem coding systems

joint source and noisy channel trellis encoding corresp in a trellis encoding communication system the decoder is a time invariant nonlinear filter with finite memory sliding block code and the encoder is a trellis search algorithm matched to the decoder a coding theorem is established for a trellis encoding of a stationary and ergodic source over a discrete memoryless noisy channel which shows that such communication systems can perform arbitrarily close to the source distortion rate function evaluated at the channel capacity

sampling of graph signals with successive local aggregations a new scheme to sample signals defined on the nodes of a graph is proposed the underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph which is captured by the so called graph shift operator instead of using the value of the signal observed at a subset of nodes to recover the signal in the entire graph the sampling scheme proposed here uses as input observations taken at a single node the observations correspond to sequential applications of the graph shift operator which are linear combinations of the information gathered by the neighbors of the node when the graph corresponds to a directed cycle which is the support of time varying signals our method is equivalent to the classical sampling in the time domain when the graph is more general we show that the vandermonde structure of the sampling matrix critical when sampling time varying signals is preserved sampling and interpolation are analyzed first in the absence of noise and then noise is considered we then study the recovery of the sampled signal when the specific set of frequencies that is active is not known moreover we present a more general sampling scheme under which either our aggregation approach or the alternative approach of sampling a graph signal by observing the value of the signal at a subset of nodes can be both viewed as particular cases numerical experiments illustrating the results in both synthetic and real world graphs close the paper

polynomial control on stability inversion and powers of matrices on simple graphs abstract spatially distributed networks of large size arise in a variety of science and engineering problems such as wireless sensor networks and smart power grids most of their features can be described by properties of their state space matrices whose entries have indices in the vertex set of a graph in this paper we introduce novel algebras of beurling type that contain matrices on a connected simple graph having polynomial off diagonal decay and we show that they are banach subalgebras of b l p 1 p the space of all bounded operators on the space l p of all p summable sequences the l p stability of state space matrices is an essential hypothesis for the robustness of spatially distributed networks in this paper we establish the equivalence among l p stabilities of matrices in beurling algebras for different exponents 1 p with quantitative analysis for the lower stability bounds admission of norm control inversion plays a crucial role in some engineering practice in this paper we prove that matrices in beurling subalgebras of b l 2 have norm controlled inversion and we find a norm controlled polynomial with close to optimal degree polynomial estimate to powers of matrices is important for numerical implementation of spatially distributed networks in this paper we apply our results on norm controlled inversion to obtain a polynomial estimate to powers of matrices in beurling algebras the polynomial estimate is a noncommutative extension about convolution powers of a complex function and is applicable to estimate the probability of hopping from one agent to another agent in a stationary markov chain on a spatially distributed network

entropy copula method for single site monthly streamflow simulation 1 an entropy copula method is proposed for single site monthly streamflow simulation in this method the joint distribution of adjacent monthly streamflows is constructed using the copula method whereas the marginal distribution of streamflow for each month is derived using the entropy method then the conditional distribution is derived from which monthly streamflow is generated moment statistics of monthly streamflow such as mean standard deviation and skewness can be modeled by the entropy based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula based joint distribution the proposed entropy copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence application to the simulation of monthly streamflow from the colorado river illustrates the effectiveness of the proposed method

spectrum adapted tight graph wavelet and vertex frequency frames we consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs while the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum the filters proposed in this paper are adapted to the distribution of graph laplacian eigenvalues and therefore lead to atoms with better discriminatory power our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph we then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph laplacian eigenvalues we use this approach to construct computationally efficient spectrum adapted tight vertex frequency and graph wavelet frames we give numerous examples of the resulting spectrum adapted graph filters and also present an illustrative example of vertex frequency analysis using the proposed construction

frequency analysis via copulas theoretical aspects and applications to hydrological events 1 in this paper we provide a general theoretical framework exploiting copulas for studying the return periods of hydrological events in particular we consider events depending upon the joint behavior of two nonindependent random variables an approach which can easily be generalized to the multivariate case we show that using copulas may greatly simplify the calculations and may even yield analytical expressions for the isolines of the return periods both in the unconditional and in the conditional case in addition we show how a new probability distribution may be associated with the return period of specific events and introduce the definitions of sub super and critical events as well as those of primary and secondary return periods an illustration of the techniques proposed is provided by analyzing some case studies already examined in literature

algebraic signal processing theory 2 d spatial hexagonal lattice we develop the framework for signal processing on a spatial or undirected 2 d hexagonal lattice for both an infinite and a finite array of signal samples this framework includes the proper notions of z transform boundary conditions filtering or convolution spectrum frequency response and fourier transform in the finite case the fourier transform is called discrete triangle transform like the hexagonal lattice this transform is nonseparable the derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced namely we construct the proper signal models given by polynomial algebras bottom up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory these signal models in turn then provide all the basic signal processing concepts the framework developed in this paper is related to mersereau s early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete fourier transform a fact that will be made rigorous in this paper

kendall distributions and level sets in bivariate exchangeable survival models for a given bivariate survival function f we study the relations between the set of the level curves of f and the kendall distribution then we characterize the survival models simultaneously admitting a specified kendall distribution and a specified set of level curves attention will be restricted to exchangeable survival models

bipartite approximation for graph wavelet signal decomposition to compactly represent a graph signal in the frequency domain critically sampled biorthogonal wavelet filterbanks have been proposed to decompose signals on bipartite graphs however in practice graph signals often reside on general graph structures that are not bipartite thus an original nonbipartite graph must be decomposed into a sequence of bipartite graph approximations so that the filterbanks can be applied successively for signal decomposition in this paper unlike previous proposals that are heuristic in nature we design new bipartite approximation strategies for model based and empirically derived probability distributions in the first case a signal prior assumes a gaussian markov random field gmrf model parametrized by the original graph in the second case beyond the gmrf signal prior empirical signal observations are available to compute a posterior probability distribution in both cases we optimize for energy compaction in the bipartite subgraphs with two criteria the kullback leibler divergence metric which encourages preserving the spectral characteristics of the original graph and multiplicity of eigenvalue at frequency 1 for graph laplacian which is the frequency with minimal energy discrimination the relative importance between the two criteria is determined by a proposed measure that evaluates the degree of mismatch between the signal prior and posterior given these criteria we first design a global numerical optimization and then propose a local heuristic approach for fast implementation with simplifications leading to local metric computation experimental results show that our proposed bipartite subgraph decomposition outperforms competing proposals in terms of energy compaction

stationary graph processes and spectral estimation stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain although time varying signals are abundant in nature in many practical scenarios the information of interest resides in more irregular graph domains this lack of regularity hampers the generalization of the classical notion of stationarity to graph signals this paper proposes a definition of weak stationarity for random graph signals that takes into account the structure of the graph where the random process takes place while inheriting many of the meaningful properties of the classical time domain definition provided that the topology of the graph can be described by a normal matrix stationary graph processes can be modeled as the output of a linear graph filter applied to a white input this is shown equivalent to requiring the correlation matrix to be diagonalized by the graph fourier transform a fact that is leveraged to define a notion of power spectral density psd properties of the graph psd are analyzed and a number of methods for its estimation are proposed this includes generalizations of nonparametric approaches such as periodograms window based average periodograms and filter banks as well as parametric approaches using moving average autoregressive and arma processes graph stationarity and graph psd estimation are investigated numerically for synthetic and real world graph signals

extending classical multirate signal processing theory to graphs part ii m channel filter banks this paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper part i and studies m channel polynomial filter banks on graphs the behavior of such graph filter banks differs from that of classical filter banks in many ways the precise details depending on the eigenstructure of the adjacency matrix boldsymbol a it is shown that graph filter banks represent linear and periodically shift variant systems only when boldsymbol a satisfies the noble identity conditions developed in part i it is then shown that perfect reconstruction graph filter banks can always be developed when boldsymbol a satisfies the eigenvector structure satisfied by m block cyclic graphs and has distinct eigenvalues further restrictions on eigenvalues being unnecessary for this if boldsymbol a is actually m block cyclic then these pr filter banks indeed become practical i e arbitrary filter polynomial orders are possible and there are robustness advantages in this case the pr condition is identical to pr in classical filter banks any classical pr example can be converted to a graph pr filter bank on an m block cyclic graph it is shown that for m block cyclic graphs with all eigenvalues on the unit circle the frequency responses of filters have meaningful correspondence with classical filter banks polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for alias cancellation and perfect reconstruction again for graphs with specific eigenstructures it is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms

subgraph based filterbanks for graph signals we design a critically sampled compact support biorthogonal transform for graph signals via graph filterbanks instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations the design is based on a partition of the graph in connected subgraphs coarsening is achieved by defining one supernode for each subgraph and the edges for this coarsened graph derives from the connectivity between the subgraphs unlike the one every two nodes downsampling on bipartite graphs this coarsening operation does not have an exact formulation in the graph fourier domain instead we rely on the local fourier bases of each subgraph to define filtering operations we apply successfully this method to decompose graph signals and show promising performance on compression and denoising

m channel oversampled graph filter banks this paper proposes m channel oversampled filter banks for graph signals the filter set satisfies the perfect reconstruction condition a method of designing oversampled graph filter banks is presented that allows us to design filters with arbitrary parameters unlike the conventional critically sampled graph filter banks the oversampled graph laplacian matrix is also introduced with a discussion of the entire redundancy of the oversampled graph signal processing system the practical performance of the proposed filter banks is validated through graph signal denoising experiments

an uncertain journey around the tails of multivariate hydrological distributions 1 moving from univariate to multivariate frequency analysis this study extends the klemes critique of the widespread belief that the increasingly refined mathematical structures of probability functions increase the accuracy and credibility of the extrapolated upper tails of the fitted distribution models in particular we discuss key aspects of multivariate frequency analysis applied to hydrological data such as the selection of multivariate design events i e appropriate subsets or scenarios of multiplets that exhibit the same joint probability to be used in design applications and the assessment of the corresponding uncertainty since these problems are often overlooked or treated separately and sometimes confused we attempt to clarify properties advantages shortcomings and reliability of results of frequency analysis we suggest a selection method of multivariate design events with prescribed joint probability based on simple monte carlo simulations that accounts for the uncertainty affecting the inference results and the multivariate extreme quantiles it is also shown that the exploration of the p level probability regions of a joint distribution returns a set of events that is a subset of the p level scenarios resulting from an appropriate assessment of the sampling uncertainty thus tending to overlook more extreme and potentially dangerous events with the same uncertain joint probability moreover a quantitative assessment of the uncertainty of multivariate quantiles is provided by introducing the concept of joint confidence intervals from an operational point of view the simulated event sets describing the distribution of the multivariate p level quantiles can be used to perform multivariate risk analysis under sampling uncertainty as an example of the practical implications of this study we analyze two case studies already presented in the literature

on the design of optimal noisy channel scalar quantizer with random index assignment the general approach in a noisy channel scalar quantizer design is an iterative descent algorithm which guarantees only a locally optimal solution while sufficient conditions under which the local optimum becomes a global optimum are known in the noiseless channel case such sufficient conditions were not derived for the noisy counterpart moreover efficient globally optimal design techniques for general discrete distributions in the noiseless case exist however they seem not to extend to the noisy scenario when a fixed index assignment is assumed recently the design of noisy channel scalar quantizer with random index assignment ria was proposed using a locally optimal iterative algorithm in this paper we derive sufficient conditions for the uniqueness of a local optimum which thus guarantee the global optimality of the solution these sufficient conditions are satisfied for a log concave probability density function which is additionally symmetric around its mean furthermore we show that assuming an ria the globally optimal design for general discrete sources can also be carried out efficiently

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

trivariate statistical analysis of extreme rainfall events via the plackett family of copulas 1 recent hydrologic studies on multivariate stochastic analysis have indicated that copulas perform well for bivariate problems in particular the frank family of archimedean copulas has been a popular choice for a dependence model however there are limitations to extending such archimedean copulas to trivariate and higher dimensions with very specific restrictions on the kinds of dependencies that can be modeled in this study we examine a non archimedean copula from the plackett family that is founded on the theory of constant cross product ratio it is shown that the plackett family not only performs well at the bivariate level but also allows a trivariate stochastic analysis where the lower level dependencies between variables can be fully preserved while allowing for specificity at the trivariate level as well the feasible range of plackett parameters that would result in valid 3 copulas is determined numerically the trivariate plackett family of copulas is then applied to the study of temporal distribution of extreme rainfall events for several stations in indiana where the estimated parameters lie in the feasible region on the basis of a given rainfall depth and duration conditional expectations of rainfall features such as expected peak intensity time to peak and percentage cumulative rainfall at 10 cumulative time increments are evaluated the results of this study suggest that while the constant cross product ratio theory was conventionally applied to discrete type random variables it is also applicable to continuous random variables and that it provides further flexibility for multivariate stochastic analyses of rainfall

binary lattice vector quantization with linear block codes and affine index assignments we determine analytic expressions for the performance of some low complexity combined source channel coding systems the main tool used is the hadamard transform in particular we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments linear block channel coding and a binary symmetric channel the distortion formulas are specialized to nonredundant channel codes for a binary symmetric channel and then extended to affine index assignments on a binary asymmetric channel various structured index assignments are compared our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes one interesting result shown is that for a uniform source and uniform quantizer the natural binary code is never optimal for a nonsymmetric channel even though it is known to be optimal for a symmetric channel

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

pseudo gray coding a pseudo gray code is an assignment of n bit binary indexes to 2 points in a euclidean space so that the hamming distance between two points corresponds closely to the euclidean distance pseudo gray coding provides a redundancy free error protection scheme for vector quantization vq of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise a globally optimal solution to this problem is generally intractable due to an inherently large computational complexity a locally optimal solution the binary switching algorithm is introduced based on the objective of minimizing a useful upper bound on the average system distortion the algorithm yields a significant reduction in average distortion and converges in reasonable running times the sue of pseudo gray coding is motivated by the increasing need for low bit rate vq based encoding systems that operate on noisy channels such as in mobile radio speech communications

fitting bivariate copulas to the dependence structure between storm characteristics a detailed analysis based on 105 year 10 min rainfall 1 the use of copulas as flexible tools for constructing marginal free distribution functions for multivariate phenomena such as rainfall recently enjoys substantial attention by researchers in hydrology in this study commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall observed at uccle belgium in the analysis various problems that can occur are highlighted and opportunities for further research are outlined after selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data a detailed seasonal dependence analysis is provided together with a study on tail dependence further different existing parameter estimation techniques and goodness of fit methods for selecting the most appropriate bivariate copulas are applied and compared finally attention is given to the presence of asymmetric dependence and nonexchangeability

copula based daily rainfall disaggregation model 1 a daily rainfall disaggregation model which uses a copula to model the dependence structure between total depth total duration of wet periods and the maximum proportional depth of a wet period is presented the wet 1 dry 0 binary sequence is modeled by the nonrandomized bartlett lewis model with diurnal effect incorporated before superimposing the ar 1 depth process submodel unlike previous studies the model is structured such that all wet day data available are considered in the analysis without the need to discard any good quality daily data embedded in a month having some missing data this increased the data size thus improving the modeling process further the daily data are classified according to the total duration of wet periods duration within the day in this way a large proportion of the model parameters become seasonal invariant the overriding factor being the total duration of wet periods the potential of the developed model has been demonstrated by disaggregating both the data set used in developing the model parameters and also a 12 year continuous rainfall data set not used in the model parameterization gross rainfall statistics of several aggregation levels down to 6 min have been very well reproduced by the disaggregation model the copula dependence structure and the variation of the depth process submodel parameters with the total duration of wet periods are also very well captured by the presented model

extending classical multirate signal processing theory to graphs part i fundamentals signal processing on graphs finds applications in many areas in recent years renewed interest on this topic was kindled by two groups of researchers narang and ortega constructed two channel filter banks on bipartitie graphs described by laplacians sandryhaila and moura developed the theory of linear systems filtering and frequency responses for the case of graphs with arbitrary adjacency matrices and showed applications in signal compression prediction etc inspired by these contributions this paper extends classical multirate signal processing ideas to graphs the graphs are assumed to be general with a possibly nonsymmetric and complex adjacency matrix the paper revisits ideas such as noble identities aliasing and polyphase decompositions in graph multirate systems drawing such a parallel to classical systems allows one to design filter banks with polynomial filters with lower complexity than arbitrary graph filters it is shown that the extension of classical multirate theory to graphs is nontrivial and requires certain mathematical restrictions on the graph thus classical noble identities cannot be taken for granted similarly one cannot claim that the so called delay chain system is a perfect reconstruction system as in classical filter banks it will also be shown that m partite extensions of the bipartite filter bank results will not work for m channel filter banks but a more restrictive condition called m block cyclic property should be imposed such graphs are studied in detail a detailed theory for m channel filter banks is developed in a companion paper

product eigenvalue problems many eigenvalue problems are most naturally viewed as product eigenvalue problems the eigenvalues of a matrix a are wanted but a is not given explicitly instead it is presented as a product of several factors a a k a k 1 cdots a 1 usually more accurate results are obtained by working with the factors rather than forming a explicitly for example if we want eigenvalues vectors of b t b it is better to work directly with b and not compute the product the intent of this paper is to demonstrate that the product eigenvalue problem is a powerful unifying concept diverse examples of eigenvalue problems are discussed and formulated as product eigenvalue problems for all but a couple of these examples it is shown that the standard algorithms for solving them are instances of a generic gr algorithm applied to a related cyclic matrix

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

a comparative copula based bivariate frequency analysis of observed and simulated storm events a case study on bartlett lewis modeled rainfall 1 because of a lack of historical rainfall time series of considerable length one often has to rely on simulated rainfall time series e g in the design of hydraulic structures one way to simulate such time series is by means of stochastic point process rainfall models such as the bartlett lewis type of model for the evaluation of model performance with a focus on the reproduction of extreme rainfall events often a univariate extreme value analysis is performed recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models in this study a copula based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms first this study performs an analysis of several storm variables which indicates a problem with the modeling of the temporal structure of rainfall by the models thereafter the bivariate frequency analysis of storms defined by their duration and volume illustrates the underestimation and overestimation of the return period of the storms simulated by the models which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume the difference in the degree of association between the latter and a different mean storm interarrival time the proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made

the intrinsic dependence structure of peak volume duration and average intensity of hyetographs and hydrographs 1 the information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value xp volume v duration d and average intensity i these variables play a fundamental role in hydrologic engineering as they are used for instance to define design hyetographs and hydrographs as well as to model and simulate the rainfall and streamflow processes given their inherent variability and the empirical evidence of the presence of a significant degree of association such quantities have been studied as correlated random variables suitable to be modeled by multivariate joint distribution functions the advent of copulas in geosciences simplified the inference procedures allowing for splitting the analysis of the marginal distributions and the study of the so called dependence structure or copula however the attention paid to the modeling task has overlooked a more thorough study of the true nature and origin of the relationships that link and i in this study we apply a set of ad hoc bootstrap algorithms to investigate these aspects by analyzing the hyetographs and hydrographs extracted from 282 daily rainfall series from central eastern europe three 5 min rainfall series from central italy 80 daily streamflow series from the continental united states and two sets of 200 simulated universal multifractal time series our results show that all the pairwise dependence structures between and i exhibit some key properties that can be reproduced by simple bootstrap algorithms that rely on a standard univariate resampling without resort to multivariate techniques therefore the strong similarities between the observed dependence structures and the agreement between the observed and bootstrap samples suggest the existence of a numerical generating mechanism based on the superposition of the effects of sampling data at finite time steps and the process of summing realizations of independent random variables over random durations we also show that the pairwise dependence structures are weakly dependent on the internal patterns of the hyetographs and hydrographs meaning that the temporal evolution of the rainfall and runoff events marginally influences the mutual relationships of and i finally our findings point out that subtle and often overlooked deterministic relationships between the properties of the event hyetographs and hydrographs exist confusing these relationships with genuine stochastic relationships can lead to an incorrect application of multivariate distributions and copulas and to misleading results

image transmission over the polya channel via channel optimized quantization we introduce two progressive methods for image transmission over binary channels with additive bursty noise modeled by the finite memory polya contagion channel the methods which are based on channel optimized scalar quantization cosq of the wavelet transform coefficients exploit channel memory to offer superior performance over a number of more complex systems designed for the fully interleaved channel

joint optimization of vq codebooks and qam signal constellations for awgn channels a joint design scheme has been proposed to optimize the source encoder and the modulation signal constellation based on the minimization of the end to end distortion including both the quantization error and channel distortion the proposed scheme first optimizes the vector quantization vq codebook for a fixed modulation signal set and then the modulation signals for the fixed vq codebook these two steps are iteratively repeated until they reach a local optimum solution it has been shown that the performance of the proposed system can be enhanced by employing a new efficient mapping scheme between codevectors and modulation signals simulation results show that a jointly optimized system based on the proposed algorithms outperforms the conventional system based on a conventional quadrature amplitude modulation signal set and the vq codebook designed for a noiseless channel

hierarchical unsupervised learning with growing via phase transitions we address unsupervised learning subject to structural constraints with particular emphasis placed on clustering with an imposed decision tree structure most known methods are greedy optimizing one node of the tree at a time to minimize a local cost by constrast we develop a joint optimization method derived based on information theoretic principles and closely related to known methods in statistical physics the approach is inspired by the deterministic annealing algorithm for unstructured data clustering which was based on maximum entropy inference the new approach is founded on the principle of minimum cross entropy using informative priors to approximate the unstructured clustering solution while imposing the structural constraint the resulting method incorporates supervised learning principles applied in an unsupervised problem setting in our approach the tree grows by a sequence of bifurcations that occur while optimizing an effective free energy cost at decreasing temperature scales thus estimates of the tree size and structure are naturally obtained at each temperature in the process examples demonstrate considerable improvement over known methods

perfect reconstruction two channel wavelet filter banks for graph structured data in this work we propose the construction of two channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph these graph based functions are referred to as graph signals as we build a framework in which many concepts from the classical signal processing domain such as fourier decomposition signal filtering and downsampling can be extended to graph domain especially we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals this property of bipartite graphs allows us to design critically sampled two channel filter banks and we propose quadrature mirror filters referred to as graph qmf for bipartite graph which cancel aliasing and lead to perfect reconstruction for arbitrary graphs we present a bipartite subgraph decomposition which produces an edge disjoint collection of bipartite subgraphs graph qmfs are then constructed on each bipartite subgraph leading to multi dimensional separable wavelet filter banks on graphs our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality aliasing cancellation and perfect reconstruction the filter banks are realized by chebychev polynomial approximations

a new rainfall model based on the neyman scott process using cubic copulas 1 a classical way to model rainfall is to use a poisson process authors generally employed cluster of rectangular pulses to reproduce the hierarchical structure of rainfall storms although independence between cell intensity and duration turned out to be a nonrealistic assumption only a few models link these variables in this paper a neyman scott cluster process considering dependence between cell depth and duration is developed we introduce this link with a cubic copula copulas are multivariate distributions modeling the dependence structure between variables preserving the marginal distributions thanks to this flexibility we are able to introduce a global concept of dependence between cell depth and duration we derive the aggregated moments first second and third order moments from the new model for several families of polynomial copulas and perform an application on belgium and american data