a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

bayesian approach with hidden markov modeling and mean field approximation for hyperspectral data analysis the main problems in hyperspectral image analysis are spectral classification segmentation and data reduction in this paper we propose a bayesian estimation approach which gives a joint solution for these problems the problem is modeled as a blind sources separation bss the data are m hyperspectral images and the sources are k m images which are composed of compact homogeneous regions and have mutually disjoint supports the set of all these regions cover the total surface of the observed scene to insure these properties we propose a hierarchical markov model for the sources with a common hidden classification field which is modeled via a potts markov field the joint bayesian estimation of the hidden variable sources and the mixing matrix of the bss gives a solution for all three problems spectra classification segmentation and data reduction of hyperspectral images the mean field approximation mfa algorithm for the posterior laws is proposed for the effective bayesian computation finally some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods such as pca and ica

blind spectral unmixing based on sparse nonnegative matrix factorization nonnegative matrix factorization nmf is a widely used method for blind spectral unmixing su which aims at obtaining the endmembers and corresponding fractional abundances knowing only the collected mixing spectral data it is noted that the abundance may be sparse i e the endmembers may be with sparse distributions and sparse nmf tends to lead to a unique result so it is intuitive and meaningful to constrain nmf with sparseness for solving su however due to the abundance sum to one constraint in su the traditional sparseness measured by l0 l1 norm is not an effective constraint any more a novel measure termed as s measure of sparseness using higher order norms of the signal vector is proposed in this paper it features the physical significance by using the s measure constraint smc a gradient based sparse nmf algorithm termed as nmf smc is proposed for solving the su problem where the learning rate is adaptively selected and the endmembers and abundances are simultaneously estimated in the proposed nmf smc there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior yet it does not require the preprocessing of dimension reduction in which some useful information may be lost experiments based on synthetic mixtures and real world images collected by aviris and hydice sensors are performed to evaluate the validity of the proposed method

online dictionary learning for kernel lms adaptive filtering algorithms operating in reproducing kernel hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification unfortunately an undesirable characteristic of these methods is that the order of the filters grows linearly with the number of input data this dramatically increases the computational burden and memory requirement a variety of strategies based on dictionary learning have been proposed to overcome this severe drawback in the literature there is no theoretical work that strictly analyzes the problem of updating the dictionary in a time varying environment in this paper we present an analytical study of the convergence behavior of the gaussian least mean square algorithm in the case where the statistics of the dictionary elements only partially match the statistics of the input data this theoretical analysis highlights the need for updating the dictionary in an online way by discarding the obsolete elements and adding appropriate ones we introduce a kernel least mean square algorithm with ell 1 norm regularization to automatically perform this task the stability in the mean of this method is analyzed and the improvement of performance due to this dictionary adaptation is confirmed by simulations

semi supervised linear spectral unmixing using a hierarchical bayesian model for hyperspectral imagery this paper proposes a hierarchical bayesian model that can be used for semi supervised hyperspectral image unmixing the model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive gaussian noise the abundance parameters appearing in this model satisfy positivity and additivity constraints these constraints are naturally expressed in a bayesian context by using appropriate abundance prior distributions the posterior distributions of the unknown model parameters are then derived a gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances an extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library the performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

toward a sparse bayesian markov random field approach to hyperspectral unmixing and classification recent work has shown that existing powerful bayesian hyperspectral unmixing algorithms can be significantly improved by incorporating the inherent local spatial correlations between pixel class labels via the use of markov random fields we here propose a new bayesian approach to joint hyperspectral unmixing and image classification such that the previous assumption of stochastic abundance vectors is relaxed to a formulation whereby a common abundance vector is assumed for pixels in each class this allows us to avoid stochastic reparameterizations and instead we propose a symmetric dirichlet distributionmodel with adjustable parameters for the common abundance vector of each class inference over the proposed model is achieved via a hybrid gibbs sampler and in particular simulated annealing is introduced for the label estimation in order to avoid the local trap problem experiments on a synthetic image and a popular publicly available real data set indicate the proposed model is faster than and outperforms the existing approach quantitatively and qualitatively moreover for appropriate choices of the dirichlet parameter it is shown that the proposed approach has the capability to induce sparsity in the inferred abundance vectors it is demonstrated that this offers increased robustness in cases where the preprocessing endmember extraction algorithms overestimate the number of active endmembers present in a given scene

nonnegative matrix factorization for spectral data analysis data analysis is pervasive throughout business engineering and science very often the data to be analyzed is nonnegative and it is often preferable to take this constraint into account in the analysis process here we are concerned with the application of analyzing data obtained using astronomical spectrometers which provide spectral data which is inherently nonnegative the identification and classification of space objects that cannot be imaged in the normal way with telescopes is an important but difficult problem for tracking thousands of objects including satellites rocket bodies debris and asteroids in orbit around the earth in this paper we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes promising numerical results are presented using laboratory and simulated datasets

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

a convex analysis based minimum volume enclosing simplex algorithm for hyperspectral unmixing hyperspectral unmixing aims at identifying the hidden spectral signatures or endmembers and their corresponding proportions or abundances from an observed hyperspectral scene many existing hyperspectral unmixing algorithms were developed under a commonly used assumption that pure pixels exist however the pure pixel assumption may be seriously violated for highly mixed data based on intuitive grounds craig reported an unmixing criterion without requiring the pure pixel assumption which estimates the endmembers by vertices of a minimum volume simplex enclosing all the observed pixels in this paper we incorporate convex analysis and craig s criterion to develop a minimum volume enclosing simplex mves formulation for hyperspectral unmixing a cyclic minimization algorithm for approximating the mves problem is developed using linear programs lps which can be practically implemented by readily available lp solvers we also provide a non heuristic guarantee of our mves problem formulation where the existence of pure pixels is proved to be a sufficient condition for mves to perfectly identify the true endmembers some monte carlo simulations and real data experiments are presented to demonstrate the efficacy of the proposed mves algorithm over several existing hyperspectral unmixing methods

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

collaborative sparse regression using spatially correlated supports application to hyperspectral unmixing this paper presents a new bayesian collaborative sparse regression method for linear unmixing of hyperspectral images our contribution is twofold first we propose a new bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels i e materials are spatially organized rather than randomly distributed at a pixel level this prior information is encoded in the model through a truncated multivariate ising markov random field which also takes into consideration the facts that pixels cannot be empty i e there is at least one material present in each pixel and that different materials may exhibit different degrees of spatial regularity second we propose an advanced markov chain monte carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel and conditionally to the maximum marginal a posteriori configuration of the support compute the minimum mean squared error estimates of the abundance vectors a remarkable property of this algorithm is that it self adjusts the values of the parameters of the markov random field thus relieving practitioners from setting regularization parameters by cross validation the performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature

supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery this paper presents a nonlinear mixing model for hyperspectral image unmixing the proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white gaussian noise these nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model a bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model the performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data

a spatial compositional model for linear unmixing and endmember uncertainty estimation the normal compositional model ncm has been extensively used in hyperspectral unmixing however previous research has mostly focused on the estimation of endmembers and or their variability based on the assumption that the pixels are independent random variables in this paper we show that this assumption does not hold if all the pixels are generated by a fixed endmember set this introduces another concept endmember uncertainty which is related to whether the pixels fit into the endmember simplex to further develop this idea we derive the ncm from the ground up without the pixel independence assumption along with 1 using different noise levels at different wavelengths and 2 using a spatial and sparsity promoting prior for the abundances the resulting new formulation is called the spatial compositional model scm to better differentiate it from the ncm the scm maximum a posteriori objective leads to an optimization problem featuring noise weighted least squares minimization for unmixing the problem is solved by projected gradient descent resulting in an algorithm that estimates endmembers abundances noise variances and endmember uncertainty simultaneously we compared scm with current state of the art algorithms on synthetic and real images the results show that scm can in the main provide more accurate endmembers and abundances moreover the estimated uncertainty can serve as a prediction of endmember error under certain conditions

unsupervised post nonlinear unmixing of hyperspectral images using a hamiltonian monte carlo algorithm this paper presents a nonlinear mixing model for hyperspectral image unmixing the proposed model assumes that the pixel reflectances are post nonlinear functions of unknown pure spectral components contaminated by an additive white gaussian noise these nonlinear functions are approximated using second order polynomials leading to a polynomial post nonlinear mixing model a bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm due to the large number of parameters to be estimated an efficient hamiltonian monte carlo algorithm is investigated the classical leapfrog steps of this algorithm are modified to handle the parameter constraints the performance of the unmixing strategy including convergence and parameter tuning is first evaluated on synthetic data simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images

a maximum entropy approach to unsupervised mixed pixel decomposition due to the wide existence of mixed pixels the derivation of constituent components endmembers and their fractional proportions abundances at the subpixel scale has been given a lot of attention the entire process is often referred to as mixed pixel decomposition or spectral unmixing although various algorithms have been proposed to solve this problem two potential issues still need to be further investigated first assuming the endmembers are known the abundance estimation is commonly performed by employing a least squares error criterion which however makes the estimation sensitive to noise and outliers second the mathematical intractability of the abundance non negative constraint results in computationally expensive numerical approaches in this paper we propose an unsupervised decomposition method based on the classic maximum entropy principle termed the gradient descent maximum entropy gdme aiming at robust and effective estimates we address the importance of the maximum entropy principle for mixed pixel decomposition from a geometric point of view and demonstrate that when the given data present strong noise or when the endmember signatures are close to each other the proposed method has the potential of providing more accurate estimates than the popular least squares methods e g fully constrained least squares we apply the proposed gdme to the subject of unmixing multispectral and hyperspectral data the experimental results obtained from both simulated and real images show the effectiveness of the proposed method

a nonnegative pca algorithm for independent component analysis we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded so that they have a nonzero probability density function pdf in the region of zero we propose the use of a nonnegative principal component analysis nonnegative pca algorithm which is a special case of the nonlinear pca algorithm but with a rectification nonlinearity and we conjecture that this algorithm will find such nonnegative well grounded independent sources under reasonable initial conditions while the algorithm has proved difficult to analyze in the general case we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation

joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a bayesian sampling approach we propose a joint segmentation algorithm for piecewise constant autoregressive ar processes recorded by several independent sensors the algorithm is based on a hierarchical bayesian model appropriate priors allow us to introduce correlations between the change locations of the observed signals numerical problems inherent to bayesian inference are solved by a gibbs sampling strategy the proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations the initial algorithm is derived for piecewise constant ar processes whose orders are fixed on each segment however an extension to models with unknown model orders is also discussed theoretical results are illustrated by many simulations conducted with synthetic signals and real arc tracking and speech signals

joint bayesian endmember extraction and linear unmixing for hyperspectral imagery this paper studies a fully bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model the estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical bayesian model this model assumes conjugate prior distributions for these parameters accounts for nonnegativity and full additivity constraints and exploits the fact that the endmember proportions lie on a lower dimensional simplex a gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution this sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples the accuracy of the joint bayesian estimator is illustrated by simulations conducted on synthetic and real aviris images

a general class of bayesian survival models with zero and nonzero cure fractions we propose a new class of survival models which naturally links a family of proper and improper population survival functions the models resulting in improper survival functions are often referred to as cure rate models this class of regression models is formulated through the box cox transformation on the population hazard function and a proper density function by adding an extra transformation parameter into the cure rate model we are able to generate models with a zero cure rate thus leading to a proper population survival function a graphical illustration of the behavior and the influence of the transformation parameter on the regression model is provided we consider a bayesian approach which is motivated by the complexity of the model prior specification needs to accommodate parameter constraints due to the non negativity of the survival function moreover the likelihood function involves a complicated integral on the survival function which may not have an analytical closed form and thus makes the implementation of gibbs sampling more difficult we propose an efficient markov chain monte carlo computational scheme based on gaussian quadrature the proposed method is illustrated with an example involving a melanoma clinical trial

a new bayesian model for survival data with a surviving fraction abstract we consider bayesian methods for right censored survival data for populations with a surviving cure fraction we propose a model that is quite different from the standard mixture model for cure rates we provide a natural motivation and interpretation of the model and derive several novel properties of it first we show that the model has a proportional hazards structure with the covariates depending naturally on the cure rate second we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates prior elicitation is discussed in detail and classes of noninformative and informative prior distributions are proposed several theoretical properties of the proposed priors and resulting posteriors are derived and comparisons are made to the standard mixture model a real dataset from a melanoma clinical trial is discussed in detail

a mixture model combining logistic regression with proportional hazards regression summary a model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event the proposed model is a semiparametric generalization of a parametric model due to farewell 1982 estimates of the regression parameters are obtained by maximizing a monte carlo approximation of a marginal likelihood and the em algorithm is used to estimate the baseline survivor function we present some simulation results to verify the validity of the suggested estimation procedure it appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions

nonlinear hyperspectral unmixing with robust nonnegative matrix factorization we introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures the new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects that are treated as sparsely distributed additive outliers with the standard nonnegativity and sum to one constraints inherent to spectral unmixing our model leads to a new form of robust nonnegative matrix factorization with a group sparse outlier term the factorization is posed as an optimization problem which is addressed with a block coordinate descent algorithm involving majorization minimization updates simulation results obtained on synthetic and real data show that the proposed strategy competes with the state of the art linear and nonlinear unmixing methods

nonnegative least mean square algorithm dynamic system modeling plays a crucial role in the development of techniques for stationary and nonstationary signal processing due to the inherent physical characteristics of systems under investigation nonnegativity is a desired constraint that can usually be imposed on the parameters to estimate in this paper we propose a general method for system identification under nonnegativity constraints we derive the so called nonnegative least mean square algorithm nnlms based on stochastic gradient descent and we analyze its convergence experiments are conducted to illustrate the performance of this approach and consistency with the analysis

nonlinearity detection in hyperspectral images using a polynomial post nonlinear mixing model this paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection the proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white gaussian noise these nonlinear functions are approximated by polynomials leading to a polynomial post nonlinear mixing model we have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods a generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model to compute the test statistic associated with the nonlinearity detection we propose to approximate the variance of the estimated nonlinearity parameter by its constrained cramer rao bound the performance of the detection strategy is evaluated via simulations conducted on synthetic and real data more precisely synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature the real data investigated in this study are extracted from the cuprite image which shows that some minerals seem to be nonlinearly mixed in this image finally it is interesting to note that the estimated abundance maps obtained with the post nonlinear mixing model are in good agreement with results obtained in previous studies

svd based initialization a head start for nonnegative matrix factorization we describe nonnegative double singular value decomposition nndsvd a new method designed to enhance the initialization stage of nonnegative matrix factorization nmf nndsvd can readily be combined with existing nmf algorithms the basic algorithm contains no randomization and is based on two svd processes one approximating the data matrix the other approximating positive sections of the resulting partial svd factors utilizing an algebraic property of unit rank matrices simple practical variants for nmf with dense factors are described nndsvd is also well suited to initialize nmf algorithms with sparse factors many numerical examples suggest that nndsvd leads to rapid reduction of the approximation error of many nmf algorithms

a flexible family of transformation cure rate models in this paper we introduce a flexible family of cure rate models mainly motivated by the biological derivation of the classical promotion time cure rate model and assuming that a metastasis competent tumor cell produces a detectable tumor mass only when a specific number of distinct biological factors affect the cell special cases of the new model are among others the promotion time proportional hazards the geometric proportional odds and the negative binomial cure rate model in addition our model generalizes specific families of transformation cure rate models and some well studied destructive cure rate models exact likelihood inference is carried out by the aid of the expectation maximization algorithm a profile likelihood approach is exploited for estimating the parameters of the model while model discrimination problem is analyzed by the aid of the likelihood ratio test a simulation study demonstrates the accuracy of the proposed inferential method finally as an illustration we fit the proposed model to a cutaneous melanoma data set copyright 2017 john wiley sons ltd

lower bounds for parametric estimation with constraints a chapman robbins form of the barankin bound is used to derive a multiparameter cramer rao cr type lower bound on estimator error covariance when the parameter theta in r sup n is constrained to lie in a subset of the parameter space a simple form for the constrained cr bound is obtained when the constraint set theta sub c can be expressed as a smooth functional inequality constraint it is shown that the constrained cr bound is identical to the unconstrained cr bound at the regular points of theta sub c i e where no equality constraints are active on the other hand at those points theta in theta sub c where pure equality constraints are active the full rank fisher information matrix in the unconstrained cr bound must be replaced by a rank reduced fisher information matrix obtained as a projection of the full rank fisher matrix onto the tangent hyperplane of the full rank fisher matrix onto the tangent hyperplane of the constraint set at theta a necessary and sufficient condition involving the forms of the constraint and the likelihood function is given for the bound to be achievable and examples for which the bound is achieved are presented in addition to providing a useful generalization of the cr bound the results permit analysis of the gain in achievable mse performance due to the imposition of particular constraints on the parameter space without the need for a global reparameterization

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

a linear rank test for use when the main interest is in differences in cure rates for diseases with a positive probability of being cured a family of alternatives to the null hypothesis of equality of survival distributions is introduced which is designed to focus power against alternatives with differences in cure rates the optimal linear rank test for this alternative is derived and found to be substantially more efficient than the log rank test for this alternative when cure rates are less than 50 while there is little difference between the tests if the cure rates are 50 or greater the simple test based on the difference of kaplan meier estimates of the proportion cured is also examined and found to be fully efficient for this alternative with no censoring while its efficiency rapidly drops as censoring is increased the new test is not a pure test of equality of cure rates when the data are censored but rather is a test of equality of survival distributions that focuses power against late differences in the survival curves

hyperspectral unmixing in presence of endmember variability nonlinearity or mismodeling effects this paper presents three hyperspectral mixture models jointly with bayesian algorithms for supervised hyperspectral unmixing based on the residual component analysis model the proposed general formulation assumes the linear model to be corrupted by an additive term whose expression can be adapted to account for nonlinearities nls endmember variability ev or mismodeling effects mes the nl effect is introduced by considering a polynomial expression that is related to bilinear models the proposed new formulation of ev accounts for shape and scale endmember changes while enforcing a smooth spectral spatial variation the me formulation considers the effect of outliers and copes with some types of ev and nl the known constraints on the parameter of each observation model are modeled via suitable priors the posterior distribution associated with each bayesian model is optimized using a coordinate descent algorithm which allows the computation of the maximum a posteriori estimator of the unknown model parameters the proposed mixture and bayesian models and their estimation algorithms are validated on both synthetic and real images showing competitive results regarding the quality of the inferences and the computational complexity when compared with the state of the art algorithms

residual component analysis of hyperspectral images application to joint nonlinear unmixing and nonlinearity detection this paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection the proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an additional nonlinear term affecting the end members and contaminated by an additive gaussian noise a markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms the observed image is segmented into regions where nonlinear terms if present share similar statistical properties a bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm the performance of the proposed strategy is first evaluated on synthetic data simulations conducted with real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images

a proportional hazards model taking account of long term survivors a proportional hazards ph model is modified to take account of long term survivors by assuming the cumulative hazard to be bounded but otherwise unspecified to yield an improper survival function a marginal likelihood is derived under the restriction for type i censoring patterns for a ph model with cure the marginal and the partial likelihood are not the same in the absence of covariate information the estimate of the cure rate based on the marginal likelihood reduces to the value of the kaplan meier estimate at the end of the study an example of low asymptotic efficiency of the partial likelihood as compared to the marginal profile and parametric likelihoods is given an algorithm is suggested to fit the full ph model with cure

blind source separation in nonlinear mixtures separability and a basic algorithm in this paper a novel approach for performing blind source separation bss in nonlinear mixtures is proposed and their separability is studied it is shown that this problem can be solved under a few assumptions which are satisfied in most practical applications the main idea can be considered as transforming a time invariant nonlinear bss problem to local linear ones varying along the time using the derivatives of both sources and observations taking into account the proposed idea numerous algorithms can be developed performing the separation in this regard an algorithm supported by simulation results is also proposed in this paper it can be seen that the algorithm well separates the mixed sources however as the conventional linear bss methods the nonlinear bss suffers from ambiguities which are discussed in this paper

analysis of sparse representation and blind source separation in this letter we analyze a two stage cluster then l1 optimization approach for sparse representation of a data matrix which is also a promising approach for blind source separation bss in which fewer sensors than sources are present first sparse representation factorization of a data matrix is discussed for a given overcomplete basis matrix the corresponding sparse solution coefficient matrix with minimum l1 norm is unique with probability one which can be obtained using a standard linear programming algorithm the equivalence of the l1 norm solution and the l0 norm solution is also analyzed according to a probabilistic framework if the obtained l1 norm solution is sufficiently sparse then it is equal to the l0 norm solution with a high probability furthermore the l1 norm solution is robust to noise but the l0 norm solution is not showing that the l1 norm is a good sparsity measure these results can be used as a recoverability analysis of bss as discussed the basis matrix in this article is estimated using a clustering algorithm followed by normalization in which the matrix columns are the cluster centers of normalized data column vectors zibulevsky pearlmutter boll and kisilev 2000 used this kind of two stage approach in underdetermined bss our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown it is also robust to additive noise and estimation error in the mixing matrix finally four simulation examples and an eeg data analysis example are presented to illustrate the algorithm s utility and demonstrate its performance

estimating the granularity coefficient of a potts markov random field within a markov chain monte carlo algorithm this paper addresses the problem of estimating the potts parameter jointly with the unknown parameters of a bayesian model within a markov chain monte carlo mcmc algorithm standard mcmc methods cannot be applied to this problem because performing inference on requires computing the intractable normalizing constant of the potts model in the proposed mcmc method the estimation of is conducted using a likelihood free metropolis hastings algorithm experimental results obtained for synthetic data show that estimating jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of on the other hand choosing an incorrect value of can degrade estimation performance significantly to illustrate the interest of this method the proposed algorithm is successfully applied to real bidimensional sar and tridimensional ultrasound images

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

a class of bayesian shared gamma frailty models with multivariate failure time data nous proposons ici dans le cadre des donnees de survie une nouvelle classe de modeles a fragilite gamma partagee en appliquant la transformation de box cox a la fonction de hasard ainsi qu au produit du risque de base et de la fragilite cette nouvelle classe de modeles offre un large eventail de formes et relations entre la fonction de hasard et le risque de base et inclut en tant que cas particuliers le modele de cox usuel a fragilite gamma ainsi qu un nouveau modele additif a fragilite gamma de par la contrainte que le risque soit non negatif ce modele a fragilite gamma partagee presente un defi calculatoire dans le paradigme bayesien les distributions conjointes a priori sont definies par une distribution conditionnelle marginale ou la distribution conditionnelle est univariee cela permet d integrer les contraintes non lineaires sur les parametres la partie marginale de la distribution a priori quant a elle est libre de toute contrainte les distributions a priori permettent de programmer facilement l integralite des distributions conditionnelles requises pour l echantillonnage de gibbs tout en integrant les contraintes un jeu reel de donnees permet d illustrer cette classe de modeles a fragilite gamma partagee

bayesian semiparametric models for survival data with a cure fraction we propose methods for bayesian inference for a new class of semiparametric survival models with a cure fraction specifically we propose a semiparametric cure rate model with a smoothing parameter that controls the degree of parametricity in the right tail of the survival distribution we show that such a parameter is crucial for these kinds of models and can have an impact on the posterior estimates several novel properties of the proposed model are derived in addition we propose a class of improper noninformative priors based on this model and examine the properties of the implied posterior also a class of informative priors based on historical data is proposed and its theoretical properties are investigated a case study involving a melanoma clinical trial is discussed in detail to demonstrate the proposed methodology

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

cavitational flow in a channel with oscillatory wall on considere un probleme de cavite symetrique bidimensionnelle dans un canal a paroi courbe unicite et existence de la solution estimation du nombre d oscillations de la frontiere libre application aux problemes de jet bidimensionnel et de cavites asymetriques

bayesian estimation of linear mixtures using the normal compositional model application to hyperspectral imagery this paper studies a new bayesian unmixing algorithm for hyperspectral images each pixel of the image is modeled as a linear combination of so called endmembers these endmembers are supposed to be random in order to model uncertainties regarding their knowledge more precisely we model endmembers as gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous n finder n findr or vertex component analysis vca algorithms this paper proposes to estimate the mixture coefficients referred to as abundances using a bayesian algorithm suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters a hybrid gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances the performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images

nonlinear unmixing of hyperspectral data with vector valued kernel functions this paper presents a kernel based nonlinear mixing model for hyperspectral data where the nonlinear function belongs to a hilbert space of vector valued functions the proposed model extends the existing ones by accounting for band dependent and neighboring nonlinear contributions the key idea is to work under the assumption that nonlinear contributions are dominant in some parts of the spectrum while they are less pronounced in other parts in addition to this we motivate the need for taking into account nonlinear contributions originating from the ground covers of neighboring pixels by practical considerations precisely the adjacency effect the relevance of the proposed model is that the nonlinear function is associated with a matrix valued kernel that allows to jointly model a wide range of nonlinearities and includes prior information regarding band dependences furthermore the choice of the nonlinear function input allows to incorporate neighboring effects the optimization problem is strictly convex and the corresponding iterative algorithm is based on the alternating direction method of multipliers finally experiments conducted using synthetic and real data demonstrate the effectiveness of the proposed approach

robust hyperspectral unmixing with correntropy based metric hyperspectral unmixing is one of the crucial steps for many hyperspectral applications the problem of hyperspectral unmixing has proved to be a difficult task in unsupervised work settings where the endmembers and abundances are both unknown in addition this task becomes more challenging in the case that the spectral bands are degraded by noise this paper presents a robust model for unsupervised hyperspectral unmixing specifically our model is developed with the correntropy based metric where the nonnegative constraints on both endmembers and abundances are imposed to keep physical significance besides a sparsity prior is explicitly formulated to constrain the distribution of the abundances of each endmember to solve our model a half quadratic optimization technique is developed to convert the original complex optimization problem into an iteratively reweighted nonnegative matrix factorization with sparsity constraints as a result the optimization of our model can adaptively assign small weights to noisy bands and put more emphasis on noise free bands in addition with sparsity constraints our model can naturally generate sparse abundances experiments on synthetic and real data demonstrate the effectiveness of our model in comparison to the related state of the art unmixing models

nonlinear unmixing of hyperspectral data based on a linear mixture nonlinear fluctuation model spectral unmixing is an important issue to analyze remotely sensed hyperspectral data although the linear mixture model has obvious practical advantages there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one in this paper we formulate a new kernel based paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra with additive nonlinear fluctuations defined in a reproducing kernel hilbert space this family of models has clear interpretation and allows to take complex interactions of endmembers into account extensive experiment results with both synthetic and real images illustrate the generality and effectiveness of this scheme compared with state of the art methods

hyperspectral image classification through bilayer graph based learning hyperspectral image classification with limited number of labeled pixels is a challenging task in this paper we propose a bilayer graph based learning framework to address this problem for graph based classification how to establish the neighboring relationship among the pixels from the high dimensional features is the key toward a successful classification our graph learning algorithm contains two layers the first layer constructs a simple graph where each vertex denotes one pixel and the edge weight encodes the similarity between two pixels unsupervised learning is then conducted to estimate the grouping relations among different pixels these relations are subsequently fed into the second layer to form a hypergraph structure on top of which semisupervised transductive learning is conducted to obtain the final classification results our experiments on three data sets demonstrate the merits of our proposed approach which compares favorably with state of the art

learning the kernel matrix with semidefinite programming kernel based learning algorithms work by embedding the data into a euclidean space and then searching for linear relations among the embedded data points the embedding is performed implicitly by specifying the inner products between each pair of points in the embedding space this information is contained in the so called kernel matrix a symmetric and positive semidefinite matrix that encodes the relative positions of all points specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space classical model selection problems in machine learning in this paper we show how the kernel matrix can be learned from data via semidefinite programming sdp techniques when applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm using the labeled part of the data one can learn an embedding also for the unlabeled part the similarity between test points is inferred from training points and their labels importantly these learning problems are convex so we obtain a method for learning both the model class and the function without local minima furthermore this approach leads directly to a convex method for learning the 2 norm soft margin parameter in support vector machines solving an important open problem

nonparametric detection of nonlinearly mixed pixels and endmember estimation in hyperspectral images mixing phenomena in hyperspectral images depend on a variety of factors such as the resolution of observation devices the properties of materials and how these materials interact with incident light in the scene different parametric and nonparametric models have been considered to address hyperspectral unmixing problems the simplest one is the linear mixing model nevertheless it has been recognized that the mixing phenomena can also be nonlinear the corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing within this context it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis and then employ the simplest possible unmixing technique to analyze each pixel in this paper we propose a technique for detecting nonlinearly mixed pixels the detection approach is based on the comparison of the reconstruction errors using both a gaussian process regression model and a linear regression model the two errors are combined into a detection statistics for which a probability density function can be reasonably approximated we also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm the proposed detect then unmix strategy which consists of extracting endmembers detecting nonlinearly mixed pixels and unmixing is tested with synthetic and real images

bayesian curve fitting using mcmc with applications to signal segmentation we propose some bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear in the parameters regression models for example autoregressive or volterra models a joint prior distribution is set up over the number of the changepoints knots their positions and over the orders of the linear regression models within each segment if these are unknown hierarchical priors are developed and as the resulting posterior probability distributions and bayesian estimators do not admit closed form analytical expressions reversible jump markov chain monte carlo mcmc methods are derived to estimate these quantities results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature these results demonstrate the performance of our methods

nonlinear spectral unmixing of hyperspectral images using gaussian processes this paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images the proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components we assume that the spectral signatures of the pure components and the nonlinear function are unknown the first step of the proposed method estimates the abundance vectors for all the image pixels using a bayesian approach an a gaussian process latent variable model for the nonlinear function relating the abundance vectors to the observations the endmembers are subsequently estimated using gaussian process regression the performance of the unmixing strategy is first evaluated on synthetic data the proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies an interesting property is its robustness to the absence of pure pixels in the image the analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classification method

optimization problems with perturbations a guided tour this paper presents an overview of some recent and significant progress in the theory of optimization problems with perturbations we put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems these methods allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of lagrange multipliers is not a singleton may be unbounded or is even empty we give rather complete results for nonlinear programming problems and describe some extensions of the method to more general problems we illustrate the results by computing the equilibrium position of a chain that is almost vertical or horizontal

a unifying view of sparse approximate gaussian process regression we provide a new unifying view including all existing proper probabilistic sparse approximations for gaussian process regression our approach relies on expressing the effective prior which the methods are using this allows new insights to be gained and highlights the relationship between existing methods it also allows for a clear theoretically justified ranking of the closeness of the known approximations to the corresponding full gps finally we point directly to designs of new better sparse approximations combining the best of the existing strategies within attractive computational constraints