finding imaging patterns of structural covariance via non negative matrix factorization in this paper we investigate the use of non negative matrix factorization nnmf for the analysis of structural neuroimaging data the goal is to identify the brain regions that co vary across individuals in a consistent way hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies nnmf offers a directly data driven way of extracting relatively localized co varying structural regions thereby transcending limitations of principal component analysis pca independent component analysis ica and other related methods that tend to produce dispersed components of positive and negative loadings in particular leveraging upon the well known ability of nnmf to produce parts based representations of image data we derive decompositions that partition the brain into regions that vary in consistent ways across individuals importantly these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split sample experiments we empirically validate nnmf in two data sets i a diffusion tensor dt mouse brain development study and ii a structural magnetic resonance smr study of human brain aging we demonstrate the ability of nnmf to produce sparse parts based representations of the data at various resolutions these representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes moreover we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like pca and ica

exploiting symmetries for single and multi agent partially observable stochastic domains while partially observable markov decision processes pomdps and their multi agent extension partially observable stochastic games posgs provide a natural and systematic approach to modeling sequential decision making problems under uncertainty the computational complexity with which the solutions are computed is known to be prohibitively expensive in this paper we show how such high computational resource requirements can be alleviated through the use of symmetries present in the problem the problem of finding the symmetries can be cast as a graph automorphism ga problem on a graphical representation of the problem we demonstrate how such symmetries can be exploited in order to speed up the solution computation and provide computational complexity results

multigrid tomographic inversion with variable resolution data and image spaces a multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements the proposed algorithm further reduces the computation relative to conventional multigrid approaches which change only the image space resolution at coarse scales the advantage is particularly important for data rich applications where data resolutions may differ for different scales applications of the approach to bayesian reconstruction algorithms in transmission and emission tomography with a generalized gaussian markov random field image prior are presented both with a poisson noise model and with a quadratic data term simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed grid iterative coordinate descent method and a multigrid method with fixed data resolution

on optimal solution of interval linear equations for interval linear algebraic systems bf a x bf b we consider the problem of component wise evaluation of the set sigma exists exists bf a bf b a 1 b mid a in bf a b in bf b formed by all solutions of ax b when a and b vary independently in bf a and bf b respectively an iterative pss algorithm is introduced that computes optimal exact componentwise estimates of sigma exists exists and its convergence is proved under fairly general conditions on the interval system we introduce the concept of a sequentially guaranteeing algorithm as a reasonable compromise between the requirements for the interval result to be guaranteed and to be obtained in a practically acceptable time

solving interval linear systems with linear programming techniques abstract in this paper we show how it is possible to use convex polyhedra for solving linear interval systems without using preconditioning we first show how to derive from an enclosure of a b a polyhedron which contains the convex hull of the solution set then a simplex like method enables us to find a new outer inclusion moreover the constraints obtained may be used to compute an inner inclusion of a b

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

geometrical fuzzy clustering algorithms fuzzy clustering algorithms are a basic tool for cluster analysis among these the geometrical fuzzy clustering algorithms are used when the clustering problem can be viewed as trying to find linear or ellipsoidal concentrations in data this paper provides a theoretical framework in which currently used geometrical fuzzy clustering algorithms become special cases also a family of functions called feasible are defined which can be used to construct such algorithms and convergence results are obtained

relations between various methods for solving linear interval and parametric equations abstract in the first part of the paper we consider standard systems of linear interval equations and we focus particularly on two solution methods the bauer skeel method and the hansen bliek rohn method we show relations between these two methods and between various modifications that are based on preconditioning of the system and on the residual form we compare as well the quality of the bounds produced by the different variants and we show that for some variants the bauer skeel bounds naturally arise from other approaches such as krawczyk of jacobi iterations too in the second part of the paper we consider interval parametric linear systems with affine linear dependencies we also investigate various forms of enclosures and we not only compare them with each other but we also show relations to some already known methods as a consequence we come up with novel and interesting relations between several algorithms

optimal space varying regularization in iterative image restoration it has been shown that space variant regularization in image restoration provides better results than space invariant regularization however the optimal choice of the regularization parameter is usually unknown a priori in previous work the generalized cross validation gcv criterion was shown to provide accurate estimates of the optimal regularization parameter the author introduces a modified form of the gcv criterion that incorporates space variant regularization and data error terms furthermore he presents an efficient method for estimating the gcv criterion for the space variant case using iterative image restoration techniques this method performs nearly as well as the exact criterion for the image restoration problem in addition he proposes a wiener filter interpretation for choosing the local weighting of the regularization this interpretation suggests the use of a multistage estimation procedure to estimate the optimal choice of the local regularization weights experiments confirm the value of the modified gcv estimation criterion as well as the multistage procedure for estimating the local regularization weights

the complexity of decentralized control of markov decision processes we consider decentralized control of markov decision processes and give complexity bounds on the worst case running time for algorithms that find optimal solutions generalizations of both the fully observable case and the partially observable case that allow for decentralized control are described for even two agents the finite horizon problems corresponding to both of these models are hard for nondeterministic exponential time these complexity results illustrate a fundamental difference between centralized and decentralized control of markov decision processes in contrast to the problems involving centralized control the problems we considerprovably do not admit polynomial time algorithms furthermore assuming exp nexp the problems require superexponential time to solve in the worst case

rough sets for bias field correction in mr images using contraharmonic mean and quantitative index one of the challenging tasks for magnetic resonance mr image analysis is to remove the intensity inhomogeneity artifact present in mr images which often degrades the performance of an automatic image analysis technique in this regard the paper presents a novel approach for bias field correction in mr images it judiciously integrates the merits of rough sets and contraharmonic mean while the contraharmonic mean is used in low pass averaging filter to estimate the bias field in multiplicative model the concept of lower approximation and boundary region of rough sets deals with vagueness and incompleteness in filter structure definition a theoretical analysis is presented to justify the use of both rough sets and contraharmonic mean for bias field estimation the integration enables the algorithm to estimate optimum or near optimum bias field some new quantitative indexes are introduced to measure intensity inhomogeneity artifact present in a mr image the performance of the proposed approach along with a comparison with other approaches is demonstrated on both simulated and real mr images for different bias fields and noise levels

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

the complexity of markov decision processes we investigate the complexity of the classical problem of optimal policy computation in markov decision processes all three variants of the problem finite horizon infinite horizon discounted and infinite horizon average cost were known to be solvable in polynomial time by dynamic programming finite horizon problems linear programming or successive approximation techniques infinite horizon we show that they are complete for p and therefore most likely cannot be solved by highly parallel algorithms we also show that in contrast the deterministic cases of all three problems can be solved very fast in parallel the version with partially observed states is shown to be pspace complete and thus even less likely to be solved in polynomial time than the np complete problems in fact we show that most likely it is not possible to have an efficient on line implementation involving polynomial time on line computations and memory of an optimal policy even if an arbitrary amount of precomputation is allowed finally the variant of the problem in which there are no observations is shown to be np complete

enclosing solutions of linear equations it is shown that rump s method for enclosing solutions of linear equations can be reformulated in an interval free form and that the underlying inclusion result can be proved by elementary means without using brouwer s fixed point theorem a sufficient condition on rump s inflation parameter eps is given under which finite termination occurs also a more general modified algorithm is studied for which the number of iterations can be expressed by an explicit formula

new operator and method for solving real preconditioned interval linear equations we deal with real preconditioned interval linear systems of equations we present a new operator which generalizes the interval gauss seidel operator also based on the new operator and properties of well known methods we propose a new algorithm called the magnitude method we illustrate by numerical examples that our approach outperforms some classical methods with respect to both time and sharpness of enclosures

planning and acting in partially observable stochastic domains in this paper we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains we begin by introducing the theory of markov decision processes mdps and partially observable mdps pomdps we then outline a novel algorithm for solving pomdps off line and show how in some cases a finite memory controller can be extracted from the solution to a pomdp we conclude with a discussion of how our approach relates to previous work the complexity of finding exact solutions to pomdps and of some possibilities for finding approximate solutions

solving over constrained systems of non linear interval equations and its robotic application abstract this paper presents and describes in details an original method developed to solve over constrained systems of non linear interval equations that arise namely in parameter identification problems deriving from physical models and uncertain measurements our approach consists of computing an interval enclosure of the least square solution set and an inner box of tolerable solution set this method is applied in a detailed example and some interesting results obtained for the calibration of a cable driven robot are shown

parameter estimation for finite mixture distributions abstract in this paper we compare numerically two approaches to the estimation of the parameters of the component densities in a univariate mixture of normal distributions one approach is based on a constrained maximum likelihood ml algorithm the other on the fuzzy c means fcm clustering algorithm our study indicates that i the ml method produces superior estimates when the component densities are well mixed while either algorithm provides good estimates for well separated distributions ii the fcm approach is almost always faster than the ml method and iii initialization of the ml method with the output of fcm almost always improves both the run time and accuracy of the statistical estimates

on the undecidability of probabilistic planning and related stochastic optimization problems automated planning the problem of how an agent achieves a goal given a repertoire of actions is one of the foundational and most widely studied problems in the ai literature the original formulation of the problem makes strong assumptions regarding the agent s knowledge and control over the world namely that its information is complete and correct and that the results of its actions are deterministic and known recent research in planning under uncertainty has endeavored te relax these assumptions providing formal and computation models wherein the agent has incomplete or noisy information about the world and has noisy sensors and effectors this research has mainly taken one of two approaches extend the classical planning paradigm to a semantics that admits uncertainty or adopt another framework for approaching the problem most commonly the markov decision process mdp model this paper presents a complexity analysis of planning under uncertainty it begins with the probabilistic classical planning problem showing that problem to be formally undecidable this fundamental result is then applied to a broad class of stochastic optimization problems in brief any problem statement where the agent a operates over an infinite or indefinite time horizon and b has available only probabilistic information about the system s state undecidability is established for policy existence problems for partially observable infinite horizon markov decision processes under discounted and undiscounted total reward models average reward models and state avoidance models the results also apply to corresponding approximation problems with undiscounted objective functions the paper answers a significant open question raised by papadimitriou and tsitsiklis math oper res 12 3 1987 441 450 about the complexity of infinite horizon pomdps

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

algorithms for highly symmetric linear and integer programs this paper deals with exploiting symmetry for solving linear and integer programming problems basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension

statistical approach to segmentation of single channel cerebral mr images a statistical model is presented that represents the distributions of major tissue classes in single channel magnetic resonance mr cerebral images using the model cerebral images are segmented into gray matter white matter and cerebrospinal fluid csf the model accounts for random noise magnetic field inhomogeneities and biological variations of the tissues intensity measurements are modeled by a finite gaussian mixture smoothness and piecewise contiguous nature of the tissue regions are modeled by a three dimensional 3 d markov random field mrf a segmentation algorithm based on the statistical model approximately finds the maximum a posteriori map estimation of the segmentation and estimates the model parameters from the image data the proposed scheme for segmentation is based on the iterative conditional modes icm algorithm in which measurement model parameters are estimated using local information at each site and the prior model parameters are estimated using the segmentation after each cycle of iterations application of the algorithm to a sample of clinical mr brain scans comparisons of the algorithm with other statistical methods and a validation study with a phantom are presented the algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of mr images in the presence of the random noise and intensity inhomogeneities

equivalence notions and model minimization in markov decision processes many stochastic planning problems can be represented using markov decision processes mdps a difficulty with using these mdp representations is that the common algorithms for solving them run in time polynomial in the size of the state space where this size is extremely large for most real world planning problems of interest recent ai research has addressed this problem by representing the mdp in a factored form factored mdps however are not amenable to traditional solution methods that call for an explicit enumeration of the state space one familiar way to solve mdp problems with very large state spaces is to form a reduced or aggregated mdp with the same properties as the original mdp by combining equivalent states in this paper we discuss applying this approach to solving factored mdp problems we avoid enumerating the state space by describing large blocks of equivalent states in factored form with the block descriptions being inferred directly from the original factored representation the resulting reduced mdp may have exponentially fewer states than the original factored mdp and can then be solved using traditional methods the reduced mdp found depends on the notion of equivalence between states used in the aggregation the notion of equivalence chosen will be fundamental in designing and analyzing algorithms for reducing mdps optimally these algorithms will be able to find the smallest possible reduced mdp for any given input mdp and notion of equivalence i e find the minimal model for the input mdp unfortunately the classic notion of state equivalence from non deterministic finite state machines generalized to mdps does not prove useful we present here a notion of equivalence that is based upon the notion of bisimulation from the literature on concurrent processes our generalization of bisimulation to stochastic processes yields a non trivial notion of state equivalence that guarantees the optimal policy for the reduced model immediately induces a corresponding optimal policy for the original model with this notion of state equivalence we design and analyze an algorithm that minimizes arbitrary factored mdps and compare this method analytically to previous algorithms for solving factored mdps we show that previous approaches implicitly derive equivalence relations that we define here

adaptive learning for event modeling and characterization adaptive learning of specific patterns or events of interest has been an area of significant research for various applications in the last two decades in developing diagnostic evaluation and safety monitoring applications of a propulsion system it is critical to detect characterize and model events of interest it is a challenging task since the detection system should allow adaptive characterization of potential events of interest and correlate them to learn new models for future detection for online health monitoring and diagnostic evaluation in this paper a novel framework is established using a hierarchical adaptive clustering approach with fuzzy membership functions to characterize specific events of interest from the measured and processed features raw engine measurement data is first analyzed using the wavelet transform to provide features for localization of frequency information for use in the classification system a method combining hierarchical and fuzzy k means clustering is then applied to a set of selected measurements and computed features to determine the events of interest during engine operations experimental results have shown that the proposed approach is effective and computationally efficient to detect characterize and model new events of interest from data collected through continuous operations