measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

least squares estimation of transformation parameters between two point patterns in many applications of computer vision the following problem is encountered two point patterns sets of points x sub i and x sub i i 1 2 n are given in m dimensional space and the similarity transformation parameters rotation translation and scaling that give the least mean squared error between these point patterns are needed recently k s arun et al 1987 and b k p horn et al 1987 presented a solution of this problem their solution however sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted the proposed theorem is a strict solution of the problem and it always gives the correct transformation parameters even when the data is corrupted

group invariant pattern recognition abstract in this paper we develop a group theoretical model for the feature extraction part of pattern recognition systems we argue that the features used should reflect the regularities in the environment in which the system exists we develop first a group theoretical model to describe these regularities and then we show how to construct a feature extraction system that reflects these regularities we show why the so found filter functions often appear as solutions to optimality problems and why they often have some nice properties such as invariance under fourier transformation we will mainly investigate problems connected to the group of rotations in 2 d and 3 d space but we will touch other types of symmetries as well

on the n back and forth types of boolean algebras the objective of this paper is to uncover the structure of the back and forth equivalence classes at the nite levels for the class of boolean algebras as an application we obtain bounds on the computational complexity of determining the back and forth equivalence classes of a boolean algebra for nite levels this result has implications for characterizing the relatively intrinsically 0 relations of boolean algebras as existential formulas over a nite set of relations

pattern identification in dynamical systems via symbolic time series analysis this paper presents symbolic time series analysis stsa of multi dimensional measurement data for pattern identification in dynamical systems the proposed methodology is built upon concepts derived from information theory and automata theory the objective is not merely to classify the time series patterns but also to identify the variations therein to achieve this goal a symbol alphabet is constructed from raw data through partitioning of the data space the maximum entropy method of partitioning is extended to multi dimensional space the resulting symbol sequences generated from time series data are used to model the dynamical information as finite state automata and the patterns are represented by the stationary state probability distributions a novel procedure for determining the structure of the finite state automata based on entropy rate is introduced the diversity among the observed patterns is quantified by a suitable measure the efficacy of the stsa technique for pattern identification is demonstrated via laboratory experimentation on nonlinear systems

a derivative free approach to constrained multiobjective nonsmooth optimization in this work we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints where objective and constraint function values can only be obtained by querying a black box we define a linesearch based solution method and we show that it converges to a set of pareto stationary points to this aim we carry out a theoretical analysis of the problem by only assuming lipschitz continuity of the functions more specifically we give new optimality conditions that take explicitly into account the bound constraints and prove that the original problem is equivalent to a bound constrained problem obtained by penalizing the nonlinear constraints with an exact merit function finally we present the results of some numerical experiments on bound constrained and nonlinearly constrained problems showing that our approach is promising when compared to a state of the art method from the literature

divergence measure between chaotic attractors we propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors this measure is defined in terms of a generalized entropy we illustrate our procedure by considering the effect of additive noise in the well known henon attractor finally we show how our approach allows one to detect nonstationary events in a time series

nonlinear lagrangian for multiobjective optimization and applications to duality and exact penalization duality and penalty methods are popular in optimization the study on duality and penalty methods for nonconvex multiobjective optimization problems is very limited in this paper we introduce vector valued nonlinear lagrangian and penalty functions and formulate nonlinear lagrangian dual problems and nonlinear penalty problems for multiobjective constrained optimization problems we establish strong duality and exact penalization results the strong duality is an inclusion between the set of infimum points of the original multiobjective constrained optimization problem and that of the nonlinear lagrangian dual problem exact penalization is established via a generalized calmness type condition

robpca a new approach to robust principal component analysis we introduce a new method for robust principal component analysis pca classical pca is based on the empirical covariance matrix of the data and hence is highly sensitive to outlying observations two robust approaches have been developed to date the first approach is based on the eigenvectors of a robust scatter matrix such as the minimum covariance determinant or an s estimator and is limited to relatively low dimensional data the second approach is based on projection pursuit and can handle high dimensional data here we propose the robpca approach which combines projection pursuit ideas with robust scatter matrix estimation robpca yields more accurate estimates at noncontaminated datasets and more robust estimates at contaminated data robpca can be computed rapidly and is able to detect exact fit situations as a by product robpca produces a diagnostic plot that displays and classifies the outliers we apply the algorithm to several datasets from chemometrics and engineering

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

a linesearch based derivative free approach for nonsmooth constrained optimization in this paper we propose new linesearch based methods for nonsmooth constrained optimization problems when first order information on the problem functions is not available in the first part we describe a general framework for bound constrained problems and analyze its convergence toward stationary points using the clarke jahn directional derivative in the second part we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth in this case we first split the constraints into two subsets difficult general nonlinear constraints and simple bound constraints on the variables then we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound constrained minimization of the proposed exact penalty function finally we use the framework developed for the bound constrained case to solve the penalized problem moreover we prove that every accumulation poin

invariant pattern recognition a review in this document we review and compare some of the classical and modern techniques for solving the problem of invariant pattern recognition such techniques include integral transforms construction of algebraic moments and the use of structured neural networks in all cases we assume that the nature of the invariance group is known a priori many of the methods described apply to specific geometrical transformation groups however some of the techniques are highly general and applicable to large classes of invariance groups we also review some results regarding the existence and structure of invariants under certain kinds of groups

direct multisearch for multiobjective optimization in practical applications of optimization it is common to have several conflicting objective functions to optimize frequently these functions are subject to noise or can be of black box type preventing the use of derivative based techniques we propose a novel multiobjective derivative free methodology calling it direct multisearch dms which does not aggregate any of the objective functions our framework is inspired by the search poll paradigm of direct search methods of directional type and uses the concept of pareto dominance to maintain a list of nondominated points from which the new iterates or poll centers are chosen the aim of our method is to generate as many points in the pareto front as possible from the polling procedure itself while keeping the whole framework general enough to accommodate other disseminating strategies in particular when using the here also optional search step dms generalizes to multiobjective optimization moo all direct search methods of directional type

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

a computability theoretic equivalent to vaught s conjecture we prove that for every theory t which is given by an l 1 sentence t has less than 2 0 many countable models if and only if we have that for every x 2 on a cone of turing degrees every x hyperarithmetic model of t has an x computable copy we also find a concrete description relative to some oracle of the turing degree spectra of all the models of a counterexample to vaught s conjecture

functional echo state network for time series classification abstract echo state networks esns are a new approach to recurrent neural networks rnns that have been successfully applied in many domains nevertheless an esn is a predictive model rather than a classifier and methods to employ esns in time series classification tsc tasks have not yet been fully explored in this paper we propose a novel esn approach named functional echo state network fesn for time series classification the basic idea behind fesn is to replace the numeric variable output weights of an esn with time varying output weight functions and introduce a temporal aggregation operator to the output layer that can project temporal signals into discrete class labels thereby transforming the esn from a predictive model into a true classifier subsequently to learn the output weight functions a spatio temporal aggregation learning algorithm is proposed based on orthogonal function basis expansion by leveraging the nonlinear mapping capacity of a reservoir and the accumulation of temporal information in the time domain fesn can not only enhance the separability of different classes in a high dimensional functional space but can also consider the relative importance of temporal data at different time steps according to dynamic output weight functions theoretical analyses and experiments on an extensive set of ucr data were conducted on fesn the results show that fesn yields better performance than single algorithm methods has comparable accuracy with ensemble based methods and exhibits acceptable computational complexity interestingly for some time series datasets we visualized some interpretable features extracted by fesn via specific patterns within the output weight functions

invariant trajectory classification of dynamical systems with a case study on ecg an invariant pattern recognition framework for classification of phase space trajectories of nonlinear dynamical systems is presented using statistical shape theory known external influences can be discriminated from true changes of the system the external effects are modeled as a transformation group acting on the phase space and variation of the trajectories not explained by the transformations is accounted for using principal component analysis the approach suggested is highly adaptable to a wide range of situations and individual differences the methodology presented is applied to detect abnormalities in electrocardiograms results based on measured data indicate that the model developed is resistant to the effects of respiration and body position changes which are abundant in ambulatory conditions and cause significant morphological artifacts in the signal the results also show that the detection of an artificially induced acute myocardial infarction is achieved with high performance due to its low computational complexity the method developed can be implemented in real time the method developed also adapts to morphological changes caused by various heart conditions

recursive labelling systems and stability of recursive structures in hyperarithmetical degrees we show that under certain assumptions of recursiveness in 2t the recursive structure 2t is ao stable for ca w we need to deal with limit ordinals and we frame an analogous result proposition 2 for yn systems where yn is an increasing sequence of ordinals propositions 1 and 2 are then established by the

interpolation revisited medical images application based on the theory of approximation this paper presents a unified analysis of interpolation and resampling techniques an important issue is the choice of adequate basis functions the authors show that contrary to the common belief those that perform best are not interpolating by opposition to traditional interpolation the authors call their use generalized interpolation they involve a prefiltering step when correctly applied the authors explain why the approximation order inherent in any basis function is important to limit interpolation artifacts the decomposition theorem states that any basis function endowed with approximation order ran be expressed as the convolution of a b spline of the same order with another function that has none this motivates the use of splines and spline based functions as a tunable way to keep artifacts in check without any significant cost penalty the authors discuss implementation and performance issues and they provide experimental evidence to support their claims

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed