Generalized Kernel-based Visual Tracking

In this work we generalize the plain MS trackers and attempt to overcome standard mean shift trackers' two limitations. It is well known that modeling and maintaining a representation of a target object is an important component of a successful visual tracker. However, little work has been done on building a robust template model for kernel-based MS tracking. In contrast to building a template from a single frame, we train a robust object representation model from a large amount of data. Tracking is viewed as a binary classification problem, and a discriminative classification rule is learned to distinguish between the object and background. We adopt a support vector machine (SVM) for training. The tracker is then implemented by maximizing the classification score. An iterative optimization scheme very similar to MS is derived for this purpose.Comment: 12 page

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaption of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz system

Distributed Estimation with Information-Seeking Control in Agent Network

We introduce a distributed, cooperative framework and method for Bayesian estimation and control in decentralized agent networks. Our framework combines joint estimation of time-varying global and local states with information-seeking control optimizing the behavior of the agents. It is suited to nonlinear and non-Gaussian problems and, in particular, to location-aware networks. For cooperative estimation, a combination of belief propagation message passing and consensus is used. For cooperative control, the negative posterior joint entropy of all states is maximized via a gradient ascent. The estimation layer provides the control layer with probabilistic information in the form of sample representations of probability distributions. Simulation results demonstrate intelligent behavior of the agents and excellent estimation performance for a simultaneous self-localization and target tracking problem. In a cooperative localization scenario with only one anchor, mobile agents can localize themselves after a short time with an accuracy that is higher than the accuracy of the performed distance measurements.Comment: 17 pages, 10 figure

Quaternion Information Theoretic Learning Adaptive Algorithms for Nonlinear Adaptive

Information Theoretic Learning (ITL) is gaining popularity for designing adaptive filters for a non-stationary or non-Gaussian environment [1] [2] . ITL cost functions such as the Minimum Error Entropy (MEE) have been applied to both linear and nonlinear adaptive filtering with better overall performance compared with the typical mean squared error (MSE) and least-squares type adaptive filtering, especially for nonlinear systems in higher-order statistic noise environments [3]. Quaternion valued data processing is beneficial in applications such as robotics and image processing, particularly for performing transformations in 3-dimensional space. Particularly the benefit for quaternion valued processing includes performing data transformations in a 3 or 4-dimensional space in a more convenient fashion than using vector algebra [4, 5, 6, 7, 8]. Adaptive filtering in quaterion domain operates intrinsically based on the augmented statistics which the quaternion input vector covariance is taken into account naturally and as a result it incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input [9]. The generalized Hamilton-real calculus (GHR) for the quaternion data simplified product and chain rules and allows us to calculate the gradient and Hessian of quaternion based cost function of the learning algorithms eciently [10][11] . The quaternion reproducing kernel Hilbert spaces and its uniqueness provide a mathematical foundation to develop the quaternion value kernel learning algorithms [12]. The reproducing property of the feature space replace the inner product of feature samples with kernel evaluation. In this dissertation, we first propose a kernel adaptive filter for quaternion data based on minimum error entropy cost function. The new algorithm is based on error entropy function and is referred to as the quaternion kernel minimum error entropy (QKMEE) algorithm [13]. We apply generalized Hamilton-real (GHR) calculus that is applicable to quaternion Hilbert space for evaluating the cost function gradient to develop the QKMEE algorithm. The minimum error entropy (MEE) algorithm [3, 14, 15] minimizes Renyis quadratic entropy of the error between the lter output and desired response or indirectly maximizing the error information potential. ITL methodology improves the performance of adaptive algorithm in biased or non-Gaussian signals and noise enviorments compared to the mean squared error (MSE) criterion algorithms such as the kernel least mean square algorithm. Second, we develop a kernel adaptive filter for quaternion data based on normalized minimum error entropy cost function [14]. We apply generalized Hamilton-real GHR) calculus that is applicable to Hilbert space for evaluating the cost function gradient to develop the quaternion kernel normalized minimum error entropy (QKNMEE) algorithm [16]. The new proposed algorithm enhanced QKMEE algorithm where the filter update stepsize selection will be independent of the input power and the kernel size. Third, we develop a kernel adaptive lter for quaternion domain data, based on information theoretic learning cost function which could be useful for quaternion based kernel applications of nonlinear filtering. The new algorithm is based on error entropy function with fiducial point and is referred to as the quaternion kernel minimum error entropy with fiducial point (QKMEEF) algorithm [17]. In our previous work we developed quaternion kernel adaptive lter based on minimum error entropy referred to as the QKMEE algorithm [13]. Since entropy does not change with the mean of the distribution, the algorithm may converge to a set of optimal weights without having zero mean error. Traditionally, to make the zero mean output error, the output during testing session was biased with the mean of errors of training session. However, for non-symmetric or heavy tails error PDF the estimation of error mean is problematic [18]. The minimum error entropy criterion, minimizes Renyi\u27s quadratic entropy of the error between the filter output and desired response or indirectly maximizing the error information potential [19]. Here, the approach is applied to quaternions. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to Hilbert space for evaluating the cost function gradient to develop the Quaternion Minimum Error Entropy Algorithm with Fiducial point. Simulation results are used to show the behavior of the new algorithm (QKMEEF) when signal is non-Gaussian in presence of unimodal noise versus bi-modal noise distributions. Simulation results also show that the new algorithm QKMEEF can track and predict the 4-Dimensional non-stationary process signals where there are correlations between components better than quadruple real-valued KMEEF and Quat-KLMS algorithms. Fourth, we develop a kernel adaptive filter for quaternion data, using stochastic information gradient (SIG) cost function based on the information theoretic learning (ITL) approach. The new algorithm (QKSIG) is useful for quaternion-based kernel applications of nonlinear ltering [20]. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to quaternion Hilbert space for evaluating the cost function gradient. The QKSIG algorithm minimizes Shannon\u27s entropy of the error between the filter output and desired response and minimizes the divergence between the joint densities of input-desired and input-output pairs. The SIG technique reduces the computational complexity of the error entropy estimation. Here, ITL with SIG approach is applied to quaternion adaptive filtering for three different reasons. First, it reduces the algorithm computational complexity compared to our previous work quaternion kernel minimum error entropy algorithm (QKMEE). Second, it improves the filtering performance by considering the coupling within the dimensions of the quaternion input. Third, it performs better in biased or non-Gaussian signal and noise environments due to ITL approach. We present convergence analysis and steady-state performance analysis results of the new algorithm (QKSIG). Simulation results are used to show the behavior of the new algorithm QKSIG in quaternion non-Gaussian signal and noise environments compared to the existing ones such as quadruple real-valued kernel stochastic information gradient (KSIG) and quaternion kernel LMS (QKLMS) algorithms. Fifth, we develop a kernel adaptive filter for quaternion data, based on stochastic information gradient (SIG) cost function with self adjusting step-size. The new algorithm (QKSIG-SAS) is based on the information theoretic learning (ITL) approach. The new algorithm (QKSIG-SAS) has faster speed of convergence as compared to our previous work QKSIG algorithm

Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version

Sequential Bayesian inference for implicit hidden Markov models and current limitations

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages, 10 figure