binet cauchy kernels on dynamical systems and its application to the analysis of dynamic scenes we propose a family of kernels based on the binet cauchy theorem and its extension to fredholm operators our derivation provides a unifying framework for all kernels on dynamical systems currently used in machine learning including kernels derived from the behavioral framework diffusion processes marginalized kernels kernels on graphs and the kernels on sets arising from the subspace angle approach in the case of linear time invariant systems we derive explicit formulae for computing the proposed binet cauchy kernels by solving sylvester equations and relate the proposed kernels to existing kernels based on cepstrum coefficients and subspace angles we show efficient methods for computing our kernels which make them viable for the practitioner besides their theoretical appeal these kernels can be used efficiently in the comparison of video sequences of dynamic scenes that can be modeled as the output of a linear time invariant dynamical system one advantage of our kernels is that they take the initial conditions of the dynamical systems into account as a first example we use our kernels to compare video sequences of dynamic textures as a second example we apply our kernels to the problem of clustering short clips of a movie experimental evidence shows superior performance of our kernels

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

optimal control of neutral functional differential inclusions this paper deals with optimal control problems for dynamical systems governed by constrained functional differential inclusions of neutral type such control systems contain time delays not only in state variables but also in velocity variables which make them essentially more complicated than delay differential or differential difference inclusions our main goal is to derive necessary optimality conditions for general optimal control problems governed by neutral functional differential inclusions with endpoint constraints while some results are available for smooth control systems governed by neutral functional differential equations we are not familiar with any results for neutral functional differential inclusions even with smooth cost functionals in the absence of endpoint constraints developing the method of discrete approximations which is certainly of independent interest and employing advanced tools of generalized differentiation we conduct a variational analysis of neutral functional d

model based online learning with kernels new optimization models and algorithms for online learning with kernels olk in classification regression and novelty detection are proposed in a reproducing kernel hilbert space unlike the stochastic gradient descent algorithm called the naive online reg minimization algorithm norma olk algorithms are obtained by solving a constrained optimization problem based on the proposed models by exploiting the techniques of the lagrange dual problem like vapnik s support vector machine svm the solution of the optimization problem can be obtained iteratively and the iteration process is similar to that of the norma this further strengthens the foundation of olk and enriches the research area of svm we also apply the obtained olk algorithms to problems in classification regression and novelty detection including real time background substraction to show their effectiveness it is illustrated that based on the experimental results of both classification and regression the accuracy of olk algorithms is comparable with traditional svm based algorithms such as svm and least square svm ls svm and with the state ofthe art algorithms such as kernel recursive least square krls method and projectron method while it is slightly higher than that of norma on the other hand the computational cost of the olk algorithm is comparable with or slightly lower than existing online methods such as above mentioned norma krls and projectron methods but much lower than that of svm based algorithms in addition different from svm and ls svm it is possible for olk algorithms to be applied to non stationary problems also the applicability of olk in novelty detection is illustrated by simulation results

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

learning over sets using kernel principal angles we consider the problem of learning with instances defined over a space of sets of vectors we derive a new positive definite kernel f a b defined over pairs of matrices a b based on the concept of principal angles between two linear subspaces we show that the principal angles can be recovered using only inner products between pairs of column vectors of the input matrices thereby allowing the original column vectors of a b to be mapped onto arbitrarily high dimensional feature spaces we demonstrate the usage of the matrix based kernel function f a b with experiments on two visual tasks the first task is the discrimination of irregular motion trajectory of an individual or a group of individuals in a video sequence we use the svm approach using f a b where an input matrix represents the motion trajectory of a group of individuals over a certain fixed time frame we show that the classification irregular versus regular greatly outperforms the conventional representation where all the trajectories form a single vector the second application is the visual recognition of faces from input video sequences representing head motion and facial expressions where f a b is used to compare two image sequences

a harmonic decomposition reconstruction algorithm for spatially varying focal length collimators spatially varying focal length fan beam collimators can be used in single photon emission computed tomography to improve detection efficiency and to reduce reconstruction artifacts resulting from the truncation of projection data it has been proven that there exists no convolution backprojection algorithm for this type of collimator so a complicated interpolation between two nonparallel projection rays is necessary for existing algorithms the interpolation may generate blurring and artifacts in the reconstructed images based on a harmonic decomposition technique and the translation property of fourier series a semifrequency resampling technique is proposed to avoid the above mentioned interpolations by this technique the harmonic decomposition of projection data for spatially varying focal length fan beam collimators has the same form as that for parallel beam collimators in the semifrequency domain fourier transform with respect to angular variables only an alternative version of the inverse cormack transform is then proposed to reconstruct the images the derived reconstruction algorithm was implemented in a pentium ii 266 pc computer numerical simulations demonstrated its efficiency 3 s for 128 spl times 128 reconstruction arrays and its robust performance compared to the existing algorithms

the circular harmonic transform for spect reconstruction and boundary conditions on the fourier transform of the sinogram the circular harmonic transform cht solution of the exponential randon transform ert is applied to single photon emission computed tomography spect for uniform attenuation within a convex boundary an important special case also considered is the linear unattenuated radon transform lrt the solution is on the form of an orthogonal function expansion matched to projections that are in parallel ray geometry this property allows for efficient and accurate processing of the projections with fast fourier transform fft without interpolation or beam matching the algorithm is optimized by the use of boundary conditions on the 2 d fourier transform of the sinogram these boundary conditions imply that the signal energy of the sinogram is concentrated in well defined sectors in transform space the angle defining the sectors depends in a direct way on the radius of the field view these results are also obtained for fan beam geometry and the linear radon transform the fourier chebyshev transform of the sinogram to demonstrate that the boundary conditions are a more general property of the radon transform and a not a property unique to rectangular coordinates

a new approximate maximal margin classification algorithm a new incremental learning algorithm is described which approximates the maximal margin hyperplane w r t norm p 2 for a set of linearly separable data our algorithm called alma p approximate large margin algorithm w r t norm p takes o p 1 2 2 corrections to separate the data with p norm margin larger than 1 where g is the normalized p norm margin of the data alma p avoids quadratic or higher order programming methods it is very easy to implement and is as fast as on line algorithms such as rosenblatt s perceptron algorithm we performed extensive experiments on both real world and artificial datasets we compared alma 2 i e alma p with p 2 to standard support vector machines svm and to two incremental algorithms the perceptron algorithm and li and long s romma the accuracy levels achieved by alma 2 are superior to those achieved by the perceptron algorithm and romma but slightly inferior to svm s on the other hand alma 2 is quite faster and easier to implement than standard svm training algorithms when learning sparse target vectors alma p with p 2 largely outperforms perceptron like algorithms such as alma 2

global hashing system for fast image search hashing methods have been widely investigated for fast approximate nearest neighbor searching in large data sets most existing methods use binary vectors in lower dimensional spaces to represent data points that are usually real vectors of higher dimensionality we divide the hashing process into two steps data points are first embedded in a low dimensional space and the global positioning system method is subsequently introduced but modified for binary embedding we devise dataindependent and data dependent methods to distribute the satellites at appropriate locations our methods are based on finding the tradeoff between the information losses in these two steps experiments show that our data dependent method outperforms other methods in different sized data sets from 100k to 10m by incorporating the orthogonality of the code matrix both our data independent and data dependent methods are particularly impressive in experiments on longer bits

exponentiated gradient versus gradient descent for linear predictors we consider two algorithm for on line prediction based on a linear model the algorithms are the well known gradient descent gd algorithm and a new algorithm which we call eg they both maintain a weight vector using simple updates for the gd algorithm the update is based on subtracting the gradient of the squared error made on a prediction the eg algorithm uses the components of the gradient in the exponents of factors that are used in updating the weight vector multiplicatively we present worst case loss bounds for eg and compare them to previously known bounds for the gd algorithm the bounds suggest that the losses of the algorithms are in general incomparable but eg has a much smaller loss if only a few components of the input are relevant for the predictions we have performed experiments which show that our worst case upper bounds are quite tight already on simple artificial data

convergence of discrete approximations to optimization problems of neutral functional differential inclusions abstract this paper deals with the convergence of discrete approximations to the optimization problem p for a neutral functional differential inclusion subject to general endpoint constraints in the first part of the paper discrete approximations to the neutral functional differential inclusion are constructed using euler finite difference methods and the convergence of discrete approximations is proved in the second part of the paper a family of discrete optimization problems p n to p is provided and the strong convergence of optimal solutions for p n to the optimal solution of p is discussed

an efficient reconstruction method for nonuniform attenuation compensation in nonparallel beam geometries based on novikov s explicit inversion formula this paper investigates an accurate reconstruction method to invert the attenuated radon transform in nonparallel beam npb geometries the reconstruction method contains three major steps 1 performing one dimensional phase shift rebinning 2 implementing nonuniform hilbert transform and 3 applying novikov s explicit inversion formula the method seems to be adaptive to different settings of fan beam geometry from very long to very short focal lengths without sacrificing reconstruction accuracy compared to the conventional bilinear rebinning technique the presented method showed a better spatial resolution as measured by modulation transfer function numerical experiments demonstrated its computational efficiency and stability to different levels of poisson noise even with complicated geometries such as varying focal length and asymmetrical fan beam collimation the presented method achieved nearly the same reconstruction quality of parallel beam geometry this effort can facilitate quantitative reconstruction of single photon emission computed tomography for cardiac imaging which may need npb collimation geometries and require high computational efficiency

a unified reconstruction framework for both parallel beam and variable focal length fan beam collimators by a cormack type inversion of exponential radon transform a variety of inversions of exponential radon transform has been derived based on the circular harmonic transform in fourier space by several research groups however these inversions cannot be directly applied to deal with the reconstruction for fan beam or variable focal length fan beam collimator geometries in single photon emission computed tomography spect in this paper the authors derived a cormack type inversion of the exponential radon transform by employing the circular harmonic transform directly in the projection space and the image space instead of the fourier space thus a unified reconstruction framework is established for parallel fan and variable focal length fan beam collimator geometries compared to many existing algorithms the presented one greatly mitigates the difficulty of image reconstruction due to the complicated collimator geometry and significantly reduces the computational burden of the special functions such as chebyshev or bessel functions by the well established fast fourier transform fft the authors algorithm is very efficient as demonstrated by several numerical simulations

discrete approximations and refined euler lagrange conditions fornonconvex differential inclusions this paper deals with the bolza problem p for differential inclusions subject to general endpoint constraints we pursue a twofold goal first we develop a finite difference method for studying p and construct a discrete approximation to p that ensures a strong convergence of optimal solutions second we use this direct method to obtain necessary optimality conditions in a refined euler lagrange form without standard convexity assumptions in general we prove necessary conditions for the so called intermediate relaxed local minimum that takes an intermediate place between the classical concepts of strong and weak minima in the case of a mayer cost functional or boundary solutions to differential inclusions this euler lagrange form holds without any relaxation the results obtained are expressed in terms of nonconvex valued generalized differentiation constructions for nonsmooth mappings and sets

quantized kernel least mean square algorithm in this paper we propose a quantization approach as an alternative of sparsification to curb the growth of the radial basis function structure in kernel adaptive filtering the basic idea behind this method is to quantize and hence compress the input or feature space different from sparsification the new approach uses the redundant data to update the coefficient of the closest center in particular a quantized kernel least mean square qklms algorithm is developed which is based on a simple online vector quantization method the analytical study of the mean square convergence has been carried out the energy conservation relation for qklms is established and on this basis we arrive at a sufficient condition for mean square convergence and a lower and upper bound on the theoretical value of the steady state excess mean square error static function estimation and short term chaotic time series prediction examples are presented to demonstrate the excellent performance

from time series to linear system part ii exact modelling abstract in the second part of this paper the problem of finding an exact model for a q dimensional infinite time series is considered first a mathematical vocabulary for discussing exact modelling is developed it is then shown how the results of part i guarantee the existence of a most powerful ar model for an observed time series two algorithms for obtaining such an ar model are subsequently derived one of these algorithms gives a shortest lag input output model the problem of obtaining a minimal state space realization of the observed time series is also considered in order to do that realization theory based on the truncated behaviour is developed as an extensive example the classical situation with impulse response measurements is discussed

online passive aggressive algorithms we present a family of margin based online learning algorithms for various prediction tasks in particular we derive and analyze algorithms for binary and multiclass categorization regression uniclass prediction and sequence prediction the update steps of our different algorithms are all based on analytical solutions to simple constrained optimization problems this unified view allows us to prove worst case loss bounds for the different algorithms and for the various decision problems based on a single lemma our bounds on the cumulative loss of the algorithms are relative to the smallest loss that can be attained by any fixed hypothesis and as such are applicable to both realizable and unrealizable settings we demonstrate some of the merits of the proposed algorithms in a series of experiments with synthetic and real data sets

a metric for arma processes autoregressive moving average arma models seek to express a system function of a discretely sampled process as a rational function in the z domain treating an arma model as a complex rational function we discuss a metric defined on the set of complex rational functions we give a natural measure of the distance between two arma processes the paper concentrates on the mathematics behind the problem and shows that the various algebraic structures endow the choice of metric with some interesting and remarkable properties which we discuss we suggest that the metric can be used in at least two circumstances i in which we have signals arising from various models that are unknown so we construct the distance matrix and perform cluster analysis and ii where there are several possible models m sub i all of which are known and we wish to find which of these is closest to an observed data sequence modeled as m

hash kernels for structured data we propose hashing to facilitate efficient kernels this generalizes previous work using sampling and we show a principled way to compute the kernel matrix for data streams and sparse feature spaces moreover we give deviation bounds from the exact kernel matrix this has applications to estimation on strings and graphs

action recognition using linear dynamic systems in this paper we propose a novel approach based on linear dynamic systems ldss for action recognition our main contributions are two fold first we introduce ldss to action recognition ldss describe the dynamic texture which exhibits certain stationarity properties in time they are adopted to model the spatiotemporal patches which are extracted from the video sequence because the spatiotemporal patch is more analogous to a linear time invariant system than the video sequence notably ldss do not live in the euclidean space so we adopt the kernel principal angle to measure the similarity between ldss and then the multiclass spectral clustering is used to generate the codebook for the bag of features representation second we propose a supervised codebook pruning method to preserve the discriminative visual words and suppress the noise in each action class the visual words which maximize the inter class distance and minimize the intra class distance are selected for classification our approach yields the state of the art performance on three benchmark datasets especially the experiments on the challenging ucf sports and feature films datasets demonstrate the effectiveness of the proposed approach in realistic complex scenarios

svms for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e p i x i y i with a 1 and b 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian rbf kernels moreover we observed that a simple remapping of the input xi x a i improves the performance of linear svms to such an extend that it makes them for this problem a valid alternative to rbf kernels keywords support vector machines radial basis functions image histogram image classification corel

sampling in fan beam tomography in fan beam tomography functions in mathbb r 2 are constructed from integrals along straight lines emanating from a finite number of sources sitting on a circle around the reconstruction region using a sampling theorem for periodic functions and asymptotic estimates for the fourier transform of the fan beam transform the exact sampling conditions are found for standard fan beam scanning necessary to obtain a certain resolution new efficient sampling schemes and corresponding reconstruction algorithms are also found these sampling schemes need significantly less data to obtain a certain resolution than a standard fan beam geometry the correctness of the sampling conditions for standard fan beam scanning and the superiority of the new schemes are shown by computer simulations

kernel independent component analysis we present a class of algorithms for independent component analysis ica which use contrast functions based on canonical correlations in a reproducing kernel hilbert space on the one hand we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence on the other hand building on recent developments in kernel methods we show that these criteria and their derivatives can be computed efficiently minimizing these criteria leads to flexible and robust algorithms for ica we illustrate with simulations involving a wide variety of source distributions showing that our algorithms outperform many of the presently known algorithms

subspace angles between arma models abstract we define a notion of subspace angles between two linear autoregressive moving average single input single output models by considering the principal angles between subspaces that are derived from these models we show how a recently defined metric for these models which is based on their cepstra relates to the subspace angles between the models

sally a tool for embedding strings in vector spaces strings and sequences are ubiquitous in many areas of data analysis however only few learning methods can be directly applied to this form of data we present sally a tool for embedding strings in vector spaces that allows for applying a wide range of learning methods to string data sally implements a generalized form of the bag of words model where strings are mapped to a vector space that is spanned by a set of string features such as words or n grams of words the implementation of sally builds on efficient string algorithms and enables processing millions of strings and features the tool supports several data formats and is capable of interfacing with common learning environments such as weka shogun matlab or pylab sally has been successfully applied for learning with natural language text dna sequences and monitored program behavior

generalized principal component analysis gpca this paper presents an algebro geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points we represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point when the number of subspaces is known we show that these polynomials can be estimated linearly from data hence subspace segmentation is reduced to classifying one point per subspace we select these points optimally from the data set by minimizing certain distance function thus dealing automatically with moderate noise in the data a basis for the complement of each subspace is then recovered by applying standard pca to the collection of derivatives normal vectors extensions of gpca that deal with data in a high dimensional space and with an unknown number of subspaces are also presented our experiments on low dimensional data show that gpca outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k subspaces and expectation maximization we also present applications of gpca to computer vision problems such as face clustering temporal video segmentation and 3d motion segmentation from point correspondences in multiple affine views

a note on the unification of adaptive online learning in online convex optimization adaptive algorithms which can utilize the second order information of the loss function s sub gradient have shown improvements over standard gradient methods this paper presents a framework follow the bregman divergence leader that unifies various existing adaptive algorithms from which new insights are revealed under the proposed framework two simple adaptive online algorithms with improvable performance guarantee are derived furthermore a general equation derived from a matrix analysis generalizes the adaptive learning to nonlinear case with kernel trick

relative loss bounds for single neurons we analyze and compare the well known gradient descent algorithm and the more recent exponentiated gradient algorithm for training a single neuron with an arbitrary transfer function both algorithms are easily generalized to larger neural networks and the generalization of gradient descent is the standard backpropagation algorithm we prove worst case loss bounds for both algorithms in the single neuron case since local minima make it difficult to prove worst case bounds for gradient based algorithms we must use a loss function that prevents the formation of spurious local minima we define such a matching loss function for any strictly increasing differentiable transfer function and prove worst case loss bounds for any such transfer function and its corresponding matching loss the different forms of the two algorithms bounds indicates that exponentiated gradient outperforms gradient descent when the inputs contain a large number of irrelevant components simulations on synthetic data confirm these analytical results

support vector machines for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e sup spl rho spl sigma sub i sup xia yia b with a spl les 1 and b spl les 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian radial basis function rbf kernels moreover we observed that a simple remapping of the input x sub i spl rarr x sub i sup a improves the performance of linear svm to such an extend that it makes them for this problem a valid alternative to rbf kernels

efficient svm training using low rank kernel representations svm training is a convex optimization problem which scales with the training set size rather than the feature space dimension while this is usually considered to be a desired quality in large scale problems it may cause training to be impractical the common techniques to handle this difficulty basically build a solution by solving a sequence of small scale subproblems our current effort is concentrated on the rank of the kernel matrix as a source for further enhancement of the training procedure we first show that for a low rank kernel matrix it is possible to design a better interior point method ipm in terms of storage requirements as well as computational complexity we then suggest an efficient use of a known factorization technique to approximate a given kernel matrix by a low rank matrix which in turn will be used to feed the optimizer finally we derive an upper bound on the change in the objective function value based on the approximation error and the number of active constraints support vectors this bound is general in the sense that it holds regardless of the approximation method

nonuniform noise propagation by using the ramp filter in fan beam computed tomography it is observed that when the homogeneity property of the ramp filter is used to derive a filtered backprojection algorithm in fan beam tomography the reconstructed images have nonstationary frequency components and nonstationary noise when a short focal length is used higher frequency components are amplified more at the edge of the image than at the center of the image resulting in higher noise at the edge of the image

online learning with kernels kernel based algorithms such as support vector machines have achieved considerable success in various problems in batch setting where all of the training data is available in advance support vector machines combine the so called kernel trick with the large margin idea there has been little use of these methods in an online setting suitable for real time applications in this paper we consider online learning in a reproducing kernel hilbert space by considering classical stochastic gradient descent within a feature space and the use of some straightforward tricks we develop simple and computationally efficient algorithms for a wide range of problems such as classification regression and novelty detection in addition to allowing the exploitation of the kernel trick in an online setting we examine the value of large margins for classification in the online setting with a drifting target we derive worst case loss bounds and moreover we show the convergence of the hypothesis to the minimizer of the regularized risk functional we present some experimental results that support the theory as well as illustrating the power of the new algorithms for online novelty detection

hilbert transform based fbp algorithm for fan beam ct full and partial scans this paper presents a new type of filtered backprojection fbp algorithm for fan beam full and partial scans the filtering is shift invariant with respect to the angular variable the backprojection does not include position dependent weights through the hilbert transform and the one dimensional transformation between the fan and parallel beam coordinates the strong symmetry of the filtered projections directly leads to an exact reconstruction for partial data the use of the hilbert transform avoids the approximation introduced by the nonuniform cutoff frequency required in the ramp filter based fbp algorithm variance analysis indicates that the algorithm might lead to a better uniformity of resolution and noise in the reconstructed image numerical simulations are provided to evaluate the algorithm with noise free and noisy projections our simulation results indicate that the algorithm does have better stability over the ramp filter based fbp and circular harmonic reconstruction algorithms this may help improve the image quality for in place computed tomography scanners with single row detectors

the forgetron a kernel based perceptron on a budget the perceptron algorithm despite its simplicity often performs well in online classification tasks the perceptron becomes especially effective when it is used in conjunction with kernel functions however a common difficulty encountered when implementing kernel based online algorithms is the amount of memory required to store the online hypothesis which may grow unboundedly as the algorithm progresses moreover the running time of each online round grows linearly with the amount of memory used to store the hypothesis in this paper we present the forgetron family of kernel based online classification algorithms which overcome this problem by restricting themselves to a predefined memory budget we obtain different members of this family by modifying the kernel based perceptron in various ways we also prove a unified mistake bound for all of the forgetron algorithms to our knowledge this is the first online kernel based learning paradigm which on one hand maintains a strict limit on the amount of memory it uses and on the other hand entertains a relative mistake bound we conclude with experiments using real datasets which underscore the merits of our approach

efficient learning and planning with compressed predictive states predictive state representations psrs offer an expressive framework for modelling partially observable systems by compactly representing systems as functions of observable quantities the psr learning approach avoids using local minima prone expectation maximization and instead employs a globally optimal moment based algorithm moreover since psrs do not require a predetermined latent state structure as an input they offer an attractive framework for model based reinforcement learning when agents must plan without a priori access to a system model unfortunately the expressiveness of psrs comes with significant computational cost and this cost is a major factor inhibiting the use of psrs in applications in order to alleviate this shortcoming we introduce the notion of compressed psrs cpsrs the cpsr learning approach combines recent advancements in dimensionality reduction incremental matrix decomposition and compressed sensing we show how this approach provides a principled avenue for learning accurate approximations of psrs drastically reducing the computational costs associated with learning while also providing effective regularization going further we propose a planning framework which exploits these learned models and we show that this approach facilitates model learning and planning in large complex partially observable domains a task that is infeasible without the principled use of compression