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Skew JensenBregman Voronoi Diagrams
, 2011
"... A JensenBregman divergence is a distortion measure defined by a Jensen convexity gap induced by a strictly convex functional generator. JensenBregman divergences unify the squared Euclidean and Mahalanobis distances with the celebrated informationtheoretic JensenShannon divergence, and can fur ..."
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A JensenBregman divergence is a distortion measure defined by a Jensen convexity gap induced by a strictly convex functional generator. JensenBregman divergences unify the squared Euclidean and Mahalanobis distances with the celebrated informationtheoretic JensenShannon divergence, and can
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a
Efficient Similarity Search for Covariance Matrices via the JensenBregman LogDet Divergence
"... Covariance matrices provide compact, informative feature descriptors for use in several computer vision applications, such as peopleappearance tracking, diffusiontensor imaging, activity recognition, among others. A key task in many of these applications is to compare different covariance matrices ..."
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Cited by 11 (3 self)
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these difficulties, we advocate a novel dissimilarity measure for covariance matrices: the JensenBregman LogDet Divergence. This divergence enjoys several useful theoretical properties, but its greatest benefits are: (i) lower computational costs (compared to standard approaches); and (ii) amenability for use
Constrained model predictive control: Stability and optimality
 AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
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Cited by 696 (15 self)
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and/or timevarying systems. We concentrate our attention on research dealing with stability and optimality; in these areas the subject has developed, in our opinion, to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control. We distill
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
JensenBregman LogDet Divergence for Efficient Similarity Computations on Positive Definite Tensors
, 2012
"... Covariance matrices provide an easy platform for fusing multiple features compactly and as a result have found immense success in several computer vision applications, including activity recognition, visual surveillance, and diffusion tensor imaging. An important task in all of these applications is ..."
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Cited by 2 (2 self)
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. To alleviate these difficulties, this paper proposes a novel dissimilarity measure for covariances, the JensenBregman LogDet Divergence (JBLD). This divergence enjoys several desirable theoretical properties, at the same time is computationally less demanding (compared to standard measures). To address
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length
The pyramid match kernel: Discriminative classification with sets of image features
 IN ICCV
, 2005
"... Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernelbased classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondenc ..."
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Cited by 546 (29 self)
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in the number of features, and it implicitly finds correspondences based on the finest resolution histogram cell where a matched pair first appears. Since the kernel does not penalize the presence of extra features, it is robust to clutter. We show the kernel function is positivedefinite, making it valid
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes
JensenBregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices
, 2012
"... Covariance matrices have found success in several computer vision applications, including activity recognition, visual surveillance, and diffusion tensor imaging. This is because they provide an easy platform for fusing multiple features compactly. An important task in all of these applications is t ..."
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Cited by 8 (2 self)
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proposes a novel dissimilarity measure for covariances, the JensenBregman LogDet Divergence (JBLD). This divergence enjoys several desirable theoretical properties, at the same time is computationally less demanding (compared to standard measures). Utilizing the fact that the squareroot of JBLD is a
Results 1  10
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37,975