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Lowrank matrix completion by riemannian optimization
 ANCHPMATHICSE, Mathematics Section, École Polytechnique Fédérale de
"... The matrix completion problem consists of finding or approximating a lowrank matrix based on a few samples of this matrix. We propose a novel algorithm for matrix completion that minimizes the least square distance on the sampling set over the Riemannian manifold of fixedrank matrices. The algorit ..."
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Cited by 39 (3 self)
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The matrix completion problem consists of finding or approximating a lowrank matrix based on a few samples of this matrix. We propose a novel algorithm for matrix completion that minimizes the least square distance on the sampling set over the Riemannian manifold of fixedrank matrices
Strategies of Discourse Comprehension
, 1983
"... El Salvador, Guatemala is a, study in black and white. On the left is a collection of extreme MarxistLeninist groups led by what one diplomat calls “a pretty faceless bunch of people.’ ’ On the right is an entrenched elite that has dominated Central America’s most populous country since a CIAbacke ..."
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Cited by 601 (27 self)
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El Salvador, Guatemala is a, study in black and white. On the left is a collection of extreme MarxistLeninist groups led by what one diplomat calls “a pretty faceless bunch of people.’ ’ On the right is an entrenched elite that has dominated Central America’s most populous country since a CIAbacked coup deposed the reformist government of Col. Jacobo Arbenz Guzmán in 1954. Moderates of the political center. embattled but alive in E1 Salvador, have virtually disappeared in Guatemalajoining more than 30.000 victims of terror over the last tifteen vears. “The situation in Guatemala is much more serious than in EI Salvador, ” declares one Latin American diplomat. “The oligarchy is that much more reactionary. and the choices are far fewer. “ ‘Zero’: The Guatemalan oligarchs hated Jimmy Carter for cutting off U.S. military aid in 1977 to protest humanrights abusesand the rightwingers hired marimba bands and set off firecrackers on the night Ronald Reagan was elected. They considered Reagan an ideological kinsman and believed they had a special
Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. Technical Report 2003/235, Cryptology ePrint archive, http://eprint.iacr.org, 2006. Previous version appeared at EUROCRYPT 2004
 34 [DRS07] [DS05] [EHMS00] [FJ01] Yevgeniy Dodis, Leonid Reyzin, and Adam
, 2004
"... We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying mater ..."
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Cited by 532 (38 self)
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We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying
Equivariant Adaptive Source Separation
 IEEE Trans. on Signal Processing
, 1996
"... Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Eq ..."
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Cited by 448 (9 self)
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(Equivariant Adaptive Separation via Independence) . The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI
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
The algebraic combinatorial approach for lowrank matrix completion
 CoRR
"... We present a novel algebraic combinatorial view on lowrank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practic ..."
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Cited by 10 (2 self)
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We present a novel algebraic combinatorial view on lowrank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted LowRank Matrices
, 2009
"... ..."
Complete discrete 2D Gabor transforms by neural networks for image analysis and compression
, 1988
"... AbstractA threelayered neural network is described for transforming twodimensional discrete signals into generalized nonorthogonal 2D “Gabor ” representations for image analysis, segmentation, and compression. These transforms are conjoint spatiahpectral representations [lo], [15], which provide ..."
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Cited by 475 (8 self)
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to compute because t e elementary expansion functions are not orthogonal. One orthogonking approach developed for 1D signals by Bastiaans [SI, based on biorthonormal expansions, is restricted by constraints on the conjoint sampling rates and invariance of the windowing function, as well as by the fact
Fast Effective Rule Induction
, 1995
"... Many existing rule learning systems are computationally expensive on large noisy datasets. In this paper we evaluate the recentlyproposed rule learning algorithm IREP on a large and diverse collection of benchmark problems. We show that while IREP is extremely efficient, it frequently gives error r ..."
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Cited by 1257 (21 self)
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Many existing rule learning systems are computationally expensive on large noisy datasets. In this paper we evaluate the recentlyproposed rule learning algorithm IREP on a large and diverse collection of benchmark problems. We show that while IREP is extremely efficient, it frequently gives error
An Efficient Boosting Algorithm for Combining Preferences
, 1999
"... The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting ..."
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Cited by 707 (18 self)
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search strategies, each of which is a query expansion for a given domain. For this task, we compare the performance of RankBoost to the individual search strategies. The second experiment is a collaborativefiltering task for making movie recommendations. Here, we present results comparing Rank
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