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Good News and Bad News: Representation Theorems and Applications
 Bell Journal of Economics
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Cited by 684 (3 self)
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prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
GOOD REPRESENTATIONS AND SOLVABLE GROUPS
, 2000
"... The purpose of this paper is to provide a characterization of solvable linear algebraic groups in terms of a geometric property of representations. Representations with a related property played an important role in the proof of the equivariant RiemannRoch theorem [EG2]. In ..."
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The purpose of this paper is to provide a characterization of solvable linear algebraic groups in terms of a geometric property of representations. Representations with a related property played an important role in the proof of the equivariant RiemannRoch theorem [EG2]. In
Finding a good representation...
, 2002
"... Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternati ..."
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Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate
Good Representations and Homogeneous Spaces
, 804
"... Let G be a complex reductive affine algebraic group. Let F, H be algebraic reductive subgroups. The homogeneous space G/F has a natural, transitive left action of G on it. We will consider the induced action of H on G/F. Hereafter a property of a space will be called generic if it occurs on a nonemp ..."
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Let G be a complex reductive affine algebraic group. Let F, H be algebraic reductive subgroups. The homogeneous space G/F has a natural, transitive left action of G on it. We will consider the induced action of H on G/F. Hereafter a property of a space will be called generic if it occurs on a nonempty Zariski open set. Our main result is the following. The following theorem and its corollaries are true for both real and complex algebraic groups. Moreover, the results actually hold for real semialgebraic groups by passing to finite index subgroups and finite covers of manifolds. We omit the details of the proofs for semialgebraic groups. Theorem 1. Consider the induced action of H on G/F, then generic Horbits are closed in G/F; that is, there is a nonempty Zariski open set of G/F such that the Horbit of any point in this open set is closed. Corollary 2. Let G, H, F be as above. If H is normal in G, then all orbits of H are closed in G/F. Consequently, if G acts on V and the orbit Gv is closed, then Hv is also closed. Corollary 3. Let G be a reductive algebraic group. If H, F are generic reductive subgroups, then H ∩ F is also reductive. More precisely, take any two reductive subgroups H, F of G. Then H ∩ gFg −1 is reductive for generic g ∈ G.
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (8 self)
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representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasiincoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function
Inductive Learning Algorithms and Representations for Text Categorization
, 1998
"... Text categorization – the assignment of natural language texts to one or more predefined categories based on their content – is an important component in many information organization and management tasks. We compare the effectiveness of five different automatic learning algorithms for text categori ..."
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Cited by 641 (8 self)
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categorization in terms of learning speed, realtime classification speed, and classification accuracy. We also examine training set size, and alternative document representations. Very accurate text classifiers can be learned automatically from training examples. Linear Support Vector Machines (SVMs
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 741 (23 self)
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. The decoding of both codes can be tackled with a practical sumproduct algorithm. We prove that these codes are "very good," in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. This result holds not only for the binarysymmetric channel
PCASIFT: A more distinctive representation for local image descriptors
, 2004
"... Stable local feature detection and representation is a fundamental component of many image registration and object recognition algorithms. Mikolajczyk and Schmid [14] recently evaluated a variety of approaches and identified the SIFT [11] algorithm as being the most resistant to common image deforma ..."
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Cited by 572 (6 self)
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Stable local feature detection and representation is a fundamental component of many image registration and object recognition algorithms. Mikolajczyk and Schmid [14] recently evaluated a variety of approaches and identified the SIFT [11] algorithm as being the most resistant to common image
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 930 (41 self)
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In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many
Results 1  10
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