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Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 822 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
Feature selection based on mutual information: Criteria of maxdepe ndency, maxrelevance, and minredundancy
 IEEE Trans. Pattern Analysis and Machine Intelligence
"... Abstract—Feature selection is an important problem for pattern classification systems. We study how to select good features according to the maximal statistical dependency criterion based on mutual information. Because of the difficulty in directly implementing the maximal dependency condition, we f ..."
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Cited by 533 (7 self)
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Abstract—Feature selection is an important problem for pattern classification systems. We study how to select good features according to the maximal statistical dependency criterion based on mutual information. Because of the difficulty in directly implementing the maximal dependency condition, we first derive an equivalent form, called minimalredundancymaximalrelevance criterion (mRMR), for firstorder incremental feature selection. Then, we present a twostage feature selection algorithm by combining mRMR and other more sophisticated feature selectors (e.g., wrappers). This allows us to select a compact set of superior features at very low cost. We perform extensive experimental comparison of our algorithm and other methods using three different classifiers (naive Bayes, support vector machine, and linear discriminate analysis) and four different data sets (handwritten digits, arrhythmia, NCI cancer cell lines, and lymphoma tissues). The results confirm that mRMR leads to promising improvement on feature selection and classification accuracy.
The 2005 pascal visual object classes challenge
, 2006
"... Abstract. The PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not presegmented objects). Four object classes were selected: motorbikes, bicycles, cars and peop ..."
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Cited by 633 (24 self)
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Abstract. The PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not presegmented objects). Four object classes were selected: motorbikes, bicycles, cars
The PASCAL Visual Object Classes (VOC) challenge
, 2009
"... ... is a benchmark in visual object category recognition and detection, providing the vision and machine learning communities with a standard dataset of images and annotation, and standard evaluation procedures. Organised annually from 2005 to present, the challenge and its associated dataset has be ..."
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Cited by 624 (20 self)
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... is a benchmark in visual object category recognition and detection, providing the vision and machine learning communities with a standard dataset of images and annotation, and standard evaluation procedures. Organised annually from 2005 to present, the challenge and its associated dataset has become accepted as the benchmark for object detection. This paper describes the dataset and evaluation procedure. We review the stateoftheart in evaluated methods for both classification and detection, analyse whether the methods are statistically different, what they are learning from the images (e.g. the object or its context), and what the methods find easy or confuse. The paper concludes with lessons learnt in the three year history of the challenge, and proposes directions for future improvement and extension.
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
, 1997
"... We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images ..."
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Cited by 2263 (18 self)
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from this linear subspace. Rather than explicitly modeling this deviation, we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation. Our projection method is based on Fisher's Linear Discriminant and produces well separated classes
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models
 Journal of Business and Economic Statistics
, 2002
"... Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled wi ..."
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Cited by 684 (17 self)
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Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 484 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Hierarchical Models of Object Recognition in Cortex
, 1999
"... The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, little quantitative modeling has been done in the last 15 years to explore th ..."
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Cited by 817 (84 self)
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the biological feasibility of this class of models to explain higher level visual processing, such as object recognition. We describe a new hierarchical model that accounts well for this complex visual task, is consistent with several recent physiological experiments in inferotemporal cortex and makes testable
Results 1  10
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728,225