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Learning Reductions to Sparse Sets
"... Abstract. We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold ..."
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majority truthtable) reduces to a sparse set then Sat ≤ p m LT1 and hence a collapse of PH to P NP also follows. Lastly we show several interesting consequences of Sat ≤ p dtt SPARSE.
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 536 (17 self)
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The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural
The "Independent Components" of Natural Scenes are Edge Filters
, 1997
"... It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attem ..."
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Cited by 617 (29 self)
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It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm
Knowledgebased Analysis of Microarray Gene Expression Data By Using Support Vector Machines
, 2000
"... We introduce a method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments. The method is based on the theory of support vector machines (SVMs). SVMs are considered a supervised computer learning method because they exploit prior knowledge of ..."
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Cited by 520 (8 self)
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analysis, including their exibility in choosing a similarity function, sparseness of solution when dealing with large data sets, the ability t...
Local features and kernels for classification of texture and object categories: a comprehensive study
 International Journal of Computer Vision
, 2007
"... Recently, methods based on local image features have shown promise for texture and object recognition tasks. This paper presents a largescale evaluation of an approach that represents images as distributions (signatures or histograms) of features extracted from a sparse set of keypoint locations an ..."
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Cited by 653 (34 self)
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Recently, methods based on local image features have shown promise for texture and object recognition tasks. This paper presents a largescale evaluation of an approach that represents images as distributions (signatures or histograms) of features extracted from a sparse set of keypoint locations
A Simple RuleBased Part of Speech Tagger
, 1992
"... Automatic part of speech tagging is an area of natural language processing where statistical techniques have been more successful than rule based methods. In this paper, we present a sim ple rulebased part of speech tagger which automatically acquires its rules and tags with accuracy coinparable ..."
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Cited by 596 (9 self)
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to stochastic taggers. The rulebased tagger has many advantages over these taggers, including: a vast reduction in stored information required, the perspicuity of a sinall set of meaningful rules, ease of finding and implementing improvements to the tagger, and better portability from one tag set, cor pus
Benchmarking Least Squares Support Vector Machine Classifiers
 NEURAL PROCESSING LETTERS
, 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
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Cited by 476 (46 self)
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problems are represented by a set of binary classifiers using different output coding schemes. While regularization is used to control the effective number of parameters of the LSSVM classifier, the sparseness property of SVMs is lost due to the choice of the 2norm. Sparseness can be imposed in a second
Learning to detect objects in images via a sparse, partbased representation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2004
"... We study the problem of detecting objects in still, grayscale images. Our primary focus is development of a learningbased approach to the problem, that makes use of a sparse, partbased representation. A vocabulary of distinctive object parts is automatically constructed from a set of sample image ..."
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Cited by 378 (1 self)
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We study the problem of detecting objects in still, grayscale images. Our primary focus is development of a learningbased approach to the problem, that makes use of a sparse, partbased representation. A vocabulary of distinctive object parts is automatically constructed from a set of sample
Online learning for matrix factorization and sparse coding
, 2010
"... Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order to ad ..."
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Cited by 330 (31 self)
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Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order
A Growing Neural Gas Network Learns Topologies
 Advances in Neural Information Processing Systems 7
, 1995
"... An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this m ..."
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Cited by 401 (5 self)
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An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994
Results 1  10
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3,458