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Signal reconstruction using sparse tree representation
 in Proc. Wavelets XI at SPIE Optics and Photonics
, 2005
"... Recent studies in linear inverse problems have recognized the sparse representation of unknown signal in a certain basis as an useful and effective prior information to solve those problems. In many multiscale bases (e.g. wavelets), signals of interest (e.g. piecewisesmooth signals) not only have f ..."
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Cited by 46 (2 self)
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few significant coefficients, but also those significant coefficients are wellorganized in trees. We propose to exploit the treestructured sparse representation as additional prior information for linear inverse problems with limited numbers of measurements. We present numerical results showing
Probabilistic PartofSpeech Tagging Using Decision Trees
, 1994
"... In this paper, a new probabilistic tagging method is presented which avoids problems that Markov Model based taggers face, when they have to estimate transition probabilities from sparse data. In this tagging method, transition probabilities are estimated using a decision tree. Based on this method, ..."
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Cited by 1019 (9 self)
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In this paper, a new probabilistic tagging method is presented which avoids problems that Markov Model based taggers face, when they have to estimate transition probabilities from sparse data. In this tagging method, transition probabilities are estimated using a decision tree. Based on this method
Singular continuous and dense point spectrum for sparse trees with finite dimensions
 Proceedings of “Probability and Mathematical Physics” a conference in honor of Stanislav Molchanov’s 65th birthday
"... Dedicated to S. Molchanov on the occasion of his 65’th birthday Abstract. Sparse trees are trees with sparse branchings. The Laplacian on some of these trees can be shown to have singular spectral measures. We focus on a simple family of sparse trees for which the dimensions can be naturally defined ..."
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Cited by 9 (3 self)
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Dedicated to S. Molchanov on the occasion of his 65’th birthday Abstract. Sparse trees are trees with sparse branchings. The Laplacian on some of these trees can be shown to have singular spectral measures. We focus on a simple family of sparse trees for which the dimensions can be naturally
Smart robot teams exploring sparse trees
 IN: PROC. OF THE 31ST INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 2006
, 2006
"... We consider a tree which has to be completely explored by a group of k robots, initially placed at the root. The robots are mobile and can communicate using radio devices, but the communication range is bounded. They decide based on local, partial knowledge, and exchange information gathered durin ..."
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Cited by 5 (1 self)
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We consider a tree which has to be completely explored by a group of k robots, initially placed at the root. The robots are mobile and can communicate using radio devices, but the communication range is bounded. They decide based on local, partial knowledge, and exchange information gathered
Treebased Algorithms for Compressed Sensing with SparseTree Prior
"... Recent studies have shown that sparse representation can be used effectively as a prior in linear inverse problems. However, in many multiscale bases (e.g. wavelets), signals of interest (e.g. piecewisesmooth signals) not only have few significant coefficients, but also those significant coefficient ..."
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coefficients are wellorganized in trees. We propose to exploit this prior, named sparsetree, for linear inverse problems with limited numbers of measurements. Toward this end, we present two efficient and effective algorithms named Treebased Orthogonal Matching Pursuit (TOMP) and Treebased Majorization
TREEBASED MAJORIZEMINIMIZE ALGORITHM FOR COMPRESSED SENSING WITH SPARSETREE PRIOR
"... Recent studies have shown that sparse representation can be used effectively as a prior in linear inverse problems. However, in many multiscale bases (e.g., wavelets), signals of interest (e.g., piecewisesmooth signals) not only have few significant coefficients, but also those significant coeffici ..."
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Cited by 3 (1 self)
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coefficients are wellorganized in trees. We propose to exploit this, named sparsetree, prior for linear inverse problems with limited numbers of measurements. In particular, we present a fast treebased majorizeminimize (TMM) algorithm for signal reconstruction in this setting. Our numerical results show
An Architecture for WideArea Multicast Routing
"... Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or ..."
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Cited by 530 (22 self)
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or membership report information are occasionally sent over many links that do not lead to receivers or senders, respectively. We have developed a multicast routing architecture that efficiently establishes distribution trees across wide area internets, where many groups will be sparsely represented. Efficiency
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 456 (46 self)
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in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LSSVM sparse approximation procedure can be successfully applied.
Optimal Reward on a Sparse Tree with Random EdgeWeights
, 2002
"... It is well known that the maximal displacement of a random walk indexed by an mary tree with bounded i.i.d. edgeweights can reliably yield much larger asymptotics than a classical random walk whose summands are drawn from the same distribution. Presently we show that if the edgeweights are meanz ..."
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It is well known that the maximal displacement of a random walk indexed by an mary tree with bounded i.i.d. edgeweights can reliably yield much larger asymptotics than a classical random walk whose summands are drawn from the same distribution. Presently we show that if the edgeweights are mean
A Data Structure for Dynamic Trees
, 1983
"... A data structure is proposed to maintain a collection of vertexdisjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) ti ..."
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Cited by 343 (21 self)
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trees. (4) Implementing the network simplex algorithm for minimumcost flows. The most significant application is (2); an O(mn log n)time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse
Results 1  10
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126,554