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DOI: 10.1007/S1133600790223 DEGENERACY IN CANDECOMP/PARAFAC AND INDSCAL EXPLAINED FOR SEVERAL THREESLICED ARRAYS WITH A TWOVALUED TYPICAL RANK
, 2007
"... The Candecomp/Parafac (CP) method decomposes a threeway array into a prespecified number R of rank1 arrays, by minimizing the sum of squares of the residual array. The practical use of CP is sometimes complicated by the occurrence of socalled degenerate sequences of solutions, in which several ra ..."
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rank1 arrays become highly correlated in all three modes and some elements of the rank1 arrays become arbitrarily large. We consider the realvalued CP decomposition of all known threesliced arrays, i.e., of size p × q × 3, with a twovalued typical rank. These are the 5 × 3 × 3and8 × 4 × 3 arrays
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 530 (21 self)
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toimplement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative and produces a sequence of matrices {X k, Y k} and at each step, mainly performs a softthresholding operation on the singular values of the matrix Y k. There are two
Tensor Decompositions and Applications
 SIAM REVIEW
, 2009
"... This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal proce ..."
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Cited by 701 (17 self)
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processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higherorder extensions of the matrix singular value decompo
sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 673 (1 self)
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problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for Kcolorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability
Optimizing Search Engines using Clickthrough Data
, 2002
"... This paper presents an approach to automatically optimizing the retrieval quality of search engines using clickthrough data. Intuitively, a good information retrieval system should present relevant documents high in the ranking, with less relevant documents following below. While previous approaches ..."
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Cited by 1262 (23 self)
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This paper presents an approach to automatically optimizing the retrieval quality of search engines using clickthrough data. Intuitively, a good information retrieval system should present relevant documents high in the ranking, with less relevant documents following below. While previous
Shape and motion from image streams under orthography: a factorization method
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1992
"... Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an illconditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orth ..."
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Cited by 1080 (38 self)
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uses the singularvalue decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a
Statistical Comparisons of Classifiers over Multiple Data Sets
, 2006
"... While methods for comparing two learning algorithms on a single data set have been scrutinized for quite some time already, the issue of statistical tests for comparisons of more algorithms on multiple data sets, which is even more essential to typical machine learning studies, has been all but igno ..."
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Cited by 710 (0 self)
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While methods for comparing two learning algorithms on a single data set have been scrutinized for quite some time already, the issue of statistical tests for comparisons of more algorithms on multiple data sets, which is even more essential to typical machine learning studies, has been all
Global mortality, disability, and the contribution of risk factors
 Global Burden of Disease Study. Lancet
, 1997
"... taken into account, our list differs substantially from other lists of the leading causes of death. DALYs provide a common metric to aid meaningful comparison of the burden of risk factors, diseases, and injuries. Lancet 1997; 349: 1436–42 ..."
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Cited by 430 (0 self)
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taken into account, our list differs substantially from other lists of the leading causes of death. DALYs provide a common metric to aid meaningful comparison of the burden of risk factors, diseases, and injuries. Lancet 1997; 349: 1436–42
Learning from demonstration
 Advances in Neural Information Processing Systems 9
, 1997
"... By now it is widely accepted that learning a task from scratch, i.e., without any prior knowledge, is a daunting undertaking. Humans, however, rarely attempt to learn from scratch. They extract initial biases as well as strategies how to approach a learning problem from instructions and/or demonstra ..."
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Cited by 392 (32 self)
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/or demonstrations of other humans. For learning control, this paper investigates how learning from demonstration can be applied in the context of reinforcement learning. We consider priming the Qfunction, the value function, the policy, and the model of the task dynamics as possible areas where demonstrations can
Understanding FaultTolerant Distributed Systems
 COMMUNICATIONS OF THE ACM
, 1993
"... We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design ..."
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Cited by 374 (23 self)
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We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design alternatives, we discuss their relative merits and we give examples of systems which adopt one approach or the other. The aim is to introduce some order in the complex discipline of designing and understanding faulttolerant distributed systems.
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