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Generic and Typical Ranks of . . .
, 2009
"... The concept of tensor rank was introduced in the twenties. In the seventies, when methods of Component Analysis on arrays with more than two indices became popular, tensor rank became a much studied topic. The generic rank may be seen as an upper bound to the number of factors that are needed to con ..."
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The concept of tensor rank was introduced in the twenties. In the seventies, when methods of Component Analysis on arrays with more than two indices became popular, tensor rank became a much studied topic. The generic rank may be seen as an upper bound to the number of factors that are needed
On the typical rank of real binary forms
, 2009
"... We determine the rank of a general real binary form of degree d = 4 and d = 5. In the case d = 5, the possible values of the rank of such general forms are 3, 4, 5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d. ..."
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Cited by 6 (1 self)
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We determine the rank of a general real binary form of degree d = 4 and d = 5. In the case d = 5, the possible values of the rank of such general forms are 3, 4, 5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.
Generic and typical ranks of threeway arrays
 Research Report ISRN I3S/RR200629FR, I3S, SophiaAntipolis
"... The concept of tensor rank, introduced in the twenties, has been popularized at the beginning of the seventies. This has allowed to carry out Factor Analysis on arrays with more than two indices. The generic rank may be seen as an upper bound to the number of factors that can be extracted from a giv ..."
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Cited by 6 (3 self)
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The concept of tensor rank, introduced in the twenties, has been popularized at the beginning of the seventies. This has allowed to carry out Factor Analysis on arrays with more than two indices. The generic rank may be seen as an upper bound to the number of factors that can be extracted from a
Generic and typical ranks of multiway arrays
 Linear Algebra Appl
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 28 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A psychophysically plausible model for typicality ranking of natural scenes
 ACM Trans. Appl. Perc
"... Natural scenes constitute a very heterogeneous stimulus class. Each semantic category contains exemplars of varying typicality. It is therefore an interesting question whether humans can categorize natural scenes consistently into a relatively small number of categories such as coasts, rivers/lakes, ..."
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Cited by 4 (1 self)
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Natural scenes constitute a very heterogeneous stimulus class. Each semantic category contains exemplars of varying typicality. It is therefore an interesting question whether humans can categorize natural scenes consistently into a relatively small number of categories such as coasts, rivers
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
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
Fig. 1. Typical rankabundance relations. Dynamic Theory of Species Abundance Distributions
"... One of the goals of ecology is to find a mechanism to stabilize largescale complex ecological systems with many species interacting each other, universally observed on the earth, e.g. in tropical forests and coral reefs. Field ecologists, therefore, have investigated the number of species and each ..."
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population, some characteristic patterns have been observed universally in various ecosystems and with different species compositions. If the species abundance is ranked in descending order as a rankabundance relation (Fig. 1), one is a straight line (A) like the geometric series (Motomura, 1932) for a
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
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