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396
Generic and typical ranks of multi-way arrays
- Linear Algebra Appl
"... HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished 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 multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished 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
Generalizing the Column-Row Matrix Decomposition to Multi-way Arrays
"... In this paper, we provide two generalizations of the CUR matrix decomposition Y = CUR (also known as pseudo-skeleton approximation method [1]) to the case of N-way arrays (tensors). These generalizations, which we called Fiber Sampling Tensor Decomposition types 1 and 2 (FSTD1 and FSTD2), provide ex ..."
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Cited by 14 (6 self)
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In this paper, we provide two generalizations of the CUR matrix decomposition Y = CUR (also known as pseudo-skeleton approximation method [1]) to the case of N-way arrays (tensors). These generalizations, which we called Fiber Sampling Tensor Decomposition types 1 and 2 (FSTD1 and FSTD2), provide
Low-rank decomposition of multi-way arrays: A signal processing perspective
- In IEEE SAM
, 2004
"... In many signal processing applications of linear algebra tools, the signal part of a postulated model lies in a so-called signal subspace, while the parameters of interest are in one-to-one correspondence with a certain basis of this subspace. The signal subspace can often be reliably estimated from ..."
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Cited by 12 (0 self)
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from measured data, but the particular basis of interest cannot be identified without additional problem-specific structure. This is a manifestation of rotational indeterminacy, i.e., non-uniqueness of low-rank matrix decomposition. The situation is very different for three- or higher-way arrays, i
LOW-RANK APPROXIMATION BASED NON-NEGATIVE MULTI-WAY ARRAY DECOMPOSITION ON EVENT-RELATED POTENTIALS
"... ∗Corresponding author. ..."
Star-Cubing: Computing Iceberg Cubes by Top-Down And Bottom-Up Integration
- In VLDB
, 2003
"... Data cube computation is one of the most essential but expensive operations in data warehousing. Previous studies have developedtwo major approaches, top-down vs. bottomup. The former, represented by the MultiWay Array Cube (called MultiWay) algorithm[25], aggregates simultaneously on multipledimens ..."
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Cited by 44 (10 self)
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Data cube computation is one of the most essential but expensive operations in data warehousing. Previous studies have developedtwo major approaches, top-down vs. bottomup. The former, represented by the MultiWay Array Cube (called MultiWay) algorithm[25], aggregates simultaneously
A multi-way analysis of starch cassava properties
"... The original methods proposed by Ledyard R. Tucker during the 1960s present the rotational freedom problem, making the interpretation of their results rather difficult to be carried out. Aiming to make the multi-way data analysis more acceptable, this work suggests a methodology for extracting meani ..."
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The original methods proposed by Ledyard R. Tucker during the 1960s present the rotational freedom problem, making the interpretation of their results rather difficult to be carried out. Aiming to make the multi-way data analysis more acceptable, this work suggests a methodology for extracting
Multi-way clustering using super-symmetric non-negative tensor factorization
- PROC. OF THE EUROPEAN CONFERENCE ON COMPUTER VISION (ECCV
, 2006
"... We consider the problem of clustering data into k ≥ 2 clusters given complex relations — going beyond pairwise — between the data points. The complex n-wise relations are modeled by an n-way array where each entry corresponds to an affinity measure over an ntuple of data points. We show that a prob ..."
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Cited by 50 (2 self)
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We consider the problem of clustering data into k ≥ 2 clusters given complex relations — going beyond pairwise — between the data points. The complex n-wise relations are modeled by an n-way array where each entry corresponds to an affinity measure over an ntuple of data points. We show that a
Optimal Joint Azimuth-Elevation and Signal-Array Response Estimation Using Parallel Factor Analysis
- in Proc. 32nd Asilomar Conf. Signals, Syst., Comput
, 1998
"... We consider deterministic joint azimuth-elevation, signal, and array response estimation, and establish a direct link to parallel factor (PARAFAC) analysis, a tool with roots in linear algebra for multi-way arrays. This link affords a powerful identifiability result, plus the opportunity to tap on a ..."
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Cited by 4 (3 self)
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We consider deterministic joint azimuth-elevation, signal, and array response estimation, and establish a direct link to parallel factor (PARAFAC) analysis, a tool with roots in linear algebra for multi-way arrays. This link affords a powerful identifiability result, plus the opportunity to tap
1Overview of Recent Advances in Numerical Tensor Algebra
"... Abstract—We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find low-rank approximations of tensors, and we describe some new resu ..."
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Abstract—We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find low-rank approximations of tensors, and we describe some new
I.: Missing values in dissimilarity-based classification of multi-way data
- In: Advances in Pattern Recognition and Applications. Proceedings of the 18th Iberoamerican Congress on Pattern Recognition CIARP 2013. Volumes 8258/8259 of LNCS
"... Abstract. Missing values can occur frequently in many real world sit-uations. Such is the case of multi-way data applications, where objects are usually represented by arrays of 2 or more dimensions e.g. biomedical signals that can be represented as time-frequency matrices. This lack of attributes t ..."
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Cited by 1 (0 self)
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Abstract. Missing values can occur frequently in many real world sit-uations. Such is the case of multi-way data applications, where objects are usually represented by arrays of 2 or more dimensions e.g. biomedical signals that can be represented as time-frequency matrices. This lack of attributes
Results 1 - 10
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396
