Results 1 - 10 of 2,359

Scalable tensor decompositions for multi-aspect data mining

by Tamara G. Kolda - In ICDM 2008: Proceedings of the 8th IEEE International Conference on Data Mining , 2008
"... Modern applications such as Internet traffic, telecommunication records, and large-scale social networks generate massive amounts of data with multiple aspects and high dimensionalities. Tensors (i.e., multi-way arrays) provide a natural representation for such data. Consequently, tensor decompositi ..."
Abstract - Cited by 64 (2 self) - Add to MetaCart
decompositions such as Tucker become important tools for summarization and analysis. One major challenge is how to deal with highdimensional, sparse data. In other words, how do we compute decompositions of tensors where most of the entries of the tensor are zero. Specialized techniques are needed for computing

Tensor Decompositions and Applications

by Tamara G. Kolda, Brett W. Bader - SIAM REVIEW , 2009
"... This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N -way array. Decompositions of higher-order tensors (i.e., N -way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal proce ..."
Abstract - Cited by 723 (18 self) - Add to MetaCart
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N -way array. Decompositions of higher-order tensors (i.e., N -way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal

A multilinear singular value decomposition

by Lieven De Lathauwer, Bart De Moor, Joos Vandewalle - SIAM J. Matrix Anal. Appl , 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are ..."
Abstract - Cited by 472 (22 self) - Add to MetaCart
Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc

Scalable Algorithms for Association Mining

by Mohammed J. Zaki - IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING , 2000
"... Association rule discovery has emerged as an important problem in knowledge discovery and data mining. The association mining task consists of identifying the frequent itemsets, and then forming conditional implication rules among them. In this paper we present efficient algorithms for the discovery ..."
Abstract - Cited by 259 (23 self) - Add to MetaCart
-lattices, which can be solved in memory. Efficient lattice traversal techniques are presented, which quickly identify all the long frequent itemsets, and their subsets if required. We also present the effect of using different database layout schemes combined with the proposed decomposition and traversal

Global Optimizations for Parallelism and Locality on Scalable Parallel Machines

by Jennifer M. Anderson, Monica S. Lam - IN PROCEEDINGS OF THE SIGPLAN '93 CONFERENCE ON PROGRAMMING LANGUAGE DESIGN AND IMPLEMENTATION , 1993
"... Data locality is critical to achieving high performance on large-scale parallel machines. Non-local data accesses result in communication that can greatly impact performance. Thus the mapping, or decomposition, of the computation and data onto the processors of a scalable parallel machine is a key i ..."
Abstract - Cited by 256 (20 self) - Add to MetaCart
Data locality is critical to achieving high performance on large-scale parallel machines. Non-local data accesses result in communication that can greatly impact performance. Thus the mapping, or decomposition, of the computation and data onto the processors of a scalable parallel machine is a key

Hierarchical singular value decomposition of tensors

by Lars Grasedyck, Lars Grasedyck - SIAM Journal on Matrix Analysis and Applications
"... Abstract. We define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in d = 2), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical fo ..."
Abstract - Cited by 178 (11 self) - Add to MetaCart
Abstract. We define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in d = 2), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical

Towards Interactive Construction of Topical Hierarchy: A Recursive Tensor Decomposition Approach

by Chi Wang , Xueqing Liu , Yanglei Song , Jiawei Han , Microsoft Research , Redmond , Wa
"... ABSTRACT Automatic construction of user-desired topical hierarchies over large volumes of text data is a highly desirable but challenging task. This study proposes to give users freedom to construct topical hierarchies via interactive operations such as expanding a branch and merging several branch ..."
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STROD, that allows efficient and consistent modification of topic hierarchies, based on a recursive generative model and a scalable tensor decomposition inference algorithm with theoretical performance guarantee. Empirical evaluation shows that STROD reduces the runtime of construction by several orders

Orthogonal Tensor Decompositions

by Tamara G. Kolda - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS , 2001
"... We explore the orthogonal decomposition of tensors (also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor ..."
Abstract - Cited by 124 (9 self) - Add to MetaCart
We explore the orthogonal decomposition of tensors (also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a

A Scalable Optimization Approach for Fitting Canonical Tensor Decompositions ∗

by Evrim Acar, Daniel M. Dunlavy, Tamara, G. Kolda
"... Abstract. Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as CANDECOMP/PARAFAC (CP), which expresses a tensor as the sum of compon ..."
Abstract - Cited by 33 (3 self) - Add to MetaCart
Abstract. Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as CANDECOMP/PARAFAC (CP), which expresses a tensor as the sum

A finite-volume, incompressible Navier–Stokes model for studies of the ocean on parallel computers.

by John Marshall , Alistair Adcroft , Chris Hill , Lev Perelman , Curt Heisey - J. Geophys. Res., , 1997
"... Abstract. The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A "pressure correction" method i ..."
Abstract - Cited by 293 (32 self) - Add to MetaCart
. The method makes possible a novel treatment of the boundary in which cells abutting the bottom or coast may take on irregular shapes and be "shaved" to fit the boundary. The algorithm can conveniently exploit massively parallel computers and suggests a domain decomposition which allocates vertical
Results 1 - 10 of 2,359