Decomposition-by-normalization (DBN): leveraging approximate functional dependencies for efficient CP and tucker decompositions.
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| Title: | Decomposition-by-normalization (DBN): leveraging approximate functional dependencies for efficient CP and tucker decompositions. |
|---|---|
| Authors: | Kim, Mijung1 mijung.kim.1@asu.edu, Candan, K.1 candan@asu.edu |
| Source: | Data Mining & Knowledge Discovery. Jan2016, Vol. 30 Issue 1, p1-46. 46p. |
| Subjects: | Functional dependencies, Data, Data analysis, Cost, Economics |
| Abstract: | For many multi-dimensional data applications, tensor operations as well as relational operations both need to be supported throughout the data lifecycle. Tensor based representations (including two widely used tensor decompositions, CP and Tucker decompositions) are proven to be effective in multi-aspect data analysis and tensor decomposition is an important tool for capturing high-order structures in multi-dimensional data. Although tensor decomposition is shown to be effective for multi-dimensional data analysis, the cost of tensor decomposition is often very high. Since the number of modes of the tensor data is one of the main factors contributing to the costs of the tensor operations, in this paper, we focus on reducing the modality of the input tensors to tackle the computational cost of the tensor decomposition process. We propose a novel decomposition-by-normalization scheme that first normalizes the given relation into smaller tensors based on the functional dependencies of the relation, decomposes these smaller tensors, and then recombines the sub-results to obtain the overall decomposition. The decomposition and recombination steps of the decomposition-by-normalization scheme fit naturally in settings with multiple cores. This leads to a highly efficient, effective, and parallelized decomposition-by-normalization algorithm for both dense and sparse tensors for CP and Tucker decompositions. Experimental results confirm the efficiency and effectiveness of the proposed decomposition-by-normalization scheme compared to the conventional nonnegative CP decomposition and Tucker decomposition approaches. [ABSTRACT FROM AUTHOR] |
| Copyright of Data Mining & Knowledge Discovery is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 112155621 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Decomposition-by-normalization (DBN): leveraging approximate functional dependencies for efficient CP and tucker decompositions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kim%2C+Mijung%22">Kim, Mijung</searchLink><relatesTo>1</relatesTo><i> mijung.kim.1@asu.edu</i><br /><searchLink fieldCode="AR" term="%22Candan%2C+K%2E%22">Candan, K.</searchLink><relatesTo>1</relatesTo><i> candan@asu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Data+Mining+%26+Knowledge+Discovery%22">Data Mining & Knowledge Discovery</searchLink>. Jan2016, Vol. 30 Issue 1, p1-46. 46p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Functional+dependencies%22">Functional dependencies</searchLink><br /><searchLink fieldCode="DE" term="%22Data%22">Data</searchLink><br /><searchLink fieldCode="DE" term="%22Data+analysis%22">Data analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Cost%22">Cost</searchLink><br /><searchLink fieldCode="DE" term="%22Economics%22">Economics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: For many multi-dimensional data applications, tensor operations as well as relational operations both need to be supported throughout the data lifecycle. Tensor based representations (including two widely used tensor decompositions, CP and Tucker decompositions) are proven to be effective in multi-aspect data analysis and tensor decomposition is an important tool for capturing high-order structures in multi-dimensional data. Although tensor decomposition is shown to be effective for multi-dimensional data analysis, the cost of tensor decomposition is often very high. Since the number of modes of the tensor data is one of the main factors contributing to the costs of the tensor operations, in this paper, we focus on reducing the modality of the input tensors to tackle the computational cost of the tensor decomposition process. We propose a novel decomposition-by-normalization scheme that first normalizes the given relation into smaller tensors based on the functional dependencies of the relation, decomposes these smaller tensors, and then recombines the sub-results to obtain the overall decomposition. The decomposition and recombination steps of the decomposition-by-normalization scheme fit naturally in settings with multiple cores. This leads to a highly efficient, effective, and parallelized decomposition-by-normalization algorithm for both dense and sparse tensors for CP and Tucker decompositions. Experimental results confirm the efficiency and effectiveness of the proposed decomposition-by-normalization scheme compared to the conventional nonnegative CP decomposition and Tucker decomposition approaches. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Data Mining & Knowledge Discovery is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10618-015-0401-6 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 46 StartPage: 1 Subjects: – SubjectFull: Functional dependencies Type: general – SubjectFull: Data Type: general – SubjectFull: Data analysis Type: general – SubjectFull: Cost Type: general – SubjectFull: Economics Type: general Titles: – TitleFull: Decomposition-by-normalization (DBN): leveraging approximate functional dependencies for efficient CP and tucker decompositions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kim, Mijung – PersonEntity: Name: NameFull: Candan, K. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2016 Type: published Y: 2016 Identifiers: – Type: issn-print Value: 13845810 Numbering: – Type: volume Value: 30 – Type: issue Value: 1 Titles: – TitleFull: Data Mining & Knowledge Discovery Type: main |
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