Sparse conjugate directions pursuit with application to fixed-size kernel models.
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| Title: | Sparse conjugate directions pursuit with application to fixed-size kernel models. |
|---|---|
| Authors: | Karsmakers, Peter peter.karsmakers@esat.kuleuven.be, Pelckmans, Kristiaan1 kp@it.uu.se, Brabanter, Kris2 kris.debrabanter@esat.kuleuven.be, hamme, Hugo2 hugo.vanhamme@esat.kuleuven.be, Suykens, Johan2 johan.suykens@esat.kuleuven.be |
| Source: | Machine Learning. Oct2011, Vol. 85 Issue 1-2, p109-148. 40p. |
| Subjects: | Sparse matrix software, Machine learning, Linear systems, Algorithms, Support vector machines |
| Abstract: | This work studies an optimization scheme for computing sparse approximate solutions of over-determined linear systems. Sparse Conjugate Directions Pursuit (SCDP) aims to construct a solution using only a small number of nonzero (i.e. nonsparse) coefficients. Motivations of this work can be found in a setting of machine learning where sparse models typically exhibit better generalization performance, lead to fast evaluations, and might be exploited to define scalable algorithms. The main idea is to build up iteratively a conjugate set of vectors of increasing cardinality, in each iteration solving a small linear subsystem. By exploiting the structure of this conjugate basis, an algorithm is found (i) converging in at most D iterations for D-dimensional systems, (ii) with computational complexity close to the classical conjugate gradient algorithm, and (iii) which is especially efficient when a few iterations suffice to produce a good approximation. As an example, the application of SCDP to Fixed-Size Least Squares Support Vector Machines (FS-LSSVM) is discussed resulting in a scheme which efficiently finds a good model size for the FS-LSSVM setting, and is scalable to large-scale machine learning tasks. The algorithm is empirically verified in a classification context. Further discussion includes algorithmic issues such as component selection criteria, computational analysis, influence of additional hyper-parameters, and determination of a suitable stopping criterion. [ABSTRACT FROM AUTHOR] |
| Copyright of Machine Learning 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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| Items | – Name: Title Label: Title Group: Ti Data: Sparse conjugate directions pursuit with application to fixed-size kernel models. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Karsmakers%2C+Peter%22">Karsmakers, Peter</searchLink><i> peter.karsmakers@esat.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22Pelckmans%2C+Kristiaan%22">Pelckmans, Kristiaan</searchLink><relatesTo>1</relatesTo><i> kp@it.uu.se</i><br /><searchLink fieldCode="AR" term="%22Brabanter%2C+Kris%22">Brabanter, Kris</searchLink><relatesTo>2</relatesTo><i> kris.debrabanter@esat.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22hamme%2C+Hugo%22">hamme, Hugo</searchLink><relatesTo>2</relatesTo><i> hugo.vanhamme@esat.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22Suykens%2C+Johan%22">Suykens, Johan</searchLink><relatesTo>2</relatesTo><i> johan.suykens@esat.kuleuven.be</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Machine+Learning%22">Machine Learning</searchLink>. Oct2011, Vol. 85 Issue 1-2, p109-148. 40p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Sparse+matrix+software%22">Sparse matrix software</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Support+vector+machines%22">Support vector machines</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work studies an optimization scheme for computing sparse approximate solutions of over-determined linear systems. Sparse Conjugate Directions Pursuit (SCDP) aims to construct a solution using only a small number of nonzero (i.e. nonsparse) coefficients. Motivations of this work can be found in a setting of machine learning where sparse models typically exhibit better generalization performance, lead to fast evaluations, and might be exploited to define scalable algorithms. The main idea is to build up iteratively a conjugate set of vectors of increasing cardinality, in each iteration solving a small linear subsystem. By exploiting the structure of this conjugate basis, an algorithm is found (i) converging in at most D iterations for D-dimensional systems, (ii) with computational complexity close to the classical conjugate gradient algorithm, and (iii) which is especially efficient when a few iterations suffice to produce a good approximation. As an example, the application of SCDP to Fixed-Size Least Squares Support Vector Machines (FS-LSSVM) is discussed resulting in a scheme which efficiently finds a good model size for the FS-LSSVM setting, and is scalable to large-scale machine learning tasks. The algorithm is empirically verified in a classification context. Further discussion includes algorithmic issues such as component selection criteria, computational analysis, influence of additional hyper-parameters, and determination of a suitable stopping criterion. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Machine Learning 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/s10994-011-5253-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 40 StartPage: 109 Subjects: – SubjectFull: Sparse matrix software Type: general – SubjectFull: Machine learning Type: general – SubjectFull: Linear systems Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Support vector machines Type: general Titles: – TitleFull: Sparse conjugate directions pursuit with application to fixed-size kernel models. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Karsmakers, Peter – PersonEntity: Name: NameFull: Pelckmans, Kristiaan – PersonEntity: Name: NameFull: Brabanter, Kris – PersonEntity: Name: NameFull: hamme, Hugo – PersonEntity: Name: NameFull: Suykens, Johan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2011 Type: published Y: 2011 Identifiers: – Type: issn-print Value: 08856125 Numbering: – Type: volume Value: 85 – Type: issue Value: 1-2 Titles: – TitleFull: Machine Learning Type: main |
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