An empirical approach for probing the definiteness of kernels
Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zaefferer, Martin [verfasserIn] Bartz-Beielstein, Thomas [verfasserIn] Rudolph, Günter [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2018 |
|---|
| Schlagwörter: |
|---|
| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 23(2018), 21 vom: 26. Nov., Seite 10939-10952 |
|---|---|
| Übergeordnetes Werk: |
volume:23 ; year:2018 ; number:21 ; day:26 ; month:11 ; pages:10939-10952 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00500-018-3648-1 |
|---|
| Katalog-ID: |
SPR006508243 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | SPR006508243 | ||
| 003 | DE-627 | ||
| 005 | 20201124002914.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 201005s2018 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s00500-018-3648-1 |2 doi | |
| 035 | |a (DE-627)SPR006508243 | ||
| 035 | |a (SPR)s00500-018-3648-1-e | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Zaefferer, Martin |e verfasserin |4 aut | |
| 245 | 1 | 3 | |a An empirical approach for probing the definiteness of kernels |
| 264 | 1 | |c 2018 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 520 | |a Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. | ||
| 650 | 4 | |a Definiteness |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Kernel |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Distance |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Sampling |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Optimization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Evolutionary algorithm |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Bartz-Beielstein, Thomas |e verfasserin |4 aut | |
| 700 | 1 | |a Rudolph, Günter |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Soft Computing |d Springer-Verlag, 2003 |g 23(2018), 21 vom: 26. Nov., Seite 10939-10952 |w (DE-627)SPR006469531 |7 nnns |
| 773 | 1 | 8 | |g volume:23 |g year:2018 |g number:21 |g day:26 |g month:11 |g pages:10939-10952 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00500-018-3648-1 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_SPRINGER | ||
| 951 | |a AR | ||
| 952 | |d 23 |j 2018 |e 21 |b 26 |c 11 |h 10939-10952 | ||
| author_variant |
m z mz t b b tbb g r gr |
|---|---|
| matchkey_str |
zaefferermartinbartzbeielsteinthomasrudo:2018----:nmiiaapocfrrbnteeii |
| hierarchy_sort_str |
2018 |
| publishDate |
2018 |
| allfields |
10.1007/s00500-018-3648-1 doi (DE-627)SPR006508243 (SPR)s00500-018-3648-1-e DE-627 ger DE-627 rakwb eng Zaefferer, Martin verfasserin aut An empirical approach for probing the definiteness of kernels 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. Definiteness (dpeaa)DE-He213 Kernel (dpeaa)DE-He213 Distance (dpeaa)DE-He213 Sampling (dpeaa)DE-He213 Optimization (dpeaa)DE-He213 Evolutionary algorithm (dpeaa)DE-He213 Bartz-Beielstein, Thomas verfasserin aut Rudolph, Günter verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2018), 21 vom: 26. Nov., Seite 10939-10952 (DE-627)SPR006469531 nnns volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 https://dx.doi.org/10.1007/s00500-018-3648-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2018 21 26 11 10939-10952 |
| spelling |
10.1007/s00500-018-3648-1 doi (DE-627)SPR006508243 (SPR)s00500-018-3648-1-e DE-627 ger DE-627 rakwb eng Zaefferer, Martin verfasserin aut An empirical approach for probing the definiteness of kernels 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. Definiteness (dpeaa)DE-He213 Kernel (dpeaa)DE-He213 Distance (dpeaa)DE-He213 Sampling (dpeaa)DE-He213 Optimization (dpeaa)DE-He213 Evolutionary algorithm (dpeaa)DE-He213 Bartz-Beielstein, Thomas verfasserin aut Rudolph, Günter verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2018), 21 vom: 26. Nov., Seite 10939-10952 (DE-627)SPR006469531 nnns volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 https://dx.doi.org/10.1007/s00500-018-3648-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2018 21 26 11 10939-10952 |
| allfields_unstemmed |
10.1007/s00500-018-3648-1 doi (DE-627)SPR006508243 (SPR)s00500-018-3648-1-e DE-627 ger DE-627 rakwb eng Zaefferer, Martin verfasserin aut An empirical approach for probing the definiteness of kernels 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. Definiteness (dpeaa)DE-He213 Kernel (dpeaa)DE-He213 Distance (dpeaa)DE-He213 Sampling (dpeaa)DE-He213 Optimization (dpeaa)DE-He213 Evolutionary algorithm (dpeaa)DE-He213 Bartz-Beielstein, Thomas verfasserin aut Rudolph, Günter verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2018), 21 vom: 26. Nov., Seite 10939-10952 (DE-627)SPR006469531 nnns volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 https://dx.doi.org/10.1007/s00500-018-3648-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2018 21 26 11 10939-10952 |
| allfieldsGer |
10.1007/s00500-018-3648-1 doi (DE-627)SPR006508243 (SPR)s00500-018-3648-1-e DE-627 ger DE-627 rakwb eng Zaefferer, Martin verfasserin aut An empirical approach for probing the definiteness of kernels 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. Definiteness (dpeaa)DE-He213 Kernel (dpeaa)DE-He213 Distance (dpeaa)DE-He213 Sampling (dpeaa)DE-He213 Optimization (dpeaa)DE-He213 Evolutionary algorithm (dpeaa)DE-He213 Bartz-Beielstein, Thomas verfasserin aut Rudolph, Günter verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2018), 21 vom: 26. Nov., Seite 10939-10952 (DE-627)SPR006469531 nnns volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 https://dx.doi.org/10.1007/s00500-018-3648-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2018 21 26 11 10939-10952 |
| allfieldsSound |
10.1007/s00500-018-3648-1 doi (DE-627)SPR006508243 (SPR)s00500-018-3648-1-e DE-627 ger DE-627 rakwb eng Zaefferer, Martin verfasserin aut An empirical approach for probing the definiteness of kernels 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. Definiteness (dpeaa)DE-He213 Kernel (dpeaa)DE-He213 Distance (dpeaa)DE-He213 Sampling (dpeaa)DE-He213 Optimization (dpeaa)DE-He213 Evolutionary algorithm (dpeaa)DE-He213 Bartz-Beielstein, Thomas verfasserin aut Rudolph, Günter verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2018), 21 vom: 26. Nov., Seite 10939-10952 (DE-627)SPR006469531 nnns volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 https://dx.doi.org/10.1007/s00500-018-3648-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2018 21 26 11 10939-10952 |
| language |
English |
| source |
Enthalten in Soft Computing 23(2018), 21 vom: 26. Nov., Seite 10939-10952 volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 |
| sourceStr |
Enthalten in Soft Computing 23(2018), 21 vom: 26. Nov., Seite 10939-10952 volume:23 year:2018 number:21 day:26 month:11 pages:10939-10952 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Definiteness Kernel Distance Sampling Optimization Evolutionary algorithm |
| isfreeaccess_bool |
false |
| container_title |
Soft Computing |
| authorswithroles_txt_mv |
Zaefferer, Martin @@aut@@ Bartz-Beielstein, Thomas @@aut@@ Rudolph, Günter @@aut@@ |
| publishDateDaySort_date |
2018-11-26T00:00:00Z |
| hierarchy_top_id |
SPR006469531 |
| id |
SPR006508243 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006508243</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002914.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-018-3648-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006508243</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-018-3648-1-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zaefferer, Martin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="3"><subfield code="a">An empirical approach for probing the definiteness of kernels</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Definiteness</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Kernel</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distance</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sampling</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Evolutionary algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bartz-Beielstein, Thomas</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rudolph, Günter</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Soft Computing</subfield><subfield code="d">Springer-Verlag, 2003</subfield><subfield code="g">23(2018), 21 vom: 26. Nov., Seite 10939-10952</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:23</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:21</subfield><subfield code="g">day:26</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:10939-10952</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-018-3648-1</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">23</subfield><subfield code="j">2018</subfield><subfield code="e">21</subfield><subfield code="b">26</subfield><subfield code="c">11</subfield><subfield code="h">10939-10952</subfield></datafield></record></collection>
|
| author |
Zaefferer, Martin |
| spellingShingle |
Zaefferer, Martin misc Definiteness misc Kernel misc Distance misc Sampling misc Optimization misc Evolutionary algorithm An empirical approach for probing the definiteness of kernels |
| authorStr |
Zaefferer, Martin |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)SPR006469531 |
| format |
electronic Article |
| delete_txt_mv |
keep |
| author_role |
aut aut aut |
| collection |
springer |
| remote_str |
true |
| illustrated |
Not Illustrated |
| topic_title |
An empirical approach for probing the definiteness of kernels Definiteness (dpeaa)DE-He213 Kernel (dpeaa)DE-He213 Distance (dpeaa)DE-He213 Sampling (dpeaa)DE-He213 Optimization (dpeaa)DE-He213 Evolutionary algorithm (dpeaa)DE-He213 |
| topic |
misc Definiteness misc Kernel misc Distance misc Sampling misc Optimization misc Evolutionary algorithm |
| topic_unstemmed |
misc Definiteness misc Kernel misc Distance misc Sampling misc Optimization misc Evolutionary algorithm |
| topic_browse |
misc Definiteness misc Kernel misc Distance misc Sampling misc Optimization misc Evolutionary algorithm |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
Soft Computing |
| hierarchy_parent_id |
SPR006469531 |
| hierarchy_top_title |
Soft Computing |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)SPR006469531 |
| title |
An empirical approach for probing the definiteness of kernels |
| ctrlnum |
(DE-627)SPR006508243 (SPR)s00500-018-3648-1-e |
| title_full |
An empirical approach for probing the definiteness of kernels |
| author_sort |
Zaefferer, Martin |
| journal |
Soft Computing |
| journalStr |
Soft Computing |
| lang_code |
eng |
| isOA_bool |
false |
| recordtype |
marc |
| publishDateSort |
2018 |
| contenttype_str_mv |
txt |
| container_start_page |
10939 |
| author_browse |
Zaefferer, Martin Bartz-Beielstein, Thomas Rudolph, Günter |
| container_volume |
23 |
| format_se |
Elektronische Aufsätze |
| author-letter |
Zaefferer, Martin |
| doi_str_mv |
10.1007/s00500-018-3648-1 |
| author2-role |
verfasserin |
| title_sort |
empirical approach for probing the definiteness of kernels |
| title_auth |
An empirical approach for probing the definiteness of kernels |
| abstract |
Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. |
| abstractGer |
Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. |
| abstract_unstemmed |
Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER |
| container_issue |
21 |
| title_short |
An empirical approach for probing the definiteness of kernels |
| url |
https://dx.doi.org/10.1007/s00500-018-3648-1 |
| remote_bool |
true |
| author2 |
Bartz-Beielstein, Thomas Rudolph, Günter |
| author2Str |
Bartz-Beielstein, Thomas Rudolph, Günter |
| ppnlink |
SPR006469531 |
| mediatype_str_mv |
c |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s00500-018-3648-1 |
| up_date |
2024-07-03T23:19:36.894Z |
| _version_ |
1803601866283548672 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006508243</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002914.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-018-3648-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006508243</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-018-3648-1-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zaefferer, Martin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="3"><subfield code="a">An empirical approach for probing the definiteness of kernels</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof of concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counterexample is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Definiteness</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Kernel</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distance</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sampling</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Evolutionary algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bartz-Beielstein, Thomas</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rudolph, Günter</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Soft Computing</subfield><subfield code="d">Springer-Verlag, 2003</subfield><subfield code="g">23(2018), 21 vom: 26. Nov., Seite 10939-10952</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:23</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:21</subfield><subfield code="g">day:26</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:10939-10952</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-018-3648-1</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">23</subfield><subfield code="j">2018</subfield><subfield code="e">21</subfield><subfield code="b">26</subfield><subfield code="c">11</subfield><subfield code="h">10939-10952</subfield></datafield></record></collection>
|
| score |
7.39935 |