Constructive Approximation to Multivariate Function by Decay RBF Neural Network
It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parame...
Saved in:
| Published in: | IEEE transactions on neural networks Vol. 21; no. 9; pp. 1517 - 1523 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York, NY
IEEE
01.09.2010
Institute of Electrical and Electronics Engineers |
| Subjects: | |
| ISSN: | 1045-9227, 1941-0093, 1941-0093 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n + 1 hidden neurons can interpolate n + 1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments. |
|---|---|
| AbstractList | It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n + 1 hidden neurons can interpolate n + 1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments. It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n+1 hidden neurons can interpolate n+1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments.It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n+1 hidden neurons can interpolate n+1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments. |
| Author | Xuli Han Muzhou Hou |
| Author_xml | – sequence: 1 givenname: Muzhou surname: Hou fullname: Hou, Muzhou email: houmuzhou@sina.com organization: Central South University, Changsha, China. houmuzhou@sina.com – sequence: 2 givenname: Xuli surname: Han fullname: Han, Xuli |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23252802$$DView record in Pascal Francis https://www.ncbi.nlm.nih.gov/pubmed/20693108$$D View this record in MEDLINE/PubMed |
| BookMark | eNqFkc9rFDEUx0Op9Kd3QZC5iKdpXzJJNjnWbdcKdQtSz0OSeYHo7MyaZLT73zftri140NNLeJ9v8nifY7I_jAMS8obCGaWgz--WyzMG5cZACKXUHjmimtMaQDf75Qxc1Jqx2SE5Tuk7AOUC5AE5ZCB1Q0Edkdv5OKQcJ5fDL6wu1us43oeVyWEcqjxWX6a-NEwMJmO1mAb31LCb6hKd2VRfPy6qJU7R9KXk32P8cUpeedMnfL2rJ-Tb4upufl3f3H76PL-4qR0HlWsPDXadZ56WUaRBPpNcWiU666RXvmFWorXOWGotdUpIQAauM9Rqqb23zQn5sH23DPxzwpTbVUgO-94MOE6pVZIK3iiu_kvOuAY6A80L-W5HTnaFXbuOZRNx0_7ZVgHe7wCTnOl9NIML6YVrmGAKWOFgy7k4phTRPyMU2kdxbRHXPoprd-JKRP4VcSE_acjRhP5fwbfbYEDE53-E4MC0bh4AAQqk2w |
| CODEN | ITNNEP |
| CitedBy_id | crossref_primary_10_1109_TNNLS_2018_2839655 crossref_primary_10_1371_journal_pone_0330429 crossref_primary_10_1109_TNNLS_2011_2178560 crossref_primary_10_1108_EC_08_2019_0387 crossref_primary_10_1186_s13662_018_1927_x crossref_primary_10_1080_21642583_2019_1699474 crossref_primary_10_1080_21642583_2023_2207593 crossref_primary_10_1016_j_dsp_2022_103498 crossref_primary_10_1007_s00500_019_03944_1 crossref_primary_10_1016_j_knosys_2011_04_018 crossref_primary_10_1016_j_neucom_2018_08_020 crossref_primary_10_1109_ACCESS_2019_2913900 crossref_primary_10_1007_s00521_011_0604_8 crossref_primary_10_1007_s10489_016_0882_z crossref_primary_10_1007_s11063_023_11254_9 crossref_primary_10_1016_j_neunet_2017_04_001 crossref_primary_10_3390_electronics11223734 crossref_primary_10_1016_j_jprocont_2012_03_007 crossref_primary_10_1109_TNNLS_2013_2263288 crossref_primary_10_1080_21642583_2021_1980130 crossref_primary_10_5370_KIEE_2012_61_1_135 crossref_primary_10_1007_s00521_015_1960_6 crossref_primary_10_1016_j_asoc_2013_10_013 crossref_primary_10_1080_09603123_2020_1745763 crossref_primary_10_1109_TNN_2011_2109736 crossref_primary_10_1016_j_knosys_2016_12_003 crossref_primary_10_1109_TSMC_2021_3076747 crossref_primary_10_1016_j_dsp_2019_102634 crossref_primary_10_1007_s10846_014_0152_4 crossref_primary_10_1109_TIE_2015_2424399 crossref_primary_10_1109_TNNLS_2013_2295813 crossref_primary_10_1002_int_21569 crossref_primary_10_1007_s00366_022_01770_y crossref_primary_10_1186_s13662_019_2131_3 crossref_primary_10_3390_sym12060876 crossref_primary_10_1007_s11042_020_09382_8 crossref_primary_10_1109_ACCESS_2018_2815503 crossref_primary_10_1109_ACCESS_2023_3260251 crossref_primary_10_1109_TNNLS_2012_2227794 |
| Cites_doi | 10.1016/j.jsv.2007.10.050 10.1007/BF02124745 10.1016/0196-8858(92)90016-P 10.1016/S0893-6080(05)80131-5 10.1016/0022-0000(92)90039-L 10.1109/72.363469 10.1016/j.neucom.2005.12.126 10.1109/TNN.2003.809401 10.1016/j.cam.2005.04.019 10.1016/0893-6080(91)90009-T 10.1016/j.neunet.2005.03.013 10.1016/S0307-904X(02)00101-4 10.1109/TNN.2007.905851 10.1007/BF01893414 10.1109/IJCNN.2004.1380068 10.1109/TNN.2006.875974 10.1109/72.557662 10.1090/S0025-5718-1994-1240656-2 10.1109/TCSI.2002.805733 10.1109/TNN.2006.875977 10.1109/ICNC.2007.498 10.1016/j.neucom.2007.02.009 10.1109/TNN.2004.836241 10.1162/neco.1991.3.2.246 10.1109/TNN.2003.811355 10.1016/j.neucom.2007.10.008 10.1109/72.655045 |
| ContentType | Journal Article |
| Copyright | 2015 INIST-CNRS |
| Copyright_xml | – notice: 2015 INIST-CNRS |
| DBID | 97E RIA RIE AAYXX CITATION IQODW CGR CUY CVF ECM EIF NPM 7X8 7SC 7SP 8FD F28 FR3 JQ2 L7M L~C L~D |
| DOI | 10.1109/TNN.2010.2055888 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE/IET Electronic Library (IEL) (UW System Shared) CrossRef Pascal-Francis Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed MEDLINE - Academic Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ANTE: Abstracts in New Technology & Engineering Engineering Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) MEDLINE - Academic Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace ANTE: Abstracts in New Technology & Engineering Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | MEDLINE MEDLINE - Academic Technology Research Database |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: RIE name: IEEE/IET Electronic Library (IEL) (UW System Shared) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher – sequence: 3 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Anatomy & Physiology Computer Science Mathematics Applied Sciences |
| EISSN | 1941-0093 |
| EndPage | 1523 |
| ExternalDocumentID | 20693108 23252802 10_1109_TNN_2010_2055888 5540299 |
| Genre | orig-research Research Support, Non-U.S. Gov't Journal Article |
| GroupedDBID | --- -~X .DC 0R~ 29I 4.4 53G 5GY 5VS 6IK 97E AAJGR AASAJ AAWTH ABAZT ABJNI ABQJQ ABVLG ACGFS AETIX AGQYO AGSQL AHBIQ AI. AIBXA ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS S10 TAE TN5 VH1 AAYXX CITATION IQODW RIG AAYOK CGR CUY CVF ECM EIF NPM 7X8 7SC 7SP 8FD F28 FR3 JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c408t-f03eddf2f12066ae47646b85dbc6f8f32b6ebbcab1bb1c8560e20cda1b969ffb3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 46 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000283231200013&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1045-9227 1941-0093 |
| IngestDate | Fri Sep 05 13:45:34 EDT 2025 Fri Sep 05 04:04:57 EDT 2025 Thu Apr 03 07:04:24 EDT 2025 Mon Jul 21 09:16:24 EDT 2025 Sat Nov 29 03:59:24 EST 2025 Tue Nov 18 22:18:26 EST 2025 Tue Aug 26 17:15:13 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | true |
| Issue | 9 |
| Keywords | Statistical analysis Constructive mathematics decay radial basis function (RBF) neural networks uniformly approximation Continuous function Neural network Radial basis function Overtraining Constructive neural networks interpolation Model matching Approximation by function Vector support machine Proof theory Feedforward |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c408t-f03eddf2f12066ae47646b85dbc6f8f32b6ebbcab1bb1c8560e20cda1b969ffb3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
| PMID | 20693108 |
| PQID | 749017094 |
| PQPubID | 23479 |
| PageCount | 7 |
| ParticipantIDs | pubmed_primary_20693108 pascalfrancis_primary_23252802 crossref_primary_10_1109_TNN_2010_2055888 ieee_primary_5540299 proquest_miscellaneous_861543848 proquest_miscellaneous_749017094 crossref_citationtrail_10_1109_TNN_2010_2055888 |
| PublicationCentury | 2000 |
| PublicationDate | 2010-09-01 |
| PublicationDateYYYYMMDD | 2010-09-01 |
| PublicationDate_xml | – month: 09 year: 2010 text: 2010-09-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY – name: United States |
| PublicationTitle | IEEE transactions on neural networks |
| PublicationTitleAbbrev | TNN |
| PublicationTitleAlternate | IEEE Trans Neural Netw |
| PublicationYear | 2010 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers |
| References | ref13 ref34 ref12 ref15 ref14 ref31 chui (ref4) 1994 ding (ref6) 2002; 3 ref30 ref32 ref10 ref2 ref17 ref19 ref18 huang (ref16) 2003 ref24 ref23 ref26 ref25 ref20 gholizadeh (ref9) 2008; 312 ref22 ref21 chang (ref1) 2001 ref28 han (ref11) 2008; lncs 4975 ref29 ref8 ref7 huang (ref33) 0 ref3 ref5 miao (ref27) 2001; 31 yang (ref35) 2007; 30 |
| References_xml | – volume: 312 start-page: 316 year: 2008 ident: ref9 article-title: Structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network publication-title: J Sound Vib doi: 10.1016/j.jsv.2007.10.050 – ident: ref3 doi: 10.1007/BF02124745 – ident: ref26 doi: 10.1016/0196-8858(92)90016-P – ident: ref23 doi: 10.1016/S0893-6080(05)80131-5 – ident: ref31 doi: 10.1016/0022-0000(92)90039-L – ident: ref5 doi: 10.1109/72.363469 – year: 2001 ident: ref1 publication-title: LIBSVM A library for support vector machines – ident: ref17 doi: 10.1016/j.neucom.2005.12.126 – volume: lncs 4975 start-page: 541 year: 2008 ident: ref11 publication-title: GMP 2008 – ident: ref13 doi: 10.1109/TNN.2003.809401 – year: 2003 ident: ref16 publication-title: Universal approximation using incremental feedforward networks with arbitrary input weights – volume: 31 start-page: 136 year: 2001 ident: ref27 article-title: applications of radius basis function neural networks in scattered data interpolation publication-title: J Univ Sci Technol China – ident: ref25 doi: 10.1016/j.cam.2005.04.019 – ident: ref12 doi: 10.1016/0893-6080(91)90009-T – ident: ref34 doi: 10.1016/j.neunet.2005.03.013 – volume: 3 start-page: 756 year: 2002 ident: ref6 article-title: algorithm of wavelet rbf neural network publication-title: Proc 3rd Int Symp Instrum Sci Technol – ident: ref7 doi: 10.1016/S0307-904X(02)00101-4 – ident: ref29 doi: 10.1109/TNN.2007.905851 – ident: ref28 doi: 10.1007/BF01893414 – ident: ref15 doi: 10.1109/IJCNN.2004.1380068 – ident: ref14 doi: 10.1109/TNN.2006.875974 – ident: ref32 doi: 10.1109/72.557662 – ident: ref2 doi: 10.1090/S0025-5718-1994-1240656-2 – ident: ref24 doi: 10.1109/TCSI.2002.805733 – year: 1994 ident: ref4 publication-title: An Introduction to Wavelets – ident: ref20 doi: 10.1109/TNN.2006.875977 – ident: ref10 doi: 10.1109/ICNC.2007.498 – ident: ref21 doi: 10.1016/j.neucom.2007.02.009 – ident: ref18 doi: 10.1109/TNN.2004.836241 – ident: ref30 doi: 10.1162/neco.1991.3.2.246 – ident: ref8 doi: 10.1109/TNN.2003.811355 – ident: ref22 doi: 10.1016/j.neucom.2007.10.008 – ident: ref19 doi: 10.1109/72.655045 – year: 0 ident: ref33 publication-title: Extreme learning machine – volume: 30 start-page: 189 year: 2007 ident: ref35 article-title: research of fractional linear neural network and its ability for nonlinear approach publication-title: Chin J Comput |
| SSID | ssj0014506 |
| Score | 2.2091627 |
| Snippet | It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of... |
| SourceID | proquest pubmed pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1517 |
| SubjectTerms | Algorithms Applied sciences Approximation Artificial Intelligence Artificial neural networks Computer science; control theory; systems Computer Simulation - standards Computers Connectionism. Neural networks Construction Constructive neural networks Convergence of numerical methods Data processing. List processing. Character string processing Decay decay radial basis function (RBF) neural networks Exact sciences and technology Feedforward neural networks interpolation Iterative algorithms Kernel Logic and foundations Machine learning Mathematical analysis Mathematical Computing Mathematical logic, foundations, set theory Mathematical models Mathematics Memory organisation. Data processing Multi-layer neural network Multivariate Analysis Networks Neural networks Neural Networks (Computer) Neurons Proof theory and constructive mathematics Sciences and techniques of general use Software uniformly approximation |
| Title | Constructive Approximation to Multivariate Function by Decay RBF Neural Network |
| URI | https://ieeexplore.ieee.org/document/5540299 https://www.ncbi.nlm.nih.gov/pubmed/20693108 https://www.proquest.com/docview/749017094 https://www.proquest.com/docview/861543848 |
| Volume | 21 |
| WOSCitedRecordID | wos000283231200013&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE/IET Electronic Library (IEL) (UW System Shared) customDbUrl: eissn: 1941-0093 dateEnd: 20111231 omitProxy: false ssIdentifier: ssj0014506 issn: 1045-9227 databaseCode: RIE dateStart: 19900101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fb9MwED5tEw_wsEELrMAqPyAkJEIdx3Hsx7Kt4ikgNKS-RfEvadJIEe0q-t9zttPAJIbEWyQ7iZXPl7vz3X0H8FqbUBqgRVYKqzOOOiNTNke58sL60ti2sDw2m6jqWi6X6vMBvBtqYZxzMfnMvQ-XMZZvV-Y2HJXNUPVR_H0ewmFViVSrNUQMeBn7aKJ3UWaKsWofkqRqdlXXKYeL0bJEjy8QAFOh0LCRd7RRbK8SkiPbNX4fnxpb3G95Rg20OPm_tT-G497SJPO0NZ7AgetGMJ536GV_25E3JOZ-xkP1EZzsmzuQXtZH8OgPpsIxfAqNPRPV7NaReSAi_3mdqh7JZkViGe8W3W60XMkCVWUc0Dty4Uy7I18-LEhgAcHl1Cnt_Cl8XVxenX_M-l4MmeFUbjJPC2etZz4P_O-t45XgQsvSaiO89AXTwmltWp1rnRuJdpRjFKHOtRLKe108g6Nu1blTINSUQinrXaEE12ghtUIypW1rWN5WhZvAbI9JY3qi8tAv46aJDgtVDQLaBECbHtAJvB3u-J5IOv4xdxzAGeb1uExgegf2YRwtzpJJyiZA9vugQQkMYZW2c6vbdVNxFUiIFL9_ikS7kReS49ufpy30-_n9Tnzx93W9hIcpXyFktb2CI0TancEDs91cr39MURCWchoF4RdNcQOc |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3di9QwEB_OU1AfPN31Y_048yCCYG_TNEmTx_VjOfGsIivcW2m-4EC74u4t7n_vJO1WDzzBt0LSNvQ36cxkZn4D8MzYWBpgZCakMxlHnZFpl-O-CtIFYV1TOJ6aTZRVpU5P9ac9eDnUwnjvU_KZP4qXKZbvlvY8HpVNUfVR_H1egauCc0a7aq0hZsBF6qSJ_oXINGPlLihJ9XRRVV0WF6NCoM8XKYCp1GjaqAv6KDVYiemRzQq_UOhaW1xueyYdND_4v9Xfhlu9rUlmnXDcgT3fjmA8a9HP_rYlz0nK_kzH6iM42LV3IP1uH8HNP7gKx_AxtvbsyGY3nswiFfnPs67ukayXJBXybtDxRtuVzFFZpgGzJW-8bbbk86s5iTwguJyqSzy_C1_mbxevj7O-G0NmOVXrLNDCOxdYyCMDfON5Kbk0SjhjZVChYEZ6Y2xjcmNyq9CS8owi2LnRUodginuw3y5b_wAItUJq7YIvtOQGbaRGKqaNayzLm7LwE5juMKltT1UeO2Z8rZPLQnWNgNYR0LoHdAIvhju-dzQd_5g7juAM83pcJnB4AfZhHG1OwRRlEyA7OahxD8bAStP65fmqLrmONESaXz5FoeXIC8Xx7fc7Efr9_F4SH_59XU_h-vHiw0l98q56_whudNkLMcftMewj6v4JXLOb9dnqx2HaDr8AztQF-w |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Constructive+approximation+to+multivariate+function+by+decay+RBF+neural+network&rft.jtitle=IEEE+transactions+on+neural+networks&rft.au=Hou%2C+Muzhou&rft.au=Han%2C+Xuli&rft.date=2010-09-01&rft.issn=1941-0093&rft.eissn=1941-0093&rft.volume=21&rft.issue=9&rft.spage=1517&rft_id=info:doi/10.1109%2FTNN.2010.2055888&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1045-9227&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1045-9227&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1045-9227&client=summon |