Data-Driven Fuzzy Transform
The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to arbitrary data in terms of dimensionality and structure. This article defines and analyzes the properties of the data-driven F-transform, with...
Uložené v:
| Vydané v: | IEEE transactions on fuzzy systems Ročník 30; číslo 9; s. 3774 - 3784 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
IEEE
01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Predmet: | |
| ISSN: | 1063-6706, 1941-0034 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to arbitrary data in terms of dimensionality and structure. This article defines and analyzes the properties of the data-driven F-transform, with a focus on the construction of the class of data-driven membership functions, which are multiscale, local, linearly independent, intrinsic, and robust to data discretization. Data-driven membership functions are defined by applying a 1-D filter to the Laplace-Beltrami operator, which encodes the geometric and topological properties of the input data. Then, we address the efficient computation of the data-driven F-transform through a polynomial or a rational polynomial approximation of the input filter. In this way, the computation of the data-driven F-transform is independent of the evaluation of the membership functions at any point of the input domain and reduces to the solution of a small set of sparse and symmetric linear systems. Finally, the data-driven F-transform is efficiently evaluated on large and arbitrary data, in terms of dimensionality, structure, and size. |
|---|---|
| AbstractList | The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to arbitrary data in terms of dimensionality and structure. This article defines and analyzes the properties of the data-driven F-transform, with a focus on the construction of the class of data-driven membership functions, which are multiscale, local, linearly independent, intrinsic, and robust to data discretization. Data-driven membership functions are defined by applying a 1-D filter to the Laplace-Beltrami operator, which encodes the geometric and topological properties of the input data. Then, we address the efficient computation of the data-driven F-transform through a polynomial or a rational polynomial approximation of the input filter. In this way, the computation of the data-driven F-transform is independent of the evaluation of the membership functions at any point of the input domain and reduces to the solution of a small set of sparse and symmetric linear systems. Finally, the data-driven F-transform is efficiently evaluated on large and arbitrary data, in terms of dimensionality, structure, and size. |
| Author | Patane, Giuseppe |
| Author_xml | – sequence: 1 givenname: Giuseppe orcidid: 0000-0002-2276-9553 surname: Patane fullname: Patane, Giuseppe email: patane@ge.imati.cnr.it organization: Consiglio Nazionale delle Ricerche, Istituto di Matematica Applicata e Tecnologie Informatiche, Genova, Italy |
| BookMark | eNp9kD1rAkEQhpdgIGryB2IjpD4zs99bBo1JQEijjc2y3u3Cid6Z3TOgvz7nBylSpJp34H1m4OmRTlVXnpBHhBEimOf5dLFcjihQHDGkWmp-Q7poOGYAjHfaDJJlUoG8I72U1gDIBeouGUxc47JJLL99NZzuj8fDcB5dlUIdt_fkNrhN8g_X2SeL6et8_J7NPt8-xi-zLKfSNFkQLAhdULcyapUL5b0M1AiZ08IVHmXugDsDKEzgujDtqlFqJnRApTwD1idPl7u7WH_tfWrsut7Hqn1pqQItORNGty19aeWxTin6YPOycU1ZV0105cYi2JMKe1ZhTyrsVUWL0j_oLpZbFw__Q4MLVHrvfwEjUWup2A8UbGp7 |
| CODEN | IEFSEV |
| CitedBy_id | crossref_primary_10_1109_TFUZZ_2024_3489227 crossref_primary_10_1016_j_engappai_2023_106500 crossref_primary_10_1016_j_ijar_2022_07_009 crossref_primary_10_3390_axioms11100501 crossref_primary_10_1016_j_dajour_2023_100241 crossref_primary_10_1109_TFUZZ_2023_3326657 |
| Cites_doi | 10.1109/TPAMI.2010.210 10.1109/TSMC.2016.2578641 10.1145/240455.240463 10.1145/170035.170072 10.1007/s00500-019-03816-8 10.1145/846183.846197 10.1631/jzus.C0910182 10.1016/j.fss.2008.11.029 10.1109/TFUZZ.2020.3012764 10.1088/1742-6596/570/4/042002 10.1007/978-3-319-46245-5_8 10.1109/72.977258 10.1109/91.649909 10.1109/ICWISE.2013.6728793 10.1016/j.asoc.2014.11.061 10.1145/2737095.2742921 10.1016/S0165-0114(02)00272-5 10.1007/s13042-015-0374-1 10.1016/j.chaos.2019.109510 10.1016/j.ins.2010.04.029 10.1016/j.fss.2010.10.011 10.1016/j.fss.2014.12.013 10.1007/s00521-018-03984-y 10.1109/21.199466 10.1016/j.fss.2005.11.012 10.1109/TFUZZ.2008.924183 10.7551/mitpress/4175.001.0001 10.1016/j.fss.2015.01.001 10.1090/cbms/092 10.1111/j.1467-8659.2011.02026.x 10.56021/9781421407944 10.1109/ICCVW.2011.6130444 10.1016/j.ijar.2007.06.005 10.1016/j.ijar.2007.06.008 10.1111/cgf.12866 10.1016/B978-0-08-092534-9.50007-2 10.1016/j.ins.2014.01.014 10.1007/978-3-319-66827-7_11 10.1016/j.fss.2010.11.009 10.1002/mma.3832 10.1504/IJBIDM.2006.010783 10.1007/s00500-015-1885-0 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022 |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/TFUZZ.2021.3128684 |
| DatabaseName | IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Technology 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 Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1941-0034 |
| EndPage | 3784 |
| ExternalDocumentID | 10_1109_TFUZZ_2021_3128684 9618867 |
| Genre | orig-research |
| GroupedDBID | -~X .DC 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P PQQKQ RIA RIE RNS TAE TN5 VH1 AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c269t-f53f58d2ab97bc57ee6f2956c2dade16ca04a90159f48d9ca08168358f177e303 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 7 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000848264000033&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1063-6706 |
| IngestDate | Sun Nov 09 08:35:59 EST 2025 Sat Nov 29 03:12:42 EST 2025 Tue Nov 18 21:27:20 EST 2025 Wed Aug 27 02:29:12 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 9 |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0/legalcode |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c269t-f53f58d2ab97bc57ee6f2956c2dade16ca04a90159f48d9ca08168358f177e303 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-2276-9553 |
| OpenAccessLink | https://ieeexplore.ieee.org/ielx7/91/9872159/09618867.pdf |
| PQID | 2708643598 |
| PQPubID | 85428 |
| PageCount | 11 |
| ParticipantIDs | crossref_citationtrail_10_1109_TFUZZ_2021_3128684 proquest_journals_2708643598 crossref_primary_10_1109_TFUZZ_2021_3128684 ieee_primary_9618867 |
| PublicationCentury | 2000 |
| PublicationDate | 2022-09-01 |
| PublicationDateYYYYMMDD | 2022-09-01 |
| PublicationDate_xml | – month: 09 year: 2022 text: 2022-09-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on fuzzy systems |
| PublicationTitleAbbrev | TFUZZ |
| PublicationYear | 2022 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref35 ref12 ref34 ref15 ref37 ref14 ref36 Pennebaker (ref32) 1992 ref30 ref11 ref33 ref10 ref2 ref1 ref17 ref39 ref16 ref38 ref19 Hurtik (ref31) 2017 ref18 Litvinov (ref45) 1993; 1 ref24 ref23 ref26 ref25 ref20 ref42 ref41 ref22 ref44 ref21 ref43 ref28 ref27 ref29 ref8 ref7 ref9 ref4 ref3 ref6 ref5 ref40 |
| References_xml | – ident: ref42 doi: 10.1109/TPAMI.2010.210 – ident: ref19 doi: 10.1109/TSMC.2016.2578641 – ident: ref24 doi: 10.1145/240455.240463 – ident: ref20 doi: 10.1145/170035.170072 – ident: ref27 doi: 10.1007/s00500-019-03816-8 – ident: ref25 doi: 10.1145/846183.846197 – ident: ref28 doi: 10.1631/jzus.C0910182 – ident: ref6 doi: 10.1016/j.fss.2008.11.029 – ident: ref3 doi: 10.1109/TFUZZ.2020.3012764 – ident: ref13 doi: 10.1088/1742-6596/570/4/042002 – ident: ref30 doi: 10.1007/978-3-319-46245-5_8 – ident: ref22 doi: 10.1109/72.977258 – ident: ref10 doi: 10.1109/91.649909 – ident: ref14 doi: 10.1109/ICWISE.2013.6728793 – ident: ref9 doi: 10.1016/j.asoc.2014.11.061 – ident: ref15 doi: 10.1145/2737095.2742921 – ident: ref21 doi: 10.1016/S0165-0114(02)00272-5 – volume-title: Tiff Still Image Data Compression Standard year: 1992 ident: ref32 – ident: ref29 doi: 10.1007/s13042-015-0374-1 – ident: ref37 doi: 10.1016/j.chaos.2019.109510 – ident: ref12 doi: 10.1016/j.ins.2010.04.029 – ident: ref8 doi: 10.1016/j.fss.2010.10.011 – ident: ref5 doi: 10.1016/j.fss.2014.12.013 – ident: ref36 doi: 10.1007/s00521-018-03984-y – ident: ref2 doi: 10.1109/21.199466 – ident: ref4 doi: 10.1016/j.fss.2005.11.012 – ident: ref18 doi: 10.1109/TFUZZ.2008.924183 – ident: ref39 doi: 10.7551/mitpress/4175.001.0001 – ident: ref34 doi: 10.1016/j.fss.2015.01.001 – ident: ref38 doi: 10.1090/cbms/092 – ident: ref41 doi: 10.1111/j.1467-8659.2011.02026.x – ident: ref44 doi: 10.56021/9781421407944 – ident: ref43 doi: 10.1109/ICCVW.2011.6130444 – ident: ref26 doi: 10.1016/j.ijar.2007.06.005 – volume: 1 start-page: 313 year: 1993 ident: ref45 article-title: Approximate construction of rational approximations and the effect of error autocorrection. applications publication-title: Russian J. Math. Phys. – start-page: 1 volume-title: Proc. Int. Conf. Fuzzy Syst. year: 2017 ident: ref31 article-title: A hybrid image compression algorithm based on tiff and fuzzy transform – ident: ref7 doi: 10.1016/j.ijar.2007.06.008 – ident: ref40 doi: 10.1111/cgf.12866 – ident: ref33 doi: 10.1016/B978-0-08-092534-9.50007-2 – ident: ref16 doi: 10.1016/j.ins.2014.01.014 – ident: ref11 doi: 10.1007/978-3-319-66827-7_11 – ident: ref1 doi: 10.1016/j.fss.2010.11.009 – ident: ref35 doi: 10.1002/mma.3832 – ident: ref23 doi: 10.1504/IJBIDM.2006.010783 – ident: ref17 doi: 10.1007/s00500-015-1885-0 |
| SSID | ssj0014518 |
| Score | 2.4300478 |
| Snippet | The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 3774 |
| SubjectTerms | Adaptation models Chebyshev approximation Chebyshev polynomials data-driven Fuzzy-transform (F-transform) data-driven membership functions F-transform Kernel Laplace equations Laplacian spectrum Linear systems Operators (mathematics) Polynomials Splines (mathematics) Transforms |
| Title | Data-Driven Fuzzy Transform |
| URI | https://ieeexplore.ieee.org/document/9618867 https://www.proquest.com/docview/2708643598 |
| Volume | 30 |
| WOSCitedRecordID | wos000848264000033&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 Electronic Library (IEL) customDbUrl: eissn: 1941-0034 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014518 issn: 1063-6706 databaseCode: RIE dateStart: 19930101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PS8MwFH5sw4MenG6Kc1N68KZxbZrmx1HU4ml42GDsUrIkBUE22TrB_fUmaTsURfDW0BcoX5L38pp87wO4kjZsJYIIZOcuQ9bhcesHqUARkczYN1pr4sUm2GjEp1Px3ICbHRfGGOMvn5lb9-jP8vVSbdyvsqFTJ-GUNaHJGCu5WrsTA5JEJe2NxoiykNYEmVAMx-lkNrOpII5shoo55eRbEPKqKj9csY8vaft_X3YEh9U-MrgrB_4YGmbRgXat0RBUS7YDB18KDnah_yALiR5WzsUF6Wa7_QjG9c71BCbp4_j-CVXyCEhhKgqUJ3GecI3lXLC5SpgxNMc23VFYS20iqmRIpAv3IidcC9t0GhtxwvOIMWND1ym0FsuFOYPA5jSKWWCUMMpx4znhVOfOHsc0NqIHUY1Xpqra4U7C4jXzOUQoMo9x5jDOKox7cL3r81ZWzvjTuutQ3VlWgPZgUA9LVi2udYaZzcOIKz14_nuvPuxjx1LwV8EG0CpWG3MBe-q9eFmvLv28-QTHbrvx |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1bS8MwFD7MKagPTjfFOS998E3r2jTN5VGcZeIcPnQw9lK6JAVBNtlFcL_eJGuLogi-NfQEypfknJwm3_kALlMdtkKOuavnLnW1w2PaDxLu-jilSr-RUmIrNkH7fTYc8ucKXJdcGKWUvXymbsyjPcuXU7E0v8raRp2EEboBmyHGyF-ztcozAxz6a-IbCVxCPVJQZDzejqPBaKSTQeTrHBUxwvC3MGR1VX44Yxthotr_vm0f9vKdpHO7HvoDqKhJHWqFSoOTL9o67H4pOdiAViddpG5nZpycEy1Xqw8nLvauhzCI7uO7rpsLJLgCEb5wszDIQiZROuZ0LEKqFMmQTngEkqlUPhGph1MT8HmGmeS6aVQ2gpBlPqVKB68jqE6mE3UMjs5qBNXACK6EYcczzIjMjD0KSKB4E_wCr0Tk1cONiMVrYrMIjycW48RgnOQYN-Gq7PO2rp3xp3XDoFpa5oA24bQYliRfXvMEUZ2JYVN88OT3Xhew3Y2feknvof_Ygh1kOAv2YtgpVBezpTqDLfG-eJnPzu0c-gS90L84 |
| 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=Data-Driven+Fuzzy+Transform&rft.jtitle=IEEE+transactions+on+fuzzy+systems&rft.au=Patane%2C+Giuseppe&rft.date=2022-09-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=1063-6706&rft.eissn=1941-0034&rft.volume=30&rft.issue=9&rft.spage=3774&rft_id=info:doi/10.1109%2FTFUZZ.2021.3128684&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1063-6706&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1063-6706&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1063-6706&client=summon |