{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:51:51Z","timestamp":1740145911765,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Braz Comput Soc"],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Recently, the maximum correntropy criterion (MCC) has been successfully applied in numerous applications regarding nonGaussian data processing. MCC employs a free parameter called kernel width, which affects the convergence rate, robustness, and steady-state performance of the adaptive filtering. However, determining the optimal value for such parameter is not always a trivial task. Within this context, this paper proposes a novel method called adaptive convex combination maximum correntropy criterion (ACCMCC), which combines an adaptive kernel algorithm with convex combination techniques. ACCMCC takes advantage from a convex combination of two adaptive MCC-based filters, whose kernel widths are adjusted iteratively as a function of the minimum error value obtained in a predefined estimation window. Results obtained in impulsive noise environment have shown that the proposed approach achieves equivalent convergence rates but with increased accuracy and robustness when compared with other similar algorithms reported in literature.<\/jats:p>","DOI":"10.1186\/s13173-021-00111-z","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T05:45:36Z","timestamp":1616478336000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An adaptive kernel width convex combination method for maximum correntropy criterion"],"prefix":"10.1186","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1888-3505","authenticated-orcid":false,"given":"Aluisio I. R.","family":"Fontes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leandro L. S.","family":"Linhares","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jo\u00e3o P.","family":"F. Guimar\u00e3es","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luiz F. Q.","family":"Silveira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allan M.","family":"Martins","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"issue":"6","key":"111_CR1","doi-asserted-by":"publisher","first-page":"2187","DOI":"10.1109\/TSP.2006.872524","volume":"54","author":"I Santamaria","year":"2006","unstructured":"Santamaria I, Pokharel P, Principe J (2006) Generalized correlation function: definition, properties, and application to blind equalization. IEEE Trans Sig Process 54(6):2187\u20132197. https:\/\/doi.org\/10.1109\/TSP.2006.872524.","journal-title":"IEEE Trans Sig Process"},{"issue":"11","key":"111_CR2","doi-asserted-by":"publisher","first-page":"4265","DOI":"10.1109\/TCSI.2019.2920773","volume":"66","author":"L Dang","year":"2019","unstructured":"Dang L, Chen B, Wang S, Gu Y, Pr\u00edncipe J (2019) Kernel Kalman filtering with conditional embedding and maximum correntropy criterion. IEEE Trans Circ Syst I Regular Pap 66(11):4265\u20134277.","journal-title":"IEEE Trans Circ Syst I Regular Pap"},{"key":"111_CR3","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.dsp.2019.01.014","volume":"88","author":"F Jin","year":"2019","unstructured":"Jin F, Qiu T (2019) Adaptive time delay estimation based on the maximum correntropy criterion. Digit Sig Process 88:23\u201332.","journal-title":"Digit Sig Process"},{"key":"111_CR4","doi-asserted-by":"publisher","first-page":"138512","DOI":"10.1109\/ACCESS.2019.2943300","volume":"7","author":"T C\u00e2mara","year":"2019","unstructured":"C\u00e2mara T, Lima A, Lima B, Fontes A, Martins A, Silveira L (2019) Automatic modulation classification architectures based on cyclostationary features in impulsive environments. IEEE Access 7:138512\u2013138527.","journal-title":"IEEE Access"},{"key":"111_CR5","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.eswa.2016.10.029","volume":"69","author":"A Fontes","year":"2017","unstructured":"Fontes A, Rego J, Martins AdM, Silveira L, Pr\u00edncipe J (2017) Cyclostationary correntropy: definition and applications. Expert Syst Appl 69:110\u2013117.","journal-title":"Expert Syst Appl"},{"issue":"4","key":"111_CR6","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s40313-019-00476-9","volume":"30","author":"\u00cdB Ara\u00fajo","year":"2019","unstructured":"Ara\u00fajo \u00cdB, Guimar\u00e3es J, Fontes A, Linhares L, Martins A, Ara\u00fajo F (2019) Narx model identification using correntropy criterion in the presence of non-Gaussian noise. J Control Autom Electr Syst 30(4):453\u2013464.","journal-title":"J Control Autom Electr Syst"},{"key":"111_CR7","doi-asserted-by":"publisher","first-page":"151652","DOI":"10.1109\/ACCESS.2019.2947764","volume":"7","author":"J Guimar\u00e3es","year":"2019","unstructured":"Guimar\u00e3es J, Da Silva F, Fontes A, Von Borries R, Martins A (2019) Complex correntropy applied to a compressive sensing problem in an impulsive noise environment. IEEE Access 7:151652\u2013151660.","journal-title":"IEEE Access"},{"key":"111_CR8","doi-asserted-by":"publisher","first-page":"137517","DOI":"10.1109\/ACCESS.2019.2942822","volume":"7","author":"P De Souza","year":"2019","unstructured":"De Souza P, Fontes A, De Souza V, Silveira L (2019) A novel signal detector in MIMO systems based on complex correntropy. IEEE Access 7:137517\u2013137527.","journal-title":"IEEE Access"},{"issue":"3","key":"111_CR9","doi-asserted-by":"publisher","first-page":"1324","DOI":"10.1109\/TFUZZ.2017.2719619","volume":"26","author":"R-J Bao","year":"2017","unstructured":"Bao R-J, Rong H-J, Angelov P, Chen B, Wong P (2017) Correntropy-based evolving fuzzy neural system. IEEE Trans Fuzzy Syst 26(3):1324\u20131338.","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"111_CR10","doi-asserted-by":"publisher","first-page":"2062","DOI":"10.1109\/ICASSP.2010.5495035","volume-title":"2010 IEEE International Conference on Acoustics, Speech and Signal Processing","author":"A Singh","year":"2010","unstructured":"Singh A, Pr\u00edncipe J (2010) Kernel width adaptation in information theoretic cost functions In: 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2062\u20132065.. IEEE, Dallas. https:\/\/doi.org\/10.1109\/ICASSP.2010.5495035."},{"issue":"8","key":"111_CR11","doi-asserted-by":"publisher","first-page":"1561","DOI":"10.1109\/TPAMI.2010.220","volume":"33","author":"R He","year":"2011","unstructured":"He R, Zheng W, Hu B (2011) Maximum correntropy criterion for robust face recognition. IEEE Trans Pattern Anal Mach Intell 33(8):1561\u20131576. https:\/\/doi.org\/10.1109\/TPAMI.2010.220.","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1","key":"111_CR12","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1002\/acs.2827","volume":"32","author":"S Hakimi","year":"2018","unstructured":"Hakimi S, Abed Hodtani G (2018) Generalized maximum correntropy detector for non-gaussian environments. Int J Adapt Control Sig Process 32(1):83\u201397. https:\/\/doi.org\/10.1002\/acs.2827.","journal-title":"Int J Adapt Control Sig Process"},{"issue":"1","key":"111_CR13","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1109\/LSP.2016.2634534","volume":"24","author":"J Guimar\u00e3es","year":"2017","unstructured":"Guimar\u00e3es J, Fontes A, Rego J, de M. Martins A, Pr\u00edncipe J (2017) Complex correntropy: probabilistic interpretation and application to complex-valued data. IEEE Sig Process Lett 24(1):42\u201345. https:\/\/doi.org\/10.1109\/LSP.2016.2634534.","journal-title":"IEEE Sig Process Lett"},{"issue":"1","key":"111_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.eswa.2014.07.023","volume":"42","author":"A Fontes","year":"2015","unstructured":"Fontes A, Martins A, Silveira L, Principe J (2015) Performance evaluation of the correntropy coefficient in automatic modulation classification. Expert Syst Appl 42(1):1\u20138. https:\/\/doi.org\/10.1016\/j.eswa.2014.07.023.","journal-title":"Expert Syst Appl"},{"key":"111_CR15","doi-asserted-by":"publisher","first-page":"10540","DOI":"10.1109\/ACCESS.2018.2808218","volume":"6","author":"S Wang","year":"2018","unstructured":"Wang S, Dang L, Wang W, Qian G, Tse C (2018) Kernel adaptive filters with feedback based on maximum correntropy. IEEE Access 6:10540\u201310552. https:\/\/doi.org\/10.1109\/ACCESS.2018.2808218.","journal-title":"IEEE Access"},{"key":"111_CR16","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.aeue.2017.03.028","volume":"76","author":"W Wang","year":"2017","unstructured":"Wang W, Zhao J, Qu H, Chen B, Principe J (2017) Convergence performance analysis of an adaptive kernel width MCC algorithm. AEU Int J Electron Commun 76:71\u201376. https:\/\/doi.org\/10.1016\/j.aeue.2017.03.028.","journal-title":"AEU Int J Electron Commun"},{"key":"111_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/IJCNN.2015.7280632","volume-title":"2015 International Joint Conference on Neural Networks (IJCNN)","author":"W Wang","year":"2015","unstructured":"Wang W, Zhao J, Qu H, Chen B, Principe J (2015) A switch kernel width method of correntropy for channel estimation In: 2015 International Joint Conference on Neural Networks (IJCNN), 1\u20137.. IEEE, Killarney. https:\/\/doi.org\/10.1109\/IJCNN.2015.7280632."},{"issue":"10","key":"111_CR18","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1109\/TCSII.2017.2671339","volume":"64","author":"F Huang","year":"2017","unstructured":"Huang F, Zhang J, Zhang S (2017) Adaptive filtering under a variable kernel width maximum correntropy criterion. IEEE Trans Circ Syst II Express Briefs 64(10):1247\u20131251. https:\/\/doi.org\/10.1109\/TCSII.2017.2671339.","journal-title":"IEEE Trans Circ Syst II Express Briefs"},{"issue":"11","key":"111_CR19","doi-asserted-by":"publisher","first-page":"1385","DOI":"10.1109\/LSP.2014.2337899","volume":"21","author":"L Shi","year":"2014","unstructured":"Shi L, Lin Y (2014) Convex combination of adaptive filters under the maximum correntropy criterion in impulsive interference. IEEE Sig Process Lett 21(11):1385\u20131388. https:\/\/doi.org\/10.1109\/LSP.2014.2337899.","journal-title":"IEEE Sig Process Lett"},{"issue":"11","key":"111_CR20","doi-asserted-by":"publisher","first-page":"5286","DOI":"10.1109\/TSP.2007.896065","volume":"55","author":"W Liu","year":"2007","unstructured":"Liu W, Pokharel P, Principe J (2007) Correntropy: properties and applications in non-Gaussian signal processing. IEEE Trans Sig Process 55(11):5286\u20135298. https:\/\/doi.org\/10.1109\/TSP.2007.896065.","journal-title":"IEEE Trans Sig Process"},{"key":"111_CR21","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1109\/ICDSP.2015.7252010","volume-title":"2015 IEEE International Conference on Digital Signal Processing (DSP)","author":"W Wang","year":"2015","unstructured":"Wang W, Zhao J, Qu H, Chen B, Principe J (2015) An adaptive kernel width update method of correntropy for channel estimation In: 2015 IEEE International Conference on Digital Signal Processing (DSP), 916\u2013920.. IEEE, Singapore. https:\/\/doi.org\/10.1109\/ICDSP.2015.7252010."},{"key":"111_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3324-9","volume-title":"Density Estimation for Statistics and Data Analysis","author":"B Silverman","year":"1986","unstructured":"Silverman B (1986) Density Estimation for Statistics and Data Analysis. Chapman & Hall\/CRC, London."},{"issue":"5","key":"111_CR23","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TCSII.2016.2594069","volume":"64","author":"F Huang","year":"2017","unstructured":"Huang F, Zhang J, Zhang S (2017) NLMS algorithm based on a variable parameter cost function robust against impulsive interferences. IEEE Trans Circ Syst II Express Briefs 64(5):600\u2013604. https:\/\/doi.org\/10.1109\/TCSII.2016.2594069.","journal-title":"IEEE Trans Circ Syst II Express Briefs"},{"issue":"3","key":"111_CR24","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1109\/6046.784467","volume":"1","author":"P Georgiou","year":"1999","unstructured":"Georgiou P, Tsakalides P, Kyriakakis C (1999) Alpha-stable modeling of noise and robust time-delay estimation in the presence of impulsive noise. IEEE Trans Multimed 1(3):291\u2013301.","journal-title":"IEEE Trans Multimed"},{"issue":"7","key":"111_CR25","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1109\/5.231338","volume":"81","author":"M Shao","year":"1993","unstructured":"Shao M, Nikias C (1993) Signal processing with fractional lower order moments: stable processes and their applications. Proc IEEE 81(7):986\u20131010.","journal-title":"Proc IEEE"},{"key":"111_CR26","volume-title":"Stable Non-gaussian Random Processes: Stochastic Models with Infinite Variance","author":"G Samorodnitsky","year":"1994","unstructured":"Samorodnitsky G, Taqqu M (1994) Stable Non-gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, New York."},{"key":"111_CR27","doi-asserted-by":"publisher","first-page":"2950","DOI":"10.1109\/IJCNN.2009.5178823","volume-title":"2009 International Joint Conference on Neural Networks","author":"A Singh","year":"2009","unstructured":"Singh A, Principe J (2009) Using correntropy as a cost function in linear adaptive filters In: 2009 International Joint Conference on Neural Networks, 2950\u20132955.. IEEE, Atlanta. https:\/\/doi.org\/10.1109\/IJCNN.2009.5178823."}],"container-title":["Journal of the Brazilian Computer Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13173-021-00111-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s13173-021-00111-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13173-021-00111-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T10:46:12Z","timestamp":1723545972000},"score":1,"resource":{"primary":{"URL":"https:\/\/journal-bcs.springeropen.com\/articles\/10.1186\/s13173-021-00111-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,23]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["111"],"URL":"https:\/\/doi.org\/10.1186\/s13173-021-00111-z","relation":{},"ISSN":["0104-6500","1678-4804"],"issn-type":[{"type":"print","value":"0104-6500"},{"type":"electronic","value":"1678-4804"}],"subject":[],"published":{"date-parts":[[2021,3,23]]},"assertion":[{"value":"29 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"7"}}