{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:26:50Z","timestamp":1760956010526,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T00:00:00Z","timestamp":1578268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["XDJK2019B011","SWU116013"],"award-info":[{"award-number":["XDJK2019B011","SWU116013"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The complex correntropy has been successfully applied to complex domain adaptive filtering, and the corresponding maximum complex correntropy criterion (MCCC) algorithm has been proved to be robust to non-Gaussian noises. However, the kernel function of the complex correntropy is usually limited to a Gaussian function whose center is zero. In order to improve the performance of MCCC in a non-zero mean noise environment, we firstly define a complex correntropy with variable center and provide its probability explanation. Then, we propose a maximum complex correntropy criterion with variable center (MCCC-VC), and apply it to the complex domain adaptive filtering. Next, we use the gradient descent approach to search the minimum of the cost function. We also propose a feasible method to optimize the center and the kernel width of MCCC-VC. It is very important that we further provide the bound for the learning rate and derive the theoretical value of the steady-state excess mean square error (EMSE). Finally, we perform some simulations to show the validity of the theoretical steady-state EMSE and the better performance of MCCC-VC.<\/jats:p>","DOI":"10.3390\/e22010070","type":"journal-article","created":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T10:34:46Z","timestamp":1578306886000},"page":"70","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Complex Correntropy with Variable Center: Definition, Properties, and Application to Adaptive Filtering"],"prefix":"10.3390","volume":"22","author":[{"given":"Fei","family":"Dong","sequence":"first","affiliation":[{"name":"College of Electronic and Information Engineering, Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0470-0154","authenticated-orcid":false,"given":"Guobing","family":"Qian","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5028-5839","authenticated-orcid":false,"given":"Shiyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,6]]},"reference":[{"key":"ref_1","unstructured":"Haykin, S. 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