{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:10:54Z","timestamp":1760195454208,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,11]],"date-time":"2018-01-11T00:00:00Z","timestamp":1515628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Minimization of the Euclidean distance between output distribution and Dirac delta functions as a performance criterion is known to match the distribution of system output with delta functions. In the analysis of the algorithm developed based on that criterion and recursive gradient estimation, it is revealed in this paper that the minimization process of the cost function has two gradients with different functions; one that forces spreading of output samples and the other one that compels output samples to move close to symbol points. For investigation the two functions, each gradient is controlled separately through individual normalization of each gradient with their related input. From the analysis and experimental results, it is verified that one gradient is associated with the role of accelerating initial convergence speed by spreading output samples and the other gradient is related with lowering the minimum mean squared error (MSE) by pulling error samples close together.<\/jats:p>","DOI":"10.3390\/e20010048","type":"journal-article","created":{"date-parts":[[2018,1,11]],"date-time":"2018-01-11T13:36:15Z","timestamp":1515677775000},"page":"48","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Function Analysis of the Euclidean Distance between Probability Distributions"],"prefix":"10.3390","volume":"20","author":[{"given":"Namyong","family":"Kim","sequence":"first","affiliation":[{"name":"Division of Electronic & Information Communication, Kangwon National University, Samcheok 25913, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,11]]},"reference":[{"key":"ref_1","unstructured":"Haykin, S. (2001). Adaptive Filter Theory, Prentice Hall. [4th ed.]."},{"key":"ref_2","unstructured":"Haykin, S. (2000). Information theoretic learning. Unsupervised Adaptive Filtering, Wiley."},{"key":"ref_3","unstructured":"Erdogmus, D., Rao, Y., and Principe, J. (2005, January 9\u201315). Supervised training of adaptive systems with partially labeled data. Proceedings of the International Conference on ASSP, Marrakech, Morocco."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.phycom.2017.09.005","article-title":"Cluster-head based feedback for simplified time reversal prefiltering in ultra-wideband systems","volume":"25","author":"Soleimani","year":"2017","journal-title":"Phys. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1007\/s11227-013-1054-0","article-title":"An efficient routing algorithm to preserve k-coverage in wireless sensor networks","volume":"68","author":"Ahmadi","year":"2014","journal-title":"J. Supercomput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/j.neunet.2005.06.018","article-title":"A new classifier based on information theoretic learning with unlabeled data","volume":"18","author":"Jeong","year":"2005","journal-title":"Neural Netw."},{"key":"ref_7","first-page":"548","article-title":"Blind signal processing algorithms based on recursive gradient estimation","volume":"5","author":"Kim","year":"2015","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"ref_8","first-page":"349","article-title":"A new approach to multipath correction of constant modulus signals","volume":"31","author":"Treichler","year":"1983","journal-title":"IEEE Trans."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"885","DOI":"10.15623\/ijret.2013.0205027","article-title":"FPGA implementation of optimal step size NLMS algorithm and its performance analysis","volume":"2","author":"Bharani","year":"2013","journal-title":"Int. J. Res. Eng. Technol."},{"key":"ref_10","first-page":"38","article-title":"Adaptive algorithms for acoustic echo cancellation in speech processing","volume":"7","author":"Chinaboina","year":"2011","journal-title":"Int. J. Res. Rev. Appl. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1119\/1.18389","article-title":"Thermodynamic entropy: The spreading and sharing of energy","volume":"64","author":"Leff","year":"1996","journal-title":"Am. J. Phys."},{"key":"ref_12","unstructured":"Proakis, J. (1989). Digital Communications, McGraw-Hill. [2nd ed.]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1109\/TSP.2006.872524","article-title":"Generalized correlation function: Definition, properties, and application to blind equalization","volume":"54","author":"Santamaria","year":"2006","journal-title":"IEEE Trans. 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