{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T17:59:42Z","timestamp":1772906382570,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,4,27]],"date-time":"2018-04-27T00:00:00Z","timestamp":1524787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents an unsupervised learning algorithm for sparse nonnegative matrix factor time\u2013frequency deconvolution with optimized fractional   \u03b2   -divergence. The   \u03b2   -divergence is a group of cost functions parametrized by a single parameter    \u03b2    . The Itakura\u2013Saito divergence, Kullback\u2013Leibler divergence and Least Square distance are special cases that correspond to    \u03b2 = 0 , \u00a0 1 , \u00a0 2    , respectively. This paper presents a generalized algorithm that uses a flexible range of   \u03b2   that includes fractional values. It describes a maximization\u2013minimization (MM) algorithm leading to the development of a fast convergence multiplicative update algorithm with guaranteed convergence. The proposed model operates in the time\u2013frequency domain and decomposes an information-bearing matrix into two-dimensional deconvolution of factor matrices that represent the spectral dictionary and temporal codes. The deconvolution process has been optimized to yield sparse temporal codes through maximizing the likelihood of the observations. The paper also presents a method to estimate the fractional   \u03b2   value. The method is demonstrated on separating audio mixtures recorded from a single channel. The paper shows that the extraction of the spectral dictionary and temporal codes is significantly more efficient by using the proposed algorithm and subsequently leads to better source separation performance. Experimental tests and comparisons with other factorization methods have been conducted to verify its efficacy.<\/jats:p>","DOI":"10.3390\/s18051371","type":"journal-article","created":{"date-parts":[[2018,4,27]],"date-time":"2018-04-27T12:04:50Z","timestamp":1524830690000},"page":"1371","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Unsupervised Learning for Monaural Source Separation Using Maximization\u2013Minimization Algorithm with Time\u2013Frequency Deconvolution \u2020"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8698-7605","authenticated-orcid":false,"given":"Wai Lok","family":"Woo","sequence":"first","affiliation":[{"name":"School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9993-1013","authenticated-orcid":false,"given":"Bin","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China"}]},{"given":"Ahmed","family":"Bouridane","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, UK"}]},{"given":"Bingo Wing-Kuen","family":"Ling","sequence":"additional","affiliation":[{"name":"Faculty of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5153-0675","authenticated-orcid":false,"given":"Cheng Siong","family":"Chin","sequence":"additional","affiliation":[{"name":"Faculty of Science Agriculture and Engineering, Newcastle University, Singapore 599493, Singapore"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1002\/acs.795","article-title":"Audio source separation: Solutions and problems","volume":"18","author":"Mitianoudis","year":"2004","journal-title":"Int. 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