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The sign algorithm (SA) is a conventional method for minimizing the magnitudes of residuals; however, this approach yields poor convergence performance compared with the least mean square algorithm. To overcome this convergence performance degradation, we propose novel adaptive algorithms based on a natural gradient: the natural-gradient sign algorithm (NGSA) and normalized NGSA. We also propose an efficient natural-gradient update method based on the AR(<jats:italic>p<\/jats:italic>) model, which requires <jats:inline-formula><jats:alternatives><jats:tex-math>$\\mathcal {O}(p)$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>O<\/mml:mi>\n                  <mml:mo>(<\/mml:mo>\n                  <mml:mi>p<\/mml:mi>\n                  <mml:mo>)<\/mml:mo>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> multiply\u2013add operations at every adaptation step. In experiments conducted using toy and real music data, the proposed algorithms achieve superior convergence performance to the SA. Furthermore, we propose a novel lossless audio codec based on the NGSA, called the natural-gradient autoregressive unlossy audio compressor (NARU), which is open-source and implemented in C. In a comparative experiment with existing, well-known codecs, NARU exhibits superior compression performance. These results suggest that the proposed methods are appropriate for practical applications.<\/jats:p>","DOI":"10.1186\/s13636-022-00243-w","type":"journal-article","created":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T11:03:06Z","timestamp":1653130986000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improving sign-algorithm convergence rate using natural gradient for lossless audio compression"],"prefix":"10.1186","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3256-5498","authenticated-orcid":false,"given":"Taiyo","family":"Mineo","sequence":"first","affiliation":[]},{"given":"Hayaru","family":"Shouno","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,21]]},"reference":[{"issue":"4","key":"243_CR1","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1109\/MSP.2003.1215233","volume":"20","author":"K. 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