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In this paper, we formulate the pairwise learning problem as a difference of convex (DC) optimization problem using the Kronecker product kernel, <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell _1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>- and <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell _0$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-regularizations, and various, possibly nonsmooth, loss functions. Our aim is to develop an efficient learning algorithm, <jats:sc>SparsePKL<\/jats:sc>, that produces accurate predictions with the desired sparsity level. In addition, we propose a novel limited memory bundle DC algorithm (<jats:sc>LMB-DCA<\/jats:sc>) for large-scale nonsmooth DC optimization and apply it as an underlying solver in the <jats:sc>SparsePKL<\/jats:sc>. The performance of the <jats:sc>SparsePKL<\/jats:sc>-algorithm is studied in seven real-world drug-target interaction data and the results are compared with those of the state-of-art methods in pairwise learning.<\/jats:p>","DOI":"10.1007\/s10898-025-01481-w","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T16:10:56Z","timestamp":1743783056000},"page":"55-85","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Limited memory bundle DC algorithm for sparse pairwise kernel learning"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8747-4836","authenticated-orcid":false,"given":"Napsu","family":"Karmitsa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaisa","family":"Joki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antti","family":"Airola","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tapio","family":"Pahikkala","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"1481_CR1","doi-asserted-by":"crossref","first-page":"3374","DOI":"10.1109\/TNNLS.2017.2727545","volume":"29","author":"A Airola","year":"2018","unstructured":"Airola, A., Pahikkala, T.: Fast Kronecker product kernel methods via generalized Vec trick. 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