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Prominent applications include predicting drug-target or protein-protein interactions, or customer-product preferences. In this work, we present a comprehensive review of pairwise kernels, that have been proposed for incorporating prior knowledge about the relationship between the objects. Specifically, we consider the standard, symmetric and anti-symmetric Kronecker product kernels, metric-learning, Cartesian, ranking, as well as linear, polynomial and Gaussian kernels. Recently, a<jats:inline-formula><jats:alternatives><jats:tex-math>$$O(nm+nq)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>O<\/mml:mi><mml:mo>(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mi>m<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>n<\/mml:mi><mml:mi>q<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>time generalized vec trick algorithm, where<jats:inline-formula><jats:alternatives><jats:tex-math>$$n$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$m$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>m<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and<jats:inline-formula><jats:alternatives><jats:tex-math>$$q$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>q<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>denote the number of pairs, drugs and targets, was introduced for training kernel methods with the Kronecker product kernel. This was a significant improvement over previous<jats:inline-formula><jats:alternatives><jats:tex-math>$$O(n^2)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>O<\/mml:mi><mml:mo>(<\/mml:mo><mml:msup><mml:mi>n<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>training methods, since in most real-world applications<jats:inline-formula><jats:alternatives><jats:tex-math>$$m,q&lt;&lt; n$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>m<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo>&lt;<\/mml:mo><mml:mo>&lt;<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In this work we show how all the reviewed kernels can be expressed as sums of Kronecker products, allowing the use of generalized vec trick for speeding up their computation. In the experiments, we demonstrate how the introduced approach allows scaling pairwise kernels to much larger data sets than previously feasible, and provide an extensive comparison of the kernels on a number of biological interaction prediction tasks.<\/jats:p>","DOI":"10.1007\/s10994-021-06127-y","type":"journal-article","created":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T20:02:31Z","timestamp":1643400151000},"page":"543-573","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Generalized vec trick for fast learning of pairwise kernel models"],"prefix":"10.1007","volume":"111","author":[{"given":"Markus","family":"Viljanen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1010-4386","authenticated-orcid":false,"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":[[2022,1,28]]},"reference":[{"issue":"8","key":"6127_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. 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