{"id":733,"date":"2017-03-12T12:11:01","date_gmt":"2017-03-12T12:11:01","guid":{"rendered":"http:\/\/www.kelp-ml.org\/?page_id=733"},"modified":"2017-03-13T15:36:18","modified_gmt":"2017-03-13T15:36:18","slug":"kernel-combinations","status":"publish","type":"page","link":"http:\/\/www.kelp-ml.org\/?page_id=733","title":{"rendered":"Kernel Combinations"},"content":{"rendered":"<p><a href=\"http:\/\/www.kelp-ml.org\/kelp-javadoc\/current-version\/it\/uniroma2\/sag\/kelp\/kernel\/KernelCombination.html\">KernelCombination<\/a>s combine different kernels, allowing the possibility to simultaneously exploit different data representations. Details on these kernels can be found in (Shawe-Taylor and Cristianini, 2004).<\/p>\n<hr \/>\n<h3>Linear Kernel Combination<\/h3>\n<p><strong>Java class<\/strong>: <a href=\"http:\/\/www.kelp-ml.org\/kelp-javadoc\/current-version\/it\/uniroma2\/sag\/kelp\/kernel\/standard\/LinearKernelCombination.html\">LinearKernelCombination<\/a><\/p>\n<p><strong>Source code<\/strong>: <a href=\"https:\/\/github.com\/SAG-KeLP\/kelp-core\/blob\/master\/src\/main\/java\/it\/uniroma2\/sag\/kelp\/kernel\/standard\/LinearKernelCombination.java\" target=\"_blank\">LinearKernelCombination.java<\/a><\/p>\n<p><strong>Maven Project<\/strong>: <a href=\"https:\/\/github.com\/SAG-KeLP\/kelp-core\">kelp-core<\/a><\/p>\n<p><strong>JSON type<\/strong>:\u00a0linearComb<\/p>\n<p><strong>Description<\/strong>: given a set <em>n<\/em> of kernels <img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/www.kelp-ml.org\/wp-content\/ql-cache\/quicklatex.com-5bb088ff56cd34f038bad5523c4aae08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;&#95;&#49;&#44;&#32;&#92;&#108;&#100;&#111;&#116;&#115;&#44;&#32;&#75;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\"\/>, it computes the weighted sum of the kernel similarities:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/www.kelp-ml.org\/wp-content\/ql-cache\/quicklatex.com-87c62e56a64f32f46a6eb03ce4ee485e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;&#40;&#120;&#44;&#121;&#41;&#92;&#115;&#117;&#109;&#95;&#123;&#105;&#92;&#108;&#101;&#113;&#32;&#110;&#125;&#99;&#95;&#105;&#75;&#95;&#105;&#40;&#120;&#44;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"181\" style=\"vertical-align: -7px;\"\/><\/p>\n<p>where\u00a0<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/www.kelp-ml.org\/wp-content\/ql-cache\/quicklatex.com-73f745a16381e58d8cc648594702fab4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/> are the parametrizable weights of the combination.<\/p>\n<p><strong>Parameters<\/strong>:<\/p>\n<ul>\n<li><em>toCombine<\/em>: the\u00a0kernels that must be combined<\/li>\n<li><em>weights<\/em>: the coefficient <em>c<\/em>\u00a0in the kernel combination<\/li>\n<\/ul>\n<hr \/>\n<h3>Kernel Multiplication<\/h3>\n<p><strong>Java class<\/strong>: <a href=\"http:\/\/www.kelp-ml.org\/kelp-javadoc\/current-version\/it\/uniroma2\/sag\/kelp\/kernel\/standard\/KernelMultiplication.html\">KernelMultiplication<\/a><\/p>\n<p><strong>Source code<\/strong>: <a href=\"https:\/\/github.com\/SAG-KeLP\/kelp-core\/blob\/master\/src\/main\/java\/it\/uniroma2\/sag\/kelp\/kernel\/standard\/KernelMultiplication.java\" target=\"_blank\">KernelMultiplication.java<\/a><\/p>\n<p><strong>Maven Project<\/strong>: <a href=\"https:\/\/github.com\/SAG-KeLP\/kelp-core\">kelp-core<\/a><\/p>\n<p><strong>JSON type<\/strong>:\u00a0multiplication<\/p>\n<p><strong>Description<\/strong>: given a set <em>n<\/em> of kernels <img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/www.kelp-ml.org\/wp-content\/ql-cache\/quicklatex.com-5bb088ff56cd34f038bad5523c4aae08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;&#95;&#49;&#44;&#32;&#92;&#108;&#100;&#111;&#116;&#115;&#44;&#32;&#75;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\"\/>, it computes the product\u00a0of the kernel similarities:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/www.kelp-ml.org\/wp-content\/ql-cache\/quicklatex.com-6deb20e4e6b9715c4f9bf946c8d1fbcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;&#40;&#120;&#44;&#32;&#121;&#41;&#32;&#61;&#32;&#92;&#112;&#114;&#111;&#100;&#95;&#123;&#105;&#92;&#108;&#101;&#113;&#32;&#110;&#125;&#75;&#95;&#105;&#40;&#120;&#44;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"186\" style=\"vertical-align: -7px;\"\/><\/p>\n<p><strong>Parameters<\/strong>:<\/p>\n<ul>\n<li><em>toCombine<\/em>: the\u00a0kernels that must be combined<\/li>\n<\/ul>\n<hr \/>\n<h3>References<\/h3>\n<p>John Shawe-Taylor and Nello Cristianini.\u00a0<em>Kernel Methods for Pattern Analysis<\/em>. Cambridge University Press, New York, NY, USA, 2004. ISBN 0521813972.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>KernelCombinations combine different kernels, allowing the possibility to simultaneously exploit different data representations. Details on these kernels can be found in (Shawe-Taylor and Cristianini, 2004). Linear Kernel Combination Java class: LinearKernelCombination Source code: LinearKernelCombination.java Maven Project: kelp-core JSON type:\u00a0linearComb Description: given a set n of kernels , it computes the weighted sum of the kernel <a href=\"http:\/\/www.kelp-ml.org\/?page_id=733\" rel=\"nofollow\"><span class=\"sr-only\">Read more about Kernel Combinations<\/span>[&hellip;]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=\/wp\/v2\/pages\/733"}],"collection":[{"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=733"}],"version-history":[{"count":5,"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=\/wp\/v2\/pages\/733\/revisions"}],"predecessor-version":[{"id":777,"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=\/wp\/v2\/pages\/733\/revisions\/777"}],"wp:attachment":[{"href":"http:\/\/www.kelp-ml.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}