{"title":"非线性模型","authors":"D. Lizotte","doi":"10.1201/9781315275772-14","DOIUrl":null,"url":null,"abstract":"Kernel functions • Whenever a learning algorithm (such as SVMs) can be written in terms of dot-products, it can be generalized to kernels. • A kernel is any function K : R × R 7→ R which corresponds to a dot product for some feature mapping φ: K(x1, x2) = φ(x1) · φ(x2) for some φ. • Conversely, by choosing feature mapping φ, we implicitly choose a kernel function • Recall that φ(x1) · φ(x2) ∝ cos∠(φ(x1), φ(x2)) where ∠ denotes the angle between the vectors, so a kernel function can be thought of as a notion of similarity.","PeriodicalId":165137,"journal":{"name":"Statistical Methods in Agriculture and Experimental Biology","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear Models\",\"authors\":\"D. Lizotte\",\"doi\":\"10.1201/9781315275772-14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Kernel functions • Whenever a learning algorithm (such as SVMs) can be written in terms of dot-products, it can be generalized to kernels. • A kernel is any function K : R × R 7→ R which corresponds to a dot product for some feature mapping φ: K(x1, x2) = φ(x1) · φ(x2) for some φ. • Conversely, by choosing feature mapping φ, we implicitly choose a kernel function • Recall that φ(x1) · φ(x2) ∝ cos∠(φ(x1), φ(x2)) where ∠ denotes the angle between the vectors, so a kernel function can be thought of as a notion of similarity.\",\"PeriodicalId\":165137,\"journal\":{\"name\":\"Statistical Methods in Agriculture and Experimental Biology\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistical Methods in Agriculture and Experimental Biology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1201/9781315275772-14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methods in Agriculture and Experimental Biology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9781315275772-14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
•只要一个学习算法(比如svm)可以用点积来表示，它就可以推广到核函数。•核函数是任意函数K: R × r7→R，它对应于一些特征映射φ: K(x1, x2) = φ(x1)·φ(x2)对于一些φ的点积。•相反，通过选择特征映射φ，我们隐式地选择了一个核函数•回想φ(x1)·φ(x2)∝cos∠(φ(x1)， φ(x2))，其中∠表示向量之间的夹角，因此核函数可以被认为是相似度的概念。
Kernel functions • Whenever a learning algorithm (such as SVMs) can be written in terms of dot-products, it can be generalized to kernels. • A kernel is any function K : R × R 7→ R which corresponds to a dot product for some feature mapping φ: K(x1, x2) = φ(x1) · φ(x2) for some φ. • Conversely, by choosing feature mapping φ, we implicitly choose a kernel function • Recall that φ(x1) · φ(x2) ∝ cos∠(φ(x1), φ(x2)) where ∠ denotes the angle between the vectors, so a kernel function can be thought of as a notion of similarity.
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