Pub Date : 2018-10-08DOI: 10.1201/9781315275772-14
D. Lizotte
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.
•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。
{"title":"Nonlinear Models","authors":"D. Lizotte","doi":"10.1201/9781315275772-14","DOIUrl":"https://doi.org/10.1201/9781315275772-14","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":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134066622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Studying Linear Relationships","authors":"A. Hasted","doi":"10.1201/9780203738559-9","DOIUrl":"https://doi.org/10.1201/9780203738559-9","url":null,"abstract":"","PeriodicalId":165137,"journal":{"name":"Statistical Methods in Agriculture and Experimental Biology","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117047428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-11-22DOI: 10.1201/9780203738559-13
A. Hasted
{"title":"The Analysis of Proportions","authors":"A. Hasted","doi":"10.1201/9780203738559-13","DOIUrl":"https://doi.org/10.1201/9780203738559-13","url":null,"abstract":"","PeriodicalId":165137,"journal":{"name":"Statistical Methods in Agriculture and Experimental Biology","volume":"170 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121036721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Assumptions Behind the Analysis","authors":"R. Mead, R. Curnow, A. Hasted","doi":"10.1201/9780203738559-8","DOIUrl":"https://doi.org/10.1201/9780203738559-8","url":null,"abstract":"","PeriodicalId":165137,"journal":{"name":"Statistical Methods in Agriculture and Experimental Biology","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127840229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"More on Factorial Treatment Structure","authors":"R. Mead, R. Curnow, A. Hasted","doi":"10.1201/9780203738559-7","DOIUrl":"https://doi.org/10.1201/9780203738559-7","url":null,"abstract":"","PeriodicalId":165137,"journal":{"name":"Statistical Methods in Agriculture and Experimental Biology","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123066345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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