{"title":"Kernel Methods","authors":"Mark Chang","doi":"10.1201/9780429345159-7","DOIUrl":null,"url":null,"abstract":"Remember the xor example of a classification problem that is not linearly separable. If we map every example into a new representation, then the problem becomes linearly separable. Specifically, ... The major disadvantage of mapping points into a new space is that the new space may have very high dimension. For example, if points lie in d-dimensional Euclidean space, and we include the product of every pair of dimensions then we have quadratic blowup with the mapping f : R 7→ Rd2. We can avoid this explosion if we can achieve two objectives:","PeriodicalId":179087,"journal":{"name":"Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare","volume":"48 8","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9780429345159-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Remember the xor example of a classification problem that is not linearly separable. If we map every example into a new representation, then the problem becomes linearly separable. Specifically, ... The major disadvantage of mapping points into a new space is that the new space may have very high dimension. For example, if points lie in d-dimensional Euclidean space, and we include the product of every pair of dimensions then we have quadratic blowup with the mapping f : R 7→ Rd2. We can avoid this explosion if we can achieve two objectives:
还记得 xor 分类问题的例子吗？如果我们把每个例子都映射到一个新的表示中，那么问题就变得线性可分了。具体来说，...将点映射到新空间的主要缺点是，新空间的维度可能非常高。例如，如果点位于 d 维欧几里得空间中，并且我们将每对维度的乘积都包括在内，那么我们就会在映射 f ：R 7→ Rd2 的映射会产生二次爆炸。如果我们能实现两个目标，就能避免这种爆炸：
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