内核方法

Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare Pub Date : 2020-05-07 DOI:10.1201/9780429345159-7

Mark Chang

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摘要

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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Kernel Methods

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:

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Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare

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