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Can you explain more about how the kernel trick specifically works?
by moultano 17y ago
Can you explain more about how the kernel trick specifically works?
- lliiffee 17y agoBasically, the idea of feature spaces is to blow up the data into high dimensions. So, we use x' = f(x) as our data, instead of x. It turns out that in lots of machine learning algorithms (notably SVMs), you end up only needing inner products between different data elements. That is, we need to compute x^T y for two data elements x and y. In feature space, we need could compute this by doing f(x)^T f(y). However, it turns out that for certain feature spaces (like polynomials) one can compute the number f(x)^T f(y) quite quickly with out ever explicitly forming the big vectors x' or y'.
- moultano 17y agoYou stopped just short of the explanation I was hoping for. :)
- deleted 17y ago[deleted]
- lliiffee 17y agoTry section 7 of these notes: http://see.stanford.edu/materials/aimlcs229/cs229-notes3.pdf http://see.stanford.edu/materials/aimlcs229/cs229-notes3.pdf
- gaika 17y agosee http://videolectures.net/mlss09uk_schoelkopf_km/ http://videolectures.net/mlss09uk_schoelkopf_km/ - kernel methods in general, not limited to SVM