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Unformatted text preview: feature space in SVM without even
knowing the function .
It's not possible to put a
hyperplane through these points. Thre e popular ke rne l choice s in the SVM
The SVM only relies on the inner product between vectors
transformation , the inner product becomes:
we only need specify the kernel If every data point is mapped into high dimensional space via some
is called the kernel function. For SVM, , without need to know the corresponding non linear mapping, . There are many types of kernels that can be used in Support Vector Machines models. These include linear, polynomial, radial basis
function (RBF) and sigmoid functions.
Linear:
Polynomial: ,
, wikicour senote.com/w/index.php?title= Stat841&pr intable= yes After a simple transformation, a
perfect classification plane can be
found.
67/74 10/09/2013 Stat841  Wiki Cour se Notes Radial Basis: , Gaussian kernel: , Two layer perceptron: , Sigmoid:
Here, , .
, and are all kernel parameters. The RBF is by far the most popular choice of kernel types used in Support Vector Machines. This is mainly because of their localized and finite responses across the entire
range of the real x axis.The art of flexible modeling using basis expansions consists of picking an appropriate family of basis functions, and then controlling the complexity of
the representation by selection, regularization, or both. Some of the families of basis functions have elements that are defined locally; for example,
 splines are defined
locally in
. If more flexibility is desired in a particular region, then that region needs to be represented by more basis functions(which in the case of
 splines translates
to more knots).Kernel methods achieve flexibility by fitting simple models in a region local to the target point . Localization is achieved via a weighting kernl
and
individual observations receive weights
. RBF combine these ideas, by treating the kernel functions as basis functions. Once we have chosen the Kernel function, we don't need to figure out what is, just use to replace Since the transformation chosen is dependent on the shape of the data, the only automated way to choose an appropriate kernel is by trial and error. Otherwise it is chosen
manually. Mercer's Th...
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This document was uploaded on 03/07/2014.
 Winter '13

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