Classification Problem 2Category Linearly Separable Case

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Classification Problem2-Category Linearly
Separable Case
Benign
Malignant
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Support Vector MachinesMaximizing the Margin
between Bounding Planes
A
A-
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Support Vector Classification
(Linearly Separable Case)
Let
be a linearly
separable training sample and represented by
matrices
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Support Vector Classification
(Linearly Separable Case, Primal)
The hyperplane
that solves the
minimization problem
realizes the maximal margin hyperplane with
geometric margin
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Support Vector Classification
(Linearly Separable Case, Dual Form)
The dual problem of previous MP
Dont forget
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Dual Representation of SVM
(Key of Kernel Methods)
The hypothesis is determined by
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Compute the Geometric Margin via Dual Solution

• The geometric margin

and

• Use KKT again (in dual)!

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Linear Machine in Feature Space
Make it in the dual form
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Kernel Represent Inner Product in Feature Space
Definition A kernel is a function
such that
where
The classifier will become
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Introduce Kernel into Dual Formulation
Let
be a linearly
separable training sample in the feature space
implicitly defined by the kernel
.
The SV classifier is determined by
that
solves
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Mercers Conditions Guarantees the Convexity of
QP