... kernel ),(),(),(),(2),(2),(),(exp),(),(exp),()),((),(1112111211zzKxxKzxKzxKzxKzzKxxKzxKzxKzxKczxKzxKd=−+−==+=σσwww.support-vector.netMaking kernels !From features: start from the features, then obtain the kernel. Example: the polynomial kernel, the string kernel, …19www.support-vector.net Learning Kernels!From ... Dual∑∑==∂∂=−=∂∂00iiiiiybLxywwLαα∑∑==0iiiiiyxywαα2www.support-vector.netBasic Idea! Kernel Methods work by embedding the data into a vector space, and by detecting linear relations in that space! Convex Optimization, Statistical Learning Theory, Functional ... ruleswww.support-vector.netClosure properties! List of closure properties:if K1 and K2arekernels, and c>o! Then also K is a kernel )()(),(:),(),(),(),(),(),(),(),(),(),(212111zfxfzxKXfzxKzxKzxKzxKzxKzxKzxKczxKzxKczxK⋅=ℜ→∀⋅=+=+=⋅=18www.support-vector.netSome...