Transcription of 1 Kernel Functions - Princeton University
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1 Kernel Functions - Princeton University
STA561: Probabilistic machine learningKernels and Kernel Methods (10/09/13)Lecturer: Barbara EngelhardtScribes: Yue Dai, Li Lu, Will Wu1 Kernel What are Kernels?Kernelsare a way to represent your data samples flexibly so that you can compare the samples in a complexspace. Kernels have shown great utility in comparing images of different sizes protein sequences of different lengths object 3D structures networks with different numbers of edges and/or nodes text documents of different lengths and of these objects have different numbers and types of features. We want to be able to cluster data samplesto find which pairs are neighbors in this complex, high dimensional space.
The Gaussian kernel, (also known as the squared exponential kernel { SE kernel { or radial basis function {RBF) is de ned by (x;x0) = exp 1 2 (x x0)T 1(x x0) (6), the covariance of each feature across observations, is a p-dimensional matrix. When is a diagonal matrix, this kernel can be written as (x;x0) = exp 0 @ 1 2 Xp j=1 1 ˙2 j:(x j x0)2 1 ...
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