Chap6.2-RadialBasisFunctions (1)

Chap6.2-RadialBasisFunctions (1) - Machine Learning Srihari...

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Unformatted text preview: Machine Learning Srihari Radial Basis Function Networks Sargur Srihari 1 Machine Learning Srihari Topics • Basis Functions • Radial Basis Functions • Gaussian Basis Functions • Nadaraya Watson Kernel Regression Model 2 Machine Learning Srihari Basis Functions • Summary of Linear Regression Models 1. Polynomial Regression with one variable y (x ,w ) = w +w 1 x+w 2 x 2 +…= Σ w i x 2. Simple Linear Regression with D variables y( x,w ) = w +w 1 x 1 +..+w D x D = w T x In one-dimensional case y(x, w ) = w + w 1 x which is a straight line 3. Linear Regression with Basis functions φ j ( x ) • There are now M parameters instead of D parameters • What form should the basis functions take? 3 y ( x,w ) = w + w j φ j ( x ) j = 1 M − 1 ∑ = w T φ ( x ) Machine Learning Srihari Radial Basis Functions • A radial basis function depends only on the radial distance (typically Euclidean) from the origin φ (x)= φ (||x||) • If the basis function is centered at μ j then φ j ( x ) =h ( || x- μ j || ) • We look at radial basis functions centered at the data points x n , n =1,…,N 4 Machine Learning Srihari History of Radial Basis Functions...
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Chap6.2-RadialBasisFunctions (1) - Machine Learning Srihari...

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