Radial Basis Functions Neural Network in Machine Learning
Explore the concept of Radial Basis Functions Neural Network (RBF NN) in Machine Learning, focusing on its properties, architecture, training process, and results. Discover how RBF NN differs from other neural networks and its applications in regression models. Dive into the intricacies of RBF NN training through unsupervised learning and matrix notation, shedding light on key principles such as best approximation and pseudo-inverse properties.
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Presentation Transcript
? Machine Learning (Part II) Test Angelo Ciaramella
Question 9 Radial Basis Functions Neural Network Question Which of the following is a property of RBF NN? Best approximation Universal approximation Compact approximation ML Verification tests
Introduction Regression regression models based on linear combinations of fixed basis functions Radial Basis Functions find f such that ML Verification tests 3
RBF NN ML Verification tests Architecture of RBF NN 4
RBF NN Outputs ? ??= ?????? + ??0 ?=1 For the case of Gaussian functions 2 ? ?? 2?? ML Verification tests ??? = ??? 2 5
RBF NN Result Best approximation - in the set of approximating functions there is one function which has minimum approximating errore for any given function to be approsimated (Girosi and Poggio, 1990) This property is not shared by MLP ML Verification tests 6
RBF NN training Basis functions Unsupervised learning (e.g., clustering) Network mapping ? ??(?) = ?????? ?=0 ML Verification tests Matrix notation ??(?) = ?? 7
RBF NN training Sum-of-squares error ? =1 ? 2 ???? ?? 2 ? ? Differentiating with respect wkj and setting the derivative to zero ML Verification tests ?= 0 ??? ???? ?? ? Matrix notation ? ??= T? 8
RBF NN training Providing the matrix is non-singular we may invert ??= ? ? Pseudo-inverse ??? ? = ??? Pseudoinverse property ML Verification tests ? ? = ? If the matrix is not singular equation does not have a unique solution In practical, use a SVD (Singular Value Decomposition) methodology ??? 9
References Material Slides Video Lessons Books J. C. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, 1995 J. C. Bishop, Pattern Recognition and Machine Learning, Springer, 2006 ML Verification tests
