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Machine Learning Lecture 6 Multilayer Perceptrons
Limitations of Single Layer Perceptron ,[object Object],y y w 0 w 1 w n x 1 x n x 2 w 0 w 1 w n x 1 x n x 2
Nonlinear Decision Surfaces ,[object Object]
Multilayer Network ,[object Object],[object Object]
Sigmoid Unit y
Multilayer Perceptron ,[object Object],Sigmoid units Fan-out units
Multilayer Perceptron ,[object Object],Hidden units Input units Output units
Error Gradient for a Sigmoid Unit y X(k) d(k)
Error Gradient for a Sigmoid Unit
Error Gradient for a Sigmoid Unit
Back-propagation Algorithm ,[object Object]
Back-propagation Algorithm ,[object Object],Step 1: Present the training sample, calculate the outputs X d 1 , d 2 , …d M
Back-propagation Algorithm ,[object Object],Step 2: For each output unit k, calculate X d 1 , d 2 , …d M
Back-propagation Algorithm ,[object Object],Step 3: For hidden unit h, calculate X d 1 , d 2 , …d M Hidden unit h Output unit k w h,k
Back-propagation Algorithm ,[object Object],Step 4: Update the output layer weights, w h,k X d 1 , d 2 , …d M Hidden unit h Output unit k w h,k where o h is the output of hidden layer h
Back-propagation Algorithm ,[object Object],X d 1 , d 2 , …d M Hidden unit h Output unit k w h,k o h is the output of hidden unit h w i, h x i
Back-propagation Algorithm ,[object Object],Step 4: Update the output layer weights, w h,k X d 1 , d 2 , …d M
Back-propagation Algorithm ,[object Object],Step 5: Update the hidden layer weights, w i,h X d 1 , d 2 , …d M Hidden unit h Output unit k w h,k w i, h x i
Back-propagation Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Learning Hidden Layer Representation Can this be learned?
Learning Hidden Layer Representation Learned hidden layer representation
Learning Hidden Layer Representation ,[object Object],The evolving sum of squared errors for each of the eight output units
Learning Hidden Layer Representation ,[object Object],The evolving hidden layer representation for the input “01000000”
Expressive Capabilities
Generalization, Overfitting and Stopping Criterion ,[object Object],[object Object],[object Object]
Generalization, Overfitting and Stopping Criterion A training set A validation set Stop training when the validation set has the lowest error
Application Examples ,[object Object],[object Object]
Application Examples ,[object Object],[object Object],[object Object],[object Object],[object Object]
Application Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Application Examples ,[object Object],[object Object],[object Object],[object Object],[object Object]
Application Examples ,[object Object]
Application Examples ,[object Object],NN Detection Model Face/ Nonface
Application Examples ,[object Object],[object Object],[object Object],[object Object]
Application Examples ,[object Object]
Application Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Application Examples ,[object Object],[object Object],[object Object],[object Object]
Application Examples ,[object Object],[object Object]
Application Examples ,[object Object],[object Object]
Application Examples ,[object Object],[object Object],[object Object],[object Object]
Further Readings ,[object Object],[object Object]
Tutorial/Exercise Question ,[object Object],[object Object],[object Object],[object Object],[object Object]
Tutorial/Exercise Question ,[object Object]
Tutorial/Exercise Question ,[object Object],[object Object],[object Object],[object Object],[object Object],a b c d w ac w bc w cd w c0 w d0 +1 +1

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