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Understanding Computation in Neural Networks

Explore different types of neural networks, functions, and learning problems, including perceptron, backpropagation, clustering, and categorization. Learn about regression, classification, and generalization in this comprehensive guide.

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Understanding Computation in Neural Networks

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  1. Computation in neural networks M. Meeter

  2. Calculating a function Perceptron learning problem Input Patterns Desired output [+1, +1, -1, -1] [+1, -1, +1] [-1, -1, +1, +1] [+1, +1, -1] [-1, -1, -1, -1] [-1, -1, +1, -1] [-1, -1, -1] [-1, +1, +1, -1] [-1, +1, +1] [+1, -1, +1, -1]

  3. Types of networks & functions • Attractor • Feedfwrd Hebbian • associative (Hebbian) • competitive • Feedfwrd error corr. • perceptron • backprop • completion, autoass. memory • association, assoc. memory • clustering • categorization, generalization • nonlinear, same

  4. Types of networks • Attractor • Feedfwrd Hebbian • associative (Hebbian) • competitive • Feedfwrd error corr. • perceptron • backprop • completion, autoass. memory • association, assoc. memory • clustering • categorization, generalization • nonlinear, same

  5. A Classification

  6. Generalization 76 128 ?

  7. Regression = generalization Univariate Linear Regression prediction of values

  8. Clustering

  9. Types of networks • Attractor • Feedfwrd Hebbian • associative (Hebbian) • competitive • Feedfwrd error corr. • perceptron • backprop • completion, autoass. memory • association, assoc. memory • clustering • categorization, generalization • nonlinear, same

  10. Classification - discrete Perceptron learning problem Prototypical Input Patterns Desired output [+1, +1, -1, -1] [+1, -1, +1] [-1, -1, +1, +1] [+1, +1, -1] [-1, -1, -1, -1] [-1, -1, +1, -1] [-1, -1, -1] [-1, +1, +1, -1] [-1, +1, +1] [+1, -1, +1, -1]

  11. Classification - discrete Perceptron learning problem Prototypical Input Patterns Desired output [+1, +1, -1, -1] [+1, -1, +1] [-1, -1, +1, +1] [+1, +1, -1] [-1, -1, -1, -1] [-1, -1, +1, -1] [-1, -1, -1] [-1, +1, +1, -1] [-1, +1, +1] [+1, -1, +1, -1]

  12. Xi X1 X2 Xn Classification in Perceptron  wji threshold

  13. Effe tussendoor… • Bij perceptron etc.: net input knoop>0 dan activatie 0 • Niet altijd gewenst: daarom heeft knoop in continue vormen perceptron / backprop een ‘bias’, een activatie die altijd bij input opgeteld wordt • Effect: verschuiven threshold

  14. - Threshold Input= + Input= mixture Threshold Classification in 2 dimensions

  15. Discriminant Analysis Find center of two categories, draw line in between, then one diagonal in middle = discrimination line Produces exact same result

  16. Generalization = Regression Univariate Linear Regression prediction of values

  17. Activation function  Xi (·) X1 X2 v =  xi*wji (v) = av + b Xn   Perceptron with linear activation rule y wji j Change weights with  rule, minimizing Se2 Bias

  18. X 1 X 2 X i X n Multivariate Multiple Linear Regression Multivariate = multiple independent variables X =multiple inputs y 1 1 y 2 2 Multiple = multiple dependent variables Y =multiple outputs Y2 X Y1

  19. linear nonlinear y y x x Linear vs. nonlinear regression • Here: quadratic • General: wrinkle-fitting

  20. X X Multi-Layer Perceptron å = v x * w i ji i  y1 y2 • Fit any function: “Universal approximators” X= [x1, x2, .., xi, .., xn]

  21. Too complex model y x Bad Extremely bad Overfitting y Too simple model x

  22. Clustering Competitive learning: • next week • ART

  23. Conclusions • Neural networks similar to statistical analyses • Perceptron -> categorization / generalization • Backprop -> same but nonlinear • Competitive l. -> clustering • But… • Whole data set vs. one pattern at a time

  24. Feature reduction with PCA

  25. ? ? Feature extraction with PCA Unsupervised Learning Hebbian Learning

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