1. Matlab Matlab Sigmoid Sigmoid Perceptron Perceptron Linear Linear Training Training Small, Round Blue-Cell Tumor Classification Example Small, Round Blue-Cell Tumor Classification Example Matlab Program for NN Analysis Matlab Program for NN Analysis Algebraic Training of a Neural Network Algebraic Training of a Neural Network

3. You can use various shapes of non-linear neurons in Neural Networks

6. Perceptron Neural Networks

8. Biases versus Weights in Perceptrons

11. Multi-Layer Perceptrons can classify with Boundaries and Clusters 1.Multi-layer perceptrons have more powerful classification capabilities 2.Based on number of layers and elements used we can make a classification of classifiers 3.We can find open and closed regions in classifications. 4.The next slide will show various strengths of classifiers.

13. Sigmoid Neural Networks

14. Smooth nonlinearity! Logsig = logistic sigmoid

15. Sigmoid Neural Network

16. Single Sigmoid Layer is Sufficient for any continuous function!

17. Typical Sigmoid Neural Network Output – create your own mapping Sigmoid gives arbitrary accuracy!

18. Thresholded Neural Network Output Strict YES / NO decision is sometimes useful

19. Linear Neural Networks Neural Networks

20. Training Error and Cost for a Single Linear Neuron Training error Quadratic error cost

21. Linear Neuron Gradient Training error Quadratic error cost Single Linear Neuron

22. Steepest-Descent Steepest-Descent Learning for a Single Linear Neuron New training parameter

23. Backpropagation – for a Single Linear Neuron

24. Backpropagation for a Single Linear Neuron Training Sets

25. Example: Microarray Training Set

27. Steepest-Descent Algorithm for a Single-Step Perceptron

28. Training Sigmoid Networks

29. Training Variables for a Single Sigmoid Neuron

30. Training a Single Sigmoid Neuron

31. Final formula for weights and biases

32. Training a Sigmoid Network

34. From previous slides

35. Example of Classification done by a Neural Network 62 samples from microarray 7000 genes 8 genes in strong feature set

38. Small, Round Blue- Cell Tumor Classification Example

43. How the training set was created?

44. Neural Network Training for the SRBCT problem Characteristics of training method for SRBCT

45. “Leave-One-Out” – another validation methodology

46. “Novel-Set” Validation methodology

47. Characteristics of methods applied

49. Cardiac Pacemaker and EKG Signals EKG Signals

55. MATLABfor Neural Networks

58. Matlab Program for NN Analysis

67. Algebraic Training of a Neural Network

70. conclusions