1. Rosenblatt's Mark I perceptron OCR
• 20*20 input
• 512 potentiometers with motors
• Output character identification
• How to set weights?
2. The simple perceptron
• McCulloch Pitts neuron with N real inputs and one binary output
• MP showed that neuron can compute many useful functions
• AND
• OR
• Low pass filter
• Image noise removal
• Perceptron can be trained to properly classify a training set
3. Geometric interpretation
• Perceptron computes a dot-product and then thresholds
• Perceptron defines a (N-1) dimensional hyperplane
• All +class patterns on one side, all -class patterns on the other
• Don't need the bias term if increase dimension by one
4. Strength of perceptron as a classifier
• XOR can't be calculated
• Cover's theorem for randomly chosen patterns
• Number of hypercube vertex dichotomies D(N)

Assignment

1. Find D(1), D(2), D*(2), D*(3).
   (D(N) is the number of dichotmies realizable by a perceptron in N-space.
   D* stands for the number of unbiased perceptron dichotomies).
2. What is the connection between D(N) and D*(N)? Why?