# CS667

# The Perceptron As a Classifier

**Rosenblatt's Mark I perceptron OCR**
- 20*20 input
- 512 potentiometers with motors
- Output character identification
- How to set weights?

**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

**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

**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

- 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).
- What is the connection between D(N) and D*(N)? Why?

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