Lines and Xor
- Note that (using a linear transfer function), a perceptron
reduces the dimension from 2 (or n) to 1.
- Using a step function, it is a linear classifier.
- It returns true if the input is on one side of a line,
and false if it's on the other.
- You can of course have three inputs, and it's a planar separator,
and four or more gives a hyperplaner separator.
- However, a line cannot solve the xor problem.
- Thus a perceptron cannot solve the xor problem.
-
![A Graph of two classes that aren't linearly separable.](twoClassNotLinearlySeparable.gif)
- Indeed any number of perceptrons together do the same thing.
- However, if you put the perceptrons in layers, you can.
- The input from one layer of perceptrons goes into a second layer.