perceptron classifier

Perceptron
Perceptron is an algorithm for binary classification
that uses a linear prediction function:
f(x) = 1, w
T
x + b ? 0
-1, w
T
x + b < 0
This is called a step function, which reads:
• the output is 1 if “w
T
x + b ? 0” is true, and the
output is -1 if instead “w
T
x + b < 0” is true
Learning the Weights
What about b?
• This is the intercept of the linear function, also called
the bias.
Common implementation:
Realize that: w
T
x + b = w
T
x + b*1.
• If we add an extra feature to every instance whose
value is always 1, then we can simply write this as w
x,
where the final feature weight is the value of the bias.
• Then we can update this parameter the same way as
all the other weights.

Learning the Weights
The vector of w values is called the
weight vector.
Is the bias b counted when we use this phrase?
• Usually… especially if you include it by using the
trick of adding an extra feature with value 1 rather
than treating it separately.
• Just be clear with your notation.