Weight and data space

A feature vector with correct answer=0

• Imagine a space in which each axis corresponds to a feature value or to the weight on that feature – A point in this space is a weight vector. Feature vectors are shown in blue translated away from the origin to reduce clutter. • Each training case defines a plane. – On one side of the plane the output is wrong. • To get all training cases right we need to find a point on the right side of all the planes. – This feasible region (if it exists) is a cone with its tip at the origin

bad weights

good weights

A feature vector with correct answer=1

the origin