Perceptron algorithm initial vector

[themagiciant95]

In a scientific paper (Neural Networks: A Systematic Introduction, page 86) about the Perceptron Algorithm I found:

A good initial heuristic is to start with the average of the positive input vectors minus the average of the negative input vectors. In many cases this yields an initial vector near the solution region.

Can you show me geometrically why this is true?

 

[Future Bruno]

Geometrically, this heuristic works because the average of the positive input vectors and the average of the negative input vectors form two separate points on the same plane. The vector between these two points will be pointing in the direction of the solution region, so starting with this vector as an initial vector will give a good starting point for finding the solution.