decision boundary of perceptron too small

问题

I am trying to plot the decision boundary of a perceptron algorithm and am really confused about a few things. My input instances are in the form [(x1,x2),target_Value], basically a 2-d input instance and a 2 class target_value [1 or 0].

My weight vector hence is in the form: [w1,w2] Now I have to incorporate an additional bias parameter w0 and hence my weight vector becomes a 3x1 vector? is it 1x3 vector? I think it should be 1x3 since a vector has only 1 row and n columns.

Now let's say I instantiate [w0,w1,w2] to random values, how would I plot the decision boundary for this? Meaning what does w0 signify here? Is w0/norm(w) the distance of the decision region from the origin? If so how do I capture this and plot it in python using matplotlib.pyplot or its matlab equivalent? I would really appreciate even a little help regarding this matter.

from pylab import norm
import matplotlib.pyplot as plt

n = norm(weight_vector) #this is of the form [w0,w1,w2], w0 is bias parameter
ww = weight_vector/n   #unit vector in the direction of weight_vector
ww1 = [ww[1],-ww[0]]
ww2 = [-ww[1],ww[0]]
plot([ww1[0], ww2[0]],[ww1[1], ww2[1]],'--k')

Here I want to incorporate the w0 parameter to indicate the distance of the displacement of the weight vector from the origin since that's what w0/norm(w) indicates?

When I plot the vector as mentioned in the comments below I get a vector of really small length, how would it be possible for me to extend this decision boundary in both directions?

The small dashed line near location [0,0] in the figure is my decision region, how can I make it longer in both directions? If I try to multiply each of its components, the figure scale changes, I am using matplotlib.pyplot.plot() function to achieve this.

回答1:

First of all, you shouldn't add the bias to the input vectors. You only need to subtract or add the bias to all of your input vectors. For plotting, you might want to try plot the linear function that passes the two weight points.

来源：https://stackoverflow.com/questions/19069971/decision-boundary-of-perceptron-too-small