How to plot decision boundaries between 3 classes using discriminant functions

Question

I have 3 discriminant functions dividing 2D space into 3 regions. I would like to plot decision boundaries between these regions. I couldn't figure out how to do that using matplotlib meshgrid in python.

In case of 2 discriminant function, the process is simple. I calculate difference between function and contour plot for values of 0.

lin_param = (-5, 5, 100)
xx = np.linspace(*lin_param)
yy = np.linspace(*lin_param)

x, y = np.meshgrid(xx, yy)

z = g1(x, y) - g2(x, y)
cp = plt.contour(x, y, z, levels=[0], colors="k")

plt.scatter(0, 0)
plt.scatter(2, 2)
plt.show()

where g1 and g2 are multivariate gaussian distributions with mean (0, 0) and (2, 2). (Distributions are not important, I want to apply this to any discriminant function)

def pdf(x, y, mean, cov):
  var = multivariate_normal(mean=mean, cov=cov)
  pos = np.empty(x.shape + (2,))
  pos[:, :, 0] = x; pos[:, :, 1] = y
  return var.pdf(pos)

def g1(x, y):
  return pdf(x, y, mean=[0,0], cov=[[1,0],[0,1]])

def g2(x, y):
  return pdf(x, y, mean=[2,2], cov=[[1,0],[0,1]])

def g3(x, y):
  return pdf(x, y, mean=[-2,2], cov=[[1,0],[0,1]])

Decision boundaries between two classes

Here one side is negative and other side is positive. Values are all zero along decision boundary. Now I would to add third function g3 whose mean is at (-2, 2). Plotting resulting decision boundaries is not straightforward. I tried taking maximum 2 values of 3 function and assigning the difference of them as z value but couldn't achieve what I want.

What I would like to see is something similar to image below:

Desired output with 3 function

Is it possible achieve it with similar meshgrid-contour plot approach? I don't want to calculate the line explicitly.

Update

By using contourf method, regions can be filled with different color. However, drawing boundary lines is still problem.

Fill Plot

Have you seen this post? Especially this link in the first answer. — Thomas Kühn
@ThomasKühn Thank you. Yes I saw that but after your comment I inspected further and played with snippets posted there. That link shows how different regions can be painted (question is updated accordingly) but I had no luck drawing boundary lines. Although It is good enough for me, I won't close the question to see if anybody manages to draw boundaries. — Seljuk Gülcan

Seljuk Gülcan Seljuk Gülcan · Accepted Answer · 2018-02-06T20:18:25

I think I achieved desired output.

Instead of assigning difference between functions to z array, I assigned index of function having largest value. Then I used numbers between class labels (or function index) as levels parameter. For example, to draw boundary between class 0 and class 1, I added 0.5 to levels parameter.

z = np.array((g1(x, y), g2(x, y), g3(x, y)))
z = np.argmax(z, axis=0)
cp = plt.contour(x, y, z, colors="k", levels=[0.5, 1.5, 2.5])

How to plot decision boundaries between 3 classes using discriminant functions

1 Answers