使用Matlab进行一维高斯贝叶斯定性

Question

If I have 2 classes and one feature and the feature is normally distributes on both class with different mean and variance, something like that

Now I want to find the equation of the discriminant surface and draw it on graph, something like that (this may not be the correct surface, it is just an illustration of what I am seeking for)

Is there a way to do that with matlab?!

Answer 1

Obviously, you'd like to classify a point as a point from distribution which has higher density at that point. Thus, the point of separation would be the one where both densities are equal. In general (multivariate) case your problem is known as Quadratic discriminant analysis .

For QDA one can find a separating curve (in general it's 2-nd order surface, a generalization of parabola) analytically. Fortunately, your case is 1-dimensional, so 1D parabola is just a point (or two).

The derivation goes as follows

The last one is a quadratic equation on x , its solution is the point of separation. In some cases there are 2 solutions, that means there are 2 points of intersection of densities.

What you need to do is to complete my derivation (write our formula(s) for x ), this x is a function of Gaussians' parameters, which you could calculate in any language you like.