1
Consider a two-dimensional class problem that involves two classes, ω1 and ω2, which are modeled by Gaussian distributions with means μ1 = [0, 0]T and
μ2 = 1.
2.
3. 4.
5.
6.
T 1 0.25 [2, 2] , respectively, and common covariance matrix Σ = 0.25 1 .
Form and plot a data set X consisting from 500 points from ω1 and another 500 points from ω2.
Assign each one of the points of X to either ω1 or ω2, according to the Bayes decision rule, and plot the points with different colors, depending on the class they are assigned to. Plot the corresponding classifier.
Based on (2), estimate the error probability. 01
Let L = 0.005 0 be a loss matrix. Assign each one of the points
of X to either ω1 or ω2, according to the average risk minimization rule, and plot the points with different colors, depending on the class they are assigned to.
Based on (4), estimate the average risk for the above loss matrix.
Comment on the results obtained by (2)-(3) and (4)-(5) scenarios.
Hint: For the estimation of the mean and covariance matrices for the training data, use their corresponding Maximum Likelihood estimates.
You can use Python or MATLAB code.
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