pattern recognition

Rules • Use basic Python, numpy and matplotlib modules. Any other modules need my approval. • Produce a LATEX-generated PDF of your report. • Ask plenty of questions to ensure you have a good understanding of the project. • The code (and reports) should look vastly different for different groups. Very similar code will incur a hefty penalty. • Everyone should participate...no excuses, no exceptions. Part 1 1. Generate 20 points of X ∼ N (  −3 4  , I) and Y ∼ N (  3 −2  , 2I). Store this dataset in a file. 2. Using Fisher’s Linear Discriminant Analysis, find the decision boundary. 3. Plot X,Y and the decision boundary. Make sure that you use a good plotting technique so that it is easy to distinguish which datapoint is X and which is Y . 4. Calculate the accuracy of your linear classifier. Part 2 In this part we will investigate the effects of mean for jointly Gaussian random variables on accuracy. 1. Generate 20 points of X ∼ N (  −3 + µ1 4 + µ1  , I) and Y ∼ N (  3 + µ2 −2 + µ2  , 2I). 2. Using Fisher’s Linear Discriminant Analysis, calculate the decision boundary and plot accuracy vs µ1 ∈ [0, 3] and µ2 ∈ [0, 3]. Note that this is a 3D plot. Part 3 1. Generate 20 points of X ∼ N (  −3 4  , Σ1) and Y ∼ N (  3 −2  , Σ2), where Σ1 =  σ1 0 0 σ1  and Σ2 =  σ2 0 0 σ2  . 2. Using Fisher’s Linear Discriminant Analysis, calculate the decision boundary and plot accuracy vs σ1 ∈ [1, 5] and σ2 ∈ [1, 5]. Note, as in the previous part this is a 3D plot.