Feature Selection and Dimension Reduction / MATLAB

Objective: The aim of this project is to study on the criteria for selecting features. Within this concern,mean and variance of the available data, their dimensions and such other properties will be examined. Below you are going to be given some data. Apply the necessary operations to these data, find the results, comment on them. Data: Datas are given from attachment. When you load these files in Matlab,you will see obtain two matrices of dimension 5x2 each. The first column is Feature-1, and the second colums is Feature-2. Work: 1. Calculate the mean and variance values of these data by hand and using Matlab's own functions. 2. Normalize the given matrices so that they become zero-mean and unity variance. 3. Test the below given hypothesis for the matrices after normalization: H0: “The mean of Feature-1 in the first matrix is -0.75 (Take the significance level as 0.90).” H0: “The mean of Feature-1 in the second matrix is 1.35 (Take the significance level as 0.95, this time)” 4. Calculate the correlation matrices of the normalized matrices. 5. Find the eigenvalues of the correlation matrices. Using these eigenvalues obtain the Principal Components. 6. Use Matlab's own PCA function and compare the results.