Description
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Description: Download the data le from the course website. The data set contains 5,000 rows to represent the numbers and their labels. For this assignment, and P matrices can be found on the course webpage.
Run PCA on the dataset. Plot the eigenvalues in descending or-der. How many components would you choose by examining this plot only?
Examine the rst 2 principal components. Create a scatter plot with each of the rows of the dataset projected onto the rst two principal components (Your plot must use a di erent color for each population and include legend). Comment on the facts about the plot and interpret the rst two principal components.
Examine the third principal component of X. Create a scatter plot with each individual projected onto the subspace spanned by the rst and third principal components. What information does the third principal component capture?
Display the sample mean for the data set as an image and display the bases which you chose as images. Comment on the covariance matrix.
Choose at least 10 subspaces with di erent dimensions and project the data.
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Assume that d -dimensional zero-mean random vector X with covari-ance matrix 2 Sd+ d,
Find the eigengap and maximum eigenvector.
Consider P 2 Sd d , nd the unique maximal eigenvector of the
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perturbed matrix = + P .
For di erent xed dimensions r=f10; 50; 100g, nd the optimal subspace and the reconstruction error of for each dimension on this r-rank projection.
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