Exercise 1 Submission Sunday Apr 26 Delayed Submission

Exercise 1 Submission Sunday Apr 26 Delayed Submission 4 points every week • How would you calculate efficiently the PCA of data where the dimensionality d is much larger than the number of vector observations n? • Download the Wisconsin Data from the UC Irvine repository, extract PCAs from the data, test scatter plots of original data and after projecting onto the principal components, plot Eigen values 1

Ex 1. Part 2 to ninbbelt@gmail. com subject: Ex 1 and last names 1. Given a high dimensional data, is there a way to know if all possible projections of the data are Gaussian? Explain - What if there is some additive Gaussian noise?

Ex 1. (cont. ) 2. Use Fast ICA (easily found in google) http: //www. cis. hut. fi/projects/ica/fastica/cod e/dlcode. html – Choose your favorite two songs – Create 3 mixture matrices and mix them – Apply fastica to de-mix

Ex 1 (cont. ) • Discuss the results – What happens when the mixing matrix is symmetric – Why did u get different results with different mixing matrices – Demonstrate that you got close to the original files – Try different nonlinearity of fastica, which one is best, can you see that from the data

Ex 1 - Final Task • Create a BCM learning rule which can go into the Fast ICA algorithm of Hyvarinen. – Run it on multi modal distributions as well as other distributions. – Running should be as the regular fast ICA but with a new option for the BCM rule. – Demonstrate how down in Fisher score can you go to still get separation