Exercise 1 Submission Monday 19 Dec 2010 Delayed

Exercise 1 Submission Monday 19 Dec, 2010 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? Give the equation and explain • Download the EEG data that appears next to the exercise. It contains frames of EEG recordings from three electrodes. There are two class labels organized in two files • Extract PCAs from the data, test scatter plots of original data and after projecting onto the principal components, plot Eigen values. • Projections on which principal components are most correlated with the class labels? 1

Ex 1. Part 2 Submit to n. intrator@gmail. com subject: Ex 1 NC and last names Additional information about the data: 1. There are four groups in the data, you can seek separation between ESP and EHP, and between ESR and EHR. I suggest that you try both and see where separation is better.

Ex 1. Part 2 Submit to n. intrator@gmail. com subject: Ex 1 NC 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 on Google) http: //www. cis. hut. fi/projects/ica/fastica/cod e/dlcode. html – Get the data from the Web site – Apply fastica to de-mix (different non-linear functions) – Devise ways to demonstrate that the new data is more independent than the original, how do you tell when non-linearity is best (show also graphically)

Ex 1 – (Cont. ) 3. Create a BCM learning rule which can go into the Fast ICA algorithm of Hyvarinen. – Run it on the previos data – Explain the results