1 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?

Ex1. Part 2 Submit to subject: Ex1 NC and last 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.

Ex1. Part 2 Submit to subject: Ex1 NC and last 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?

Ex1. (cont.) 2. Use Fast ICA (easily found on Google) e/dlcode.html 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)

Ex1 – (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