1. We are given two sets, s={P,T,Q,L,M} and t={Q,L,F,M,A,C}. Assume that we are looking for pairs of points that have a Jaccard similarity at least 0.6/0.8/0.9.
Using length based and prefix based filtering and the above thresholds when can we reject the explicit pairwise comparision of the two sets?

2. A factory which manufactures products A and B has a cost function of C(x, y) = 6x^2+12y^2 depending on the amount of products manufactured (x for product A and y for peoduct B). How many products of type A and B shall the company produce respectively, if they can sell a total of 180 of the two products together and the two products are sold for the same price?

3. Load into Octave the pca.mat dataset and perform PCA on it!
a) What difference it makes if you use the scatter matrix versus the covariance matrix during calculation? Can you come up with a vectorized implementation of the scatter matrix?
b) Don't forget to standardize the data points
Useful functions regardning standardization: bsxfun (with parameters 'minus' and 'rdivide') and repmat
After standardization and performing PCA we get the following 5 coordinates for the first 5 data points:
[-1.48127   0.91291  -1.21209  -1.62734  -1.26042] (Or these values negated. Any idea why?)

4. Run eigenfaces.m method!
a) On default images are transformed into 100 dimensional data points. Note that the original representation was 1024 (32x32) dimensional. Examine what happens if you alter the parameter on the reduced number of dimensionality from 100 to some other number!
b) Add some noise to the images. The noise should be uniformly distributed from the range [-28,28]. Now repeat PCA!

Extra:
Using Lagrange multipliers verify that the entropy of a binary random variable is maximized at (0.5, 0.5)! Comapre your results to the output you obtain when running the function plotter.m!