Questions

1. A dataset, X, has a covariance matrix C=diag(2, 1). What do you expect from PCA?
2. Considering the previous question, if X is zero-centered and the ball, B_0.5(0, 0), is empty, can we suppose that a threshold of x = 0 (the first principal component) allows for horizontal discrimination?
3. The components extracted by PCA are statistically independent. Is this correct?
4. A distribution with Kurt(X) = 5 is suitable for ICA. Is this correct?
5. What is the NNMF of a dataset, X, containing the samples (1, 2) and (0, -3)?
6. A corpus of 10 documents is associated with a dictionary with 10 terms. We know that the fixed length of each document is 30 words. Is the dictionary over-complete?
7. Kernel PCA is employed with a quadratic kernel. If the original dimensionality is 2, what is the dimensionality of the new space where the PCA is performed?

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