1.       Consider the string ababcdef. List all 2-shingles and 3-shingles, using each alphabet as a token.

2.       Show that the PageRank computation with teleportation is an eigenvector computation on an appropriately constructed probability transition matrix.

3.       Show that the hub and authority scores in HITS can be computed by dominant eigenvector computations on AAT and AT A respectively. Here, A is the adjacency matrix of the graph G = (S, A), as defined in the chapter.

4.       Propose an alternative to the ranking SVM based on logistic regression. Discuss how you would formulate the optimization problem and how the stochastic gradientdescent steps are related to traditional logistic regression.