1. Suppose that you are only given pairwise similarities between text sentences in a document, but you are not given the sentences themselves. Show how you can use these pairwise similarities in order to create a summary of the document.
2. Consider a background corpus with 100,000 tokens in which the word “politics” occurs 250 times. Furthermore, a document with 70 tokens contains this word twice. Calculate the likelihood ratio that this word is a topic signature.
3. Suppose that you use nonnegative matrix factorization instead of LSA for the latent method discussed in Sect. 11.3.1. Discuss the intuitive relationship of such a technique with the clustering method discussed in Sect. 11.3.4.
