Assume you are given a data set in the form of a n x m term-by document matrix X corresponding to a large collection of news articles. Precisely, the (i, j) entry in X is the frequency of the word i in the document j. We would like to visualize this data set on a two-dimensional plot. Explain how you would do to do the following (describe your steps carefully in terms of the SVD of an appropriately centered version of X).

1. Plot the different news sources as points in word space, with maximal variance of the points.

2. Plot the different words as points in news-source space, with maximal variance of the points.