Visualizing the newsgroups data with t-SNE

We have just converted text from each raw newsgroup document into a sparse vector of a size of 500. For a vector from a document, each element represents the number of times a word token occurring in this document. Also, these 500 word tokens are selected based on their overall occurrences after text preprocessing, removal of stop words, and lemmatization. Now you may ask questions such as, is such occurrence vector representative enough, or does such an occurrence vector convey enough information that can be used to differentiate the document itself from documents on other topics? We can answer these questions easily by visualizing those representation vectors—we did a good job if document vectors from the same topic are nearby. But how? They are of 500 dimensions, while we can visualize data of at most three dimensions. We can...