Below is a spatial visualization of the document vectors for the four Shakespeare play documents, showing just two of the dimensions, corresponding to the words battle and fool. The comedies have high values for the fool dimension and low values for the battle dimension.

We can think of the vector for a document as a point in |V|-dimensional space; thus the documents in Fig. 6.3 are points in 4-dimensional space. Since 4-dimensional spaces are hard to visualize, Fig. 6.4 shows a visualization in two dimensions; we’ve arbitrarily chosen the dimensions corresponding to the words battle and fool.