Term-document matrices were originally defined as a means of finding similar
documents for the task of document information retrieval. Two documents that are similar will tend to have similar words, and if two documents have similar words their column vectors will tend to be similar.

Boston University

Term-document Matrix: In a term-document matrix, each row represents a word in the vocabulary and each column represents a document from some collection of documents. The fig. below show a small selection from a term-document matrix showing the occurrence of four words in four plays by Shakespeare.

Vector Space Model: The term-document matrix of fig below was first defined as part of the vector space model of information retrieval. In this model, a document is represented as a count vector.

Vector is just a list or array of numbers. A vector space is a collection of vectors, characterized by their dimension. The ordering of the numbers in a vector space indicates different meaningful dimensions on which documents vary.Thus the first dimension for both these vectors corresponds to the number of times the word battle occurs, and we can compare each dimension, noting for example that the vectors for As You Like It and Twelfth Night have similar values (1 and 0, respectively) for the first dimension.


Vectors and documents

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

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.

Learn Before

Related