Abstract: To identify and describe one or more topics in one or more documents in a document set, a term set process creates a basic term set from the document set where the term set comprises one or more basic terms of one or more words in the document. A document vector process then creates a document vector for each document. The document vector has a document vector direction representing what the document is about. A topic vector process then creates one or more topic vectors from the document vectors. Each topic vector has a topic vector direction representing a topic in the document set. A topic term set process creates a topic term set for each topic vector that comprises one or more of the basic terms describing the topic represented by the topic vector. Each of the basic terms in the topic term set associated with the relevancy of the basic term. A topic-document relevance process creates a topic-document relevance for each topic vector and each document vector.