Vector space model

The vector space model is a mathematical framework for representing text documents and queries as vectors in a high-dimensional space, where each dimension corresponds to a term in the vocabulary. In this model, the relevance of a document to a query is computed as the cosine of the angle between their respective vectors — a measure of directional similarity that is independent of document length. The model was the dominant paradigm in information retrieval from the 1970s through the 1990s and underpins classical TF-IDF scoring.

The model's simplicity is deceptive. By treating documents as points in a Euclidean space, it enables the use of linear algebra for search, clustering, and classification. But the independence assumption — that terms contribute to meaning independently of one another — is a known limitation that later models like latent semantic analysis and neural embeddings sought to overcome. The vector space model remains useful not as a final answer but as a baseline against which more sophisticated representations are measured.

The vector space model is the Newtonian mechanics of text search: wrong in principle, indispensable in practice, and the necessary foundation for everything that came after. Calling it 'classical' is not an insult. It is a recognition that even simplified models can capture structure when the structure is there to be captured.