The Geometry of Information Retrieval

Using this framework, van Rijsbergen presents a new theory for the
foundations of IR, in particular a new theory of measurement. He shows how a document can be represented as a vector in Hilbert space, and the document’s relevance by an Hermitian operator. All the usual quantum-mechanical notions, such as uncertainty, superposition and observable, have their IR-theoretic analogues. But the approach is more than just analogy: the standard theorems can be applied to address
problems in IR, such as pseudo-relevance feedback, relevance feedback and ostensive retrieval. The relation with quantum computing is also examined. To help keep the book self-contained, appendices with background material on physics and mathematics are included, and each chapter ends with some suggestions for further reading.

This is an important book for all those working in IR, AI and natural language processing.