Combining Word Semantics within Complex Hilbert Space for Information Retrieval

Abstract. Complex numbers are a fundamental aspect of the mathematical for-malism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) have ignored complex numbers. In this paper, we argue that in order to advance the use of quantum models of IR, one has to lift the con-straint of real-valued representations of the information space, and package more information within the representation by means of complex numbers. As a first attempt, we propose a complex-valued representation for IR, which explicitly uses complex valued Hilbert spaces, and thus where terms, documents and queries are represented as complex-valued vectors. The proposal consists of integrating distri-butional semantics evidence within the real component of a term vector; whereas, ontological information is encoded in the imaginary component. Our proposal has the merit of lifting the role of complex numbers from a computational byprod-uct of the model to the very mathematical texture that unifies different levels of semantic information. An empirical instantiation of our proposal is tested in the TREC Medical Record task of retrieving cohorts for clinical studies.