Combining Word Semantics within Complex Hilbert Space for Information Retrieval

Abstract

Abstract. Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) ignored complex numbers. We argue that to advance the use of quantum models of IR, one has to lift the constraint 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 distributional 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 byproduct 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.

A Survey of Quantum Theory Inspired Approaches to Information Retrieval

“…In [Zuccon et al 2011], this proposal was investigated and found to be performing poorly than the baseline Vector Space models. In [Wittek et al 2014], different types of word semantics are combined using a complex Hilbert Space. The main idea is to represent distributional semantics, like the word co-occurrence information as real part and represent ontological information about words as the imaginary part of a complex valued vector.…”

“…Projection Models [van Rijsbergen 2004], [Melucci 2005a], [Melucci 2005b], [Piwowarski and Lalmas 2009a], [Piwowarski et al 2008], [Piwowarski et al 2010a], [Piwowarski et al 2010c], [Piwowarski et al 2010b], [Caputo et al 2011], ] Quantum Language Models [Sordoni et al 2013b], [Xie et al 2015], [Zhang et al 2018d] [Hou andSong 2009], [Hou et al 2013], [Zhang et al 2018b], [Zhang et al 2018a], [Zhang et al 2018d] , [Blacoe et al 2013], [Blacoe 2015], [Basile and Tamburini 2017], [Li et al 2018a] Quantum-inspired Ranking [Zuccon et al 2009], , ], Multimodal IR [Wang et al 2010a], [Kaliciak et al 2011], [Kaliciak et al 2013], [Gkoumas et al 2018], [Zhang et al 2018c], ] Quantum-inspired Representation Learning [Aerts and Czachor 2004], [Bruza and Cole 2005], [Sordoni et al 2013a], [Zuccon et al 2011], [Wittek et al 2014], ], [Jaiswal et al 2018], ], , [Buccio et al 2018], User Interactions Projection Models [Melucci and White 2007], [Melucci 2008], [Piwowarski and Lalmas 2009a], [Frommholz et al 2011], ], ], [Wang et al 2017] Feedback...…”

Single or Multiple? Combining Word Representations Independently Learned from Text and WordNet

“…Two vectorial word representations can be easily combined concatenating the two vectors (CAT), computing the centroid (CEN), or creating a complex number (CMP). The latter, is based on the proposal of (Wittek et al 2014) in which, on the one hand, they used the real component of the complex vectors to represent the distributional semantics, and on the other, they encoded the ontological data in the imaginary component. In our particular case, we introduced the corpora-based embeddings in the real part and the WordNetbased ones in the imaginary part.…”

A Physical Metaphor to Study Semantic Drift

“…First, can the observed features be regarded as entries in a vocabulary? If so, distributional semantics applies and, given more complex representations, other types may do so as well [52]. The second question is, do they form sentences?…”