<XML><RECORDS><RECORD><REFERENCE_TYPE>3</REFERENCE_TYPE><REFNUM>9074</REFNUM><AUTHORS><AUTHOR>Zuccon,G.</AUTHOR><AUTHOR>Azzopardi,L.</AUTHOR><AUTHOR>van Rijsbergen,C.J.</AUTHOR></AUTHORS><YEAR>2009</YEAR><TITLE>Semantic Spaces: Measuring the Distance between Subspaces</TITLE><PLACE_PUBLISHED>QI 2009, LNAI 5494</PLACE_PUBLISHED><PUBLISHER>LNCS, Springer</PUBLISHER><LABEL>Zuccon:2009:9074</LABEL><KEYWORDS><KEYWORD>Quantum Theory</KEYWORD></KEYWORDS<ABSTRACT>Semantic Space models, which provide a numerical representation of words’ meaning extracted from corpus of documents, have been formalized in terms of Hermitian operators over real valued Hilbert spaces by Bruza et al. [1]. The collapse of a word into a particular meaning has been investigated applying the notion of quantum collapse of superpositional states [2]. While the semantic association between words in a Semantic Space can be computed by means of the Minkowski distance [3] or the cosine of the angle between the vector representation of each pair of words, a new procedure is needed in order to establish relations between two or more Semantic Spaces. We address the question: how can the distance between di?erent1 Semantic Spaces be computed? By representing each Semantic Space as a subspace of a more general Hilbert space, the relationship between Semantic Spaces can be computed by means of the subspace distance. Such distance needs to take into account the di?erence in the dimensions between subspaces. The availability of a distance for comparing di?erent Semantic Subspaces would enable to achieve a deeper understanding about the geometry of Semantic Spaces which would possibly translate into better e?ectiveness in Information Retrieval tasks.</ABSTRACT></RECORD></RECORDS></XML>