This paper illustrates the research work being in progress at the University of Padua within the VII FP Marie Curie International Research Sta Exchange Scheme project QONTEXT, which shows a new vision of information access and retrieval based on Quantum Theory. In particular, this paper describes the basics of QT, the use of the formalism for relevance feedback, music retrieval and visual cluster-based data mining.
Notion Classical Quantum Event space Hilbert vector space H Random event Set Orthonormal basis fjBi; jBig
Probability Measure Set measure State vector j'i Table 1. The correspondence between classical probability and quantum probability $" !" ! #"
P( A) = 6 15 ! ! !
A
B B " In the classical probabilistic model, events (e.g., word occurrences, category memberships, relevance, location, task, genre) are represented as sets and the probability measure is based on a set measure, e.g., set cardinality. In contrast, in quantum probability, events are represented as orthonormal vectors and the probability measure is the trace of the product between a density matrix and the matrix representing an event as summarized in Table 1. The simple example in Figure 1 depicts that when vectors are used to implement both events and densities the probability in the vector space is the squared inner product between the vectors, that is, the squared size of the projection of jAi onto j'i. 3
Diverse are the sources of evidence can be adopted, e.g. the behavior of the user when interacting with the results or judgments explicitly provided by the user for Relevance Feedback (RF) purpose. The combination of diverse sources of evidence is complex because of the feature heterogeneity (e.g. term frequency for the documents content and display-time for the user interaction behavior) and the lack of knowledge of the factors a ecting relevance assessment. QT can cope with this complexity because it provides a uniform formalism to model the diverse factors. In RF, a document can be represented as a density matrix. The factors may be extracted from the training documents using local co-occurrence data of terms to obtain a term correlation matrix, thus applying SVD to the matrix and obtaining a vector basis. Thus, the probability of relevance can be computed by the trace function. Factors can also model user location or di erent behavioral patterns extracted from the behavior of the user when interacting with the results. The main issue is to obtain a vector basis starting from the evidence gathered from each source of evidence and the mechanism for the basis computation should be able to unveil the most meaningful factors from the data. The main advantage is, from the one hand, the uniform modeling of diverse sources of evidence and, on the other hand, the greater generality of quantum probability than that of classical probability.
Our aim within QONTEXT is to employ QT for modeling RF within a complex and heterogenous feature space. 4
Music Information Retrieval (MIR) is an emerging research area that focus on providing new access methodologies and interaction paradigms to very large music collections. The wide availability of portable music players, paired by the increasing amount of digital music available to the end user, makes music access particularly related to context: music can be used as a background at work and study, as a distinctive for social groups, as a way to promote personal's image (especially within young generations). Moreover, it is generally acknowledge that neither textual metadata nor content-based descriptors alone can completely describe the music content and the user information need.
For these reasons, the application of QT to music access and retrieval is
particularly promising. On the one hand, it will allow to model in a uni ed
framework di erent sources of evidence, related both to the social role of music
{ i.e., genre, usage, user provided tags { and to the pure acoustic features { i.e.,
melody, rhythm, timbre. Some initial e orts to represent this complex
characteristics has been presented in [
Our goal within QONTEXT is to investigate a methodology for measuring the relevance of music items to a particular interaction context by merging different sources of evidence. 5
Data Mining is a wide area of research which involves di erent tasks such as, for example, clustering, categorization, and regression. The main idea behind all these di erent facets of data mining is the extraction of useful information from data, information which is often implicit or previously unknown. The question is how to model data and how to integrate the outcome of the analyses with visualization components which may help researchers to validate their models.
During the last decade, the research area of Quantum Clustering (QC) has
given a signi cant contribution in terms of \non-classical" approaches with
efcient clustering algorithms which take advantage of the Quantum Mechanics
principles. The work presented by [
Therefore, within QONTEXT, the aim is to explore a more user oriented version of QC. In particular, we want to study the interaction between the contexts of the search process and the clusters, and how the selection of one (or more) cluster by the user can generate a new spaces by means of visual representations of the clusters. 6
The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement N. 247590.