Quantum Latent Semantic Analysis

The main goal of this paper is to explore latent topic analysis (LTA), in the context of quantum information retrieval. LTA is a valuable technique for document analysis and representation, which has been extensively used in information retrieval and machine learning. Different LTA techniques have been proposed, some based on geometrical modeling (such as latent semantic analysis, LSA) and others based on a strong statistical foundation. However, these two different approaches are not usually mixed. Quantum information retrieval has the remarkable virtue of combining both geometry and probability in a common principled framework. We built on this quantum framework to propose a new LTA method, which has a clear geometrical motivation but also supports a well-founded probabilistic interpretation. An initial exploratory experimentation was performed on three standard data sets. The results show that the proposed method outperforms LSA on two of the three datasets. These results suggests that the quantum-motivated representation is an alternative for geometrical latent topic modeling worthy of further exploration.