Sparse latent semantic analysis

Latent semantic analysis (LSA), as one of the most pop-ular unsupervised dimension reduction tools, has a wide range of applications in text mining and information re-trieval. The key idea of LSA is to learn a projection matrix that maps the high dimensional vector space representations of documents to a lower dimensional la-tent space, i.e. so called latent topic space. In this pa-per, we propose a new model called Sparse LSA, which produces a sparse projection matrix via the `1 regu-larization. Compared to the traditional LSA, Sparse LSA selects only a small number of relevant words for each topic and hence provides a compact representation of topic-word relationships. Moreover, Sparse LSA is computationally very efficient with much less memory usage for storing the projection matrix. Furthermore, we propose two important extensions of Sparse LSA: group structured Sparse LSA and non-negative Sparse LSA. We conduct experiments on several benchmark datasets and compare Sparse LSA and its extensions with several widely used methods, e.g. LSA, Sparse Coding and LDA. Empirical results suggest that Sparse LSA achieves similar performance gains to LSA, but is more efficient in projection computation, storage, and also well explain the topic-word relationships.