Document clustering based on diffusion maps and a comparison of the k-means performances in various spaces

A great challenge of text mining arises from the increasingly large text datasets and the high dimensionality associated with natural language. In this research, a systematic study is conducted in the context of the document clustering, using the recently introduced diffusion framework and some characteristics of the singular value decomposition. This study is three-fold. First, we propose to construct a diffusion kernel based on the cosine distance. Second, we compare the performances of the k-means algorithm in four different vector spaces: Salton space, latent semantic analysis space, diffusion space based on the cosine distance, and diffusion space based on the Euclidian distance. Third, we undertake a statistical study of the k-means algorithm in the LSA space and the diffusion space based on the cosine distance. In most of our experiments, k-means in diffusion space, based on the cosine distance performs better. In addition, the running time in this space is negligible compared to the time needed for k-means in Salton space.