Nonlinear Manifold Clustering By Dimensionality

Because of variable dependence, high dimensional data typically have much lower intrinsic dimensionality than the number of its variables. Hence high dimensional data can be expected to lie in (nonlinear) lower dimensional manifold. In this paper, we describe a nonlinear manifold clustering algorithm. By connecting data vectors with their neighbors in feature space, we construct a neighborhood graph from given set data vectors. Furthermore, geometrical invariance, namely dimensionality, are extracted from the neighborhood of vectors, and used to facilitate the clustering procedure. In addition, we discuss a latent model for data cluster descriptions and an EM algorithm to find such descriptions. Preliminary experiments illustrate that this new algorithm can be used to explore the nonlinear structure of data.