Abstract-Many high-dimensional data sets of practical interest exhibit a varying complexity in different parts of the data space. This is the case, for example, of databases of images containing many samples of a few textures of different complexity. Such phenomena can be modeled by assuming that the data lies on a collection of manifolds with different intrinsic dimensionalities. In this extended abstract, we introduce a method to estimate the local dimensionality associated with each point in a data set, without any prior information about the manifolds, their quantity and their sampling distributions. The proposed method uses a global dimensionality estimator based on knearest neighbor (k-NN) graphs, together with an algorithm for computing neighborhoods in the data with similar topological properties.

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