document: Dimension induced clustering It is commonly assumed that high-dimensional datasets contain points most of which are located in low-dimensional manifolds . Detection of low-dimensional clusters is an extremely useful task for performing operations such as clustering and classification , however , it is a challenging computational problem . In this paper we study the problem of finding subsets of points with low intrinsic dimensionality . Our main contribution is to extend the definition of fractal correlation dimension , which measures average volume growth rate , in order to estimate the intrinsic dimensionality of the data in local neighborhoods . We provide a careful analysis of several key examples in order to demonstrate the properties of our measure . Based on our proposed measure , we introduce a novel approach to discover clusters with low dimensionality . The resulting algorithms extend previous density based measures , which have been successfully used for clustering . We demonstrate the effectiveness of our algorithms for discovering low-dimensional m-flats embedded in high dimensional spaces , and for detecting low-rank sub-matrices .
doc_bio_tags: O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O