Random Projection Trees Revisited

The Random Projection Tree (RPTREE) structures proposed in [1] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTREE-MAX and the RPTREE-MEAN data structures. Our result for RPTREE-MAX gives a nearoptimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor s 2. We also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds have bounded Local Covariance Dimension. As a consequence we show that RPTREE-MEAN adapts to manifold dimension as well.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Aman Dhesi, Purushottam Kar
• Keywords: CORR 2010, Data Structure, Education, Partitioning Data Structures, Random Projection Tree