We call these random projection trees (Figure 1, right), or RP trees for short, and we show the following. Pick any cell C in the RP tree. If the data in C have ...
We present a simple variant of the k-d tree which automatically adapts to intrinsic low dimensional structure in data without having to explicitly learn this ...
If the data in RD has intrinsic dimension d, then an RP tree halves the diameter in just d levels: no dependence on D. Pick coordinate direction. Split at ...
The k-d tree (Bentley, 1975) is a spatial data structure that partitions RD into hyperrectangular cells. It is built in a recursive manner, splitting along ...
Oct 19, 2010 · Title:Random Projection Trees Revisited ... Our final result shows that low-dimensional manifolds have bounded Local Covariance Dimension.
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We present a simple variant of the k-d tree which automatically adapts to intrinsic low dimensional structure in data without having to explicitly learn ...
Jan 16, 2024 · ... An rpForest is a collection of random projection trees (rpTree). rpTrees use random directions to partition the data points into tree nodes ...
The RPTREE-MAX structure adapts to the doubling dimension of data (see definition below). Since low-dimensional manifolds have low doubling dimension (see [1] ...
Our final result shows that low-dimensional manifolds possess bounded Local Covariance Dimension. As a consequence we show that RPTree-Mean adapts to ...
The Random Projection Tree (RPTREE) structures proposed in [1] are space par- titioning data structures that automatically adapt to various notions of ...