Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
Temporal classification: extending the classification paradigm to multivariate time series
Temporal classification: extending the classification paradigm to multivariate time series
Nearest-neighbor-preserving embeddings
ACM Transactions on Algorithms (TALG)
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Random projection trees and low dimensional manifolds
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Random Projections of Smooth Manifolds
Foundations of Computational Mathematics
Minimax-optimal classification with dyadic decision trees
IEEE Transactions on Information Theory
A tree-based regressor that adapts to intrinsic dimension
Journal of Computer and System Sciences
Similar image search with a tiny bag-of-delegates representation
Proceedings of the 20th ACM international conference on Multimedia
| Hi-index | 0.00 |
Recent theory work has found that a special type of spatial partition tree -- called a random projection tree -- is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination of theory and experiments, for a broader class of trees that includes k-d trees, dyadic trees, and PCA trees. Our motivation is to get a feel for (i) the kind of intrinsic low dimensional structure that can be empirically verified, (ii) the extent to which a spatial partition can exploit such structure, and (iii) the implications for standard statistical tasks such as regression, vector quantization, and nearest neighbor search.