Randomized algorithms
Matrix computations (3rd ed.)
Journal of the ACM (JACM)
Shape Dimension and Intrinsic Metric from Samples of Manifolds
Discrete & Computational Geometry
Provable dimension detection using principal component analysis
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Intrinsic dimensionality estimation of submanifolds in Rd
ICML '05 Proceedings of the 22nd international conference on Machine learning
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Manifold-adaptive dimension estimation
Proceedings of the 24th international conference on Machine learning
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Integral estimation from point cloud in d-dimensional space: a geometric view
Proceedings of the twenty-fifth annual symposium on Computational geometry
| Hi-index | 0.00 |
We present a novel approach to estimate the dimension m of an unknown manifold M ⊂ Rd with positive reach from a set of point samples P ⊂ M. It works by analyzing the shape of simplices formed by point samples. Suppose that P is drawn from M according to a Poisson process with an unknown parameter λ. Let k be some fixed positive integer. When λ is large enough, we prove that the dimension can be correctly output in O(kd|P|1+1/k) time with probability greater than 1-2-k. We experimented with a practical variant and showed that its performance is competitive with several previous methods.