From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Manifold-adaptive dimension estimation
Proceedings of the 24th international conference on Machine learning
Dimension detection via slivers
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Intrinsic dimension estimation of manifolds by incising balls
Pattern Recognition
On local intrinsic dimension estimation and its applications
IEEE Transactions on Signal Processing
Feature fusion using locally linear embedding for classification
IEEE Transactions on Neural Networks
Estimating the indexability of multimedia descriptors for similarity searching
RIAO '10 Adaptivity, Personalization and Fusion of Heterogeneous Information
Diffusion maps as a framework for shape modeling
Computer Vision and Image Understanding
Minimum neighbor distance estimators of intrinsic dimension
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
IDEA: intrinsic dimension estimation algorithm
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
MBIA'12 Proceedings of the Second international conference on Multimodal Brain Image Analysis
Motion planning and reactive control on learnt skill manifolds
International Journal of Robotics Research
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We present a new method to estimate the intrinsic dimensionality of a submanifold M in Rd from random samples. The method is based on the convergence rates of a certain U-statistic on the manifold. We solve at least partially the question of the choice of the scale of the data. Moreover the proposed method is easy to implement, can handle large data sets and performs very well even for small sample sizes. We compare the proposed method to two standard estimators on several artificial as well as real data sets.