Intrinsic Dimensionality Estimation With Optimally Topology Preserving Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Provable dimension detection using principal component analysis
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Intrinsic dimensionality estimation of submanifolds in Rd
ICML '05 Proceedings of the 22nd international conference on Machine learning
Manifold-adaptive dimension estimation
Proceedings of the 24th international conference on Machine learning
An Algorithm for Finding Intrinsic Dimensionality of Data
IEEE Transactions on Computers
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Nonlinear Dimensionality Reduction with Local Spline Embedding
IEEE Transactions on Knowledge and Data Engineering
Neighborhood MinMax projections
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Information Sciences: an International Journal
Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA
Pattern Recognition Letters
An Intrinsic Dimensionality Estimator from Near-Neighbor Information
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
IEEE Transactions on Multimedia
Regression Reformulations of LLE and LTSA With Locally Linear Transformation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Estimating intrinsic dimension of data is an important problem in feature extraction and feature selection. It provides an estimation of the number of desired features. Principal Components Analysis (PCA) is a powerful tool in discovering the dimension of data sets with a linear structure; it, however, becomes ineffective when data have a nonlinear structure. In this paper, we propose a new PCA-based method to estimate the embedding dimension of data with nonlinear structures. Our method works by first finding a minimal cover of the data set, then performing PCA locally on each subset in the cover to obtain local intrinsic dimension estimations and finally giving the estimation result as the average of the local estimations. There are two main innovations in our method. (1) A novel noise filtering procedure is applied in the PCA procedure for local intrinsic dimension estimation. (2) A minimal cover is constructed over the whole data set. Because of these two innovations, our method is fast, robust to noise and outliers, converges to a stable estimation with a wide range of sub-region sizes and can be used in the incremental sense, where the subregion refers to the local approximation of the distributed manifold. Experiments on synthetic and image data sets show effectiveness of the proposed method.