A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Representing Edge Models via Local Principal Component Analysis
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Nonlinear Intrinsic Dimensionality Computations
IEEE Transactions on Computers
Representation of Nonlinear Data Surfaces
IEEE Transactions on Computers
An Algorithm for Determining the Topological Dimensionality of Point Clusters
IEEE Transactions on Computers
Modeling Stroke Diagnosis with the Use of Intelligent Techniques
SETN '08 Proceedings of the 5th Hellenic conference on Artificial Intelligence: Theories, Models and Applications
REDUS: finding reducible subspaces in high dimensional data
Proceedings of the 17th ACM conference on Information and knowledge management
Local Metric Learning on Manifolds with Application to Query---Based Operations
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Intrinsic dimension estimation of manifolds by incising balls
Pattern Recognition
On the Quantization Error in SOM vs. VQ: A Critical and Systematic Study
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
A new approach to discover interlacing data structures in high-dimensional space
Journal of Intelligent Information Systems
Stastical Estimation of the Intrinsic Dimensionality of a Noisy Signal Collection
IEEE Transactions on Computers
On local intrinsic dimension estimation and its applications
IEEE Transactions on Signal Processing
Fuzzy PCA-guided robust k-means clustering
IEEE Transactions on Fuzzy Systems
Cumulative global distance for dimension reduction in handwritten digits database
VISUAL'07 Proceedings of the 9th international conference on Advances in visual information systems
SSPS: A Semi-Supervised Pattern Shift for Classification
Neural Processing Letters
Automatic configuration of spectral dimensionality reduction methods
Pattern Recognition Letters
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Using correlation dimension for analysing text data
ICANN'10 Proceedings of the 20th international conference on Artificial neural networks: Part I
Manifold learning for object tracking with multiple motion dynamics
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Mining interlacing manifolds in high dimensional spaces
Proceedings of the 2011 ACM Symposium on Applied Computing
Non-manifold surface reconstruction from high-dimensional point cloud data
Computational Geometry: Theory and Applications
Locally Defined Principal Curves and Surfaces
The Journal of Machine Learning Research
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
Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA
Pattern Recognition Letters
Parameterless isomap with adaptive neighborhood selection
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Intrinsic dimensionality maps with the PCASOM
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Intrinsic dimension induced similarity measure for clustering
ADMA'11 Proceedings of the 7th international conference on Advanced Data Mining and Applications - Volume Part II
Hybrid Linear Modeling via Local Best-Fit Flats
International Journal of Computer Vision
A multi-manifold semi-supervised Gaussian mixture model for pattern classification
Pattern Recognition Letters
Intrinsic dimension estimation via nearest constrained subspace classifier
Pattern Recognition
Towards a space reduction approach for efficient structural shape optimization
Structural and Multidisciplinary Optimization
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An algorithm for the analysis of multivariant data is presented along with some experimental results. The basic idea of the method is to examine the data in many small subregions, and from this determine the number of governing parameters, or intrinsic dimensionality. This intrinsic dimensionality is usually much lower than the dimensionality that is given by the standard Karhunen-Loève technique. An analysis that demonstrates the feasability of this approach is presented.