Convergence of an EM-type algorithm for spatial clustering
Pattern Recognition Letters
Using the fractal dimension to cluster datasets
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Combined central and subspace clustering for computer vision applications
ICML '06 Proceedings of the 23rd international conference on Machine learning
Robust Statistical Estimation and Segmentation of Multiple Subspaces
CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
Nonlinear Manifold Clustering By Dimensionality
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inferring Local Homology from Sampled Stratified Spaces
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Biometric authentication: a machine learning approach
Biometric authentication: a machine learning approach
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Generalized principal component analysis (GPCA)
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Segmentation of Multivariate Mixed Data via Lossy Data Coding and Compression
IEEE Transactions on Pattern Analysis and Machine Intelligence
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A framework for the regularized and robust estimation of non-uniform dimensionality and density in high dimensional noisy data is introduced in this work. This leads to learning stratifications, that is, mixture of manifolds representing different characteristics and complexities in the data set. The basic idea relies on modeling the high dimensional sample points as a process of translated Poisson mixtures, with regularizing restrictions, leading to a model which includes the presence of noise. The translated Poisson distribution is useful to model a noisy counting process, and it is derived from the noise-induced translation of a regular Poisson distribution. By maximizing the log-likelihood of the process counting the points falling into a local ball, we estimate the local dimension and density. We show that the sequence of all possible local countings in a point cloud formed by samples of a stratification can be modeled by a mixture of different translated Poisson distributions, thus allowing the presence of mixed dimensionality and densities in the same data set. With this statistical model, the parameters which best describe the data, estimated via expectation maximization, divide the points in different classes according to both dimensionality and density, together with an estimation of these quantities for each class. Theoretical asymptotic results for the model are presented as well. The presentation of the theoretical framework is complemented with artificial and real examples showing the importance of regularized stratification learning in high dimensional data analysis in general and computer vision and image analysis in particular.