Intrinsic Dimension Estimation by Maximum Likelihood in Probabilistic PCA

Keywords

Dimension (graph theory), Principal component analysis, Consistency (knowledge bases), Probabilistic logic, Intrinsic dimension

References

• Statistical Factor Analysis and Related MethodsAlexander Basilevsky — 1994
• A global geometric framework for nonlinear dimensionality reduction.Joshua B. Tenenbaum, Vin de Silva, John Langford — 2000
• An Algorithm for Finding Intrinsic Dimensionality of DataKeinosuke Fukunaga, D.R. Olsen — 1971
• Data dimensionality estimation methods: a surveyFrancesco Camastra — 2003
• Asymptotic Inference for EigenvectorsDavid E. Tyler — 1981
• Nonlinear dimensionality reduction by locally linear embedding.Sam T. Roweis, Lawrence K. Saul — 2000
• Representation and separation of signals using nonlinear PCA type learningJuha Karhunen, J. Joutsensalo — 1994
• Latent Variable Models and Factor AnalysisStan Lipovetsky — 2001
• Intrinsic dimension estimation of manifolds by incising ballsMingyu Fan, Hong Qiao, Bo Zhang — 2009
• Products of Gaussians and Probabilistic Minor Component AnalysisChristopher K. I. Williams, Felix Agakov — 2002
• Extreme Components AnalysisMax Welling, Christopher Williams, Felix Agakov — 2003
• An Intrinsic Dimensionality Estimator from Near-Neighbor InformationKarl Pettis, Thomas A. Bailey, Anil K. Jain — 1979
• Estimating the Intrinsic Dimension of Data with a Fractal-Based MethodFrancesco Camastra, Alessandro Vinciarelli — 2002
• Intrinsic Dimensionality Estimation With Optimally Topology Preserving MapsJörg Brüske, Gerald Sommer — 1998
• An Evaluation of Intrinsic Dimensionality EstimatorsPeter J. Verveer, Robert P. W. Duin — 1995
• Probabilistic Principal Component AnalysisMichael E. Tipping, Chris Bishop — 1999
• Intrinsic Dimension Estimation Using Packing NumbersBalázs Kégl — 2002
• Automatic Choice of Dimensionality for PCAThomas P. Minka — 2000
• The Scree Test For The Number Of Factors.Raymond B. Cattell — 1966
• High-Dimensional Discriminant AnalysisCharles Bouveyron, Stéphane Girard, Cordelia Schmid — 2005

Cited by

• Classification et modélisation de sorties fonctionnelles de codes de calcul : application aux calculs thermo-hydrauliques accidentels dans les réacteurs à eau pressurisés (REP)Benjamin Auder — 2011
• Model-based clustering of time series in group-specific functional subspacesCharles Bouveyron, Julien Jacques — 2011
• Vector quantization based approximate spectral clustering of large datasetsKadim Taşdemi̇r — 2012
• Gaussian mixture models for the classification of high‐dimensional vibrational spectroscopy dataJulien Jacques, Charles Bouveyron, Stéphane Girard — 2010
• HDclassif: an R Package for Model-Based Clustering and Discriminant Analysis of High-Dimensional DataLaurent Bergé, Charles Bouveyron, Stéphane Girard — 2012
• Contributions à l'apprentissage statistique en grande dimension, adaptatif et sur données atypiquesCharles Bouveyron — 2012
• Robust clustering of high-dimensional dataCharles Bouveyron, Anastasios Bellas — 2012
• A Proposition for Fixing the Dimensionality of a Laplacian Low-rank Approximation of any Binary Data-matrixAlain Lelu, Martine Cadot, Université De Lorraine — 2013
• Espace intrinsèque d'un graphe et recherche de communautésAlain Lelu, Martine Cadot — 2010
• Relevant Eigen-Subspace of a Graph : A Randomization Test.Alain Lelu — 2011
• Slimming down a high-dimensional binary datatable: relevant eigen-subspace and substantial contentA. Lelu — 2010
• Modeling and AlgorithmsS. Suthaharan — 2016
• Project-Team mistis Modelling and Inference of Complex and Structured Stochastic SystemsGrenoble-Rhône-Alpes — 2009
• Characteristics of Local Intrinsic Dimensionality (LID) in Subspaces: Local Neighbourhood AnalysisTahrima Hashem, Lida Rashidi, J. Bailey — 2019
• II Model-based Clustering of Time Series in Group-speci c Functional Subspaces ∗Bouveyron, Jacques — 2012

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