Automatic Choice of Dimensionality for PCA

By Tom Minka. Neural Information Processing Systems, 2000

655 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2d4ebfd71c8c69e30c3dd1b24d0332cab5de9137

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Citations in the corpus

Determining the number of components in a factor model from limited noisy data (2008, methodology): “Independently, methods to detect the number of sources have also been developed both in the statistics and signal processing communities, with emphasis on model selection criteria and information theoretic approaches, such as minimum description length (MDL), Bayesian model selection, Bayesian infor”
Bayesian Gaussian Process Latent Variable Model (2010, methodology): “The latent variables X in the standard GP-LVM and the means of the variational distribution in Bayesian GP-LVM were initialized through PCA.”
Non-linear matrix factorization with Gaussian processes (2009, background): “This is not analytically tractable, but the Laplace approximation (Bishop, 1999a; Minka, 2001) and variational approaches (Bishop, 1999b) have been proposed.”
Investigations into resting-state connectivity using independent component analysis (2005, unknown): “Within the PICA approach, we use the Laplace approximation to the posterior distribution of the model evidence that can be calculated efficiently from the adjusted eigenspectrum (Minka 2000; Beckmann & Smith 2004).”
Segmenting Motion Capture Data into Distinct Behaviors (2004, methodology): “A number of more sophisticated approaches for computing intrinsic dimensionality of the data are available [20, 12, 4], but this simple method worked well in our experiments.”
Tensorial extensions of independent component analysis for multisubject FMRI analysis (2005, methodology): “We use the Laplace approximation to the model order (Minka, 2000) to infer on the number of source processes R.”
Generalized Low Rank Models (2014, methodology): “. For example, if the model (X;Y) is dense, and the regularizer is invariant under orthogonal transformations (e.g., r(x) = kxk2 2 ), then the number of degrees of freedom is (m+ n)k k2 [TB99]. Minka [Min01] proposes a method based on the BIC to automatically choose the dimensionality in PCA, and ob”
Principal components of functional connectivity: A new approach to study dynamic brain connectivity during rest (2013, methodology): “Analytic methods to estimate the dimensionality currently employed for activity time courses, such as Laplace PCA (Minka, 2000), overestimate the dimensionality in the presence of correlated noise (Cordes and Nandy, 2006).”
Subspace Inference for Bayesian Deep Learning (2019, methodology): “One could also develop Bayesian PCA approaches (Minka, 2001) to automatically select the dimensionality of the subspace.”
Matrix factorization algorithms for the identification of muscle synergies: evaluation on simulated and experimental data sets. (2006, methodology): “This data set was previously used to examine the production of behaviors through combination of muscle synergies, using a variant of the nonnegative matrix factorization (NMF) algorithm (Lee and Seung 1999).”
Spontaneous brain activity and EEG microstates. A novel EEG/fMRI analysis approach to explore resting-state networks (2010, methodology): “The following data pre-processing was applied to the input data: masking of non-brain voxels; voxel-wise de-meaning of the data; normalization of the voxel-wise variance; pre-processed data were whitened and projected into a 13-dimensional subspace using probabilistic principal component analysis wh”