Mixtures of Probabilistic Principal Component Analyzers

By Michael E. Tipping, Charles M. Bishop. 1999

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

A Generative Process for Contractive Auto-Encoders (2012, background): “ssian model, where the variances in directions orthogonal to the manifold are small and constant (across all these directions), and this can be extended to non-linear structures with a mixture model (Tipping and Bishop, 1999) or the kernel trick (Scholkopf et al., 1998). In many manifold learning al”
Bayesian group factor analysis with structured sparsity (2016, methodology): “With an isotropic noise assumption, Σ = Iσ 2 , this model has a probabilistic principal components analysis interpretation (Roweis, 1998; Tipping and Bishop, 1999b).”
Sparse subspace clustering (2009, methodology): “Statistical approaches, such as Mixtures of Probabilistic PCA (MPPCA) [24], Multi-Stage Learning (MSL) [22], or [13], assume that the distribution of the data inside each subspace is Gaussian and alternate between data clustering and subspace estimation by applying Expectation Maximization (EM) to a”
Multilinear Analysis of Image Ensembles: TensorFaces (2002, methodology): “Multilinear analysis subsumes mixtures of probabilistic PCA or view-based models [15,11] when one uses a different choice of basis functions.”
Functional data clustering: a survey (2013, unknown): “…( mclust package Banﬁeld and Raftery 1993) and two methods dedicated to the clustering of high-dimensional data— HDDC (Bouveyron et al. 2007) and MixtPPCA (Tipping and Bishop 1999)—both available in the HDclassif package (Bergé et al. 2012), – these methods are applied: on the FPCA scores, with…”
Realtime performance-based facial animation (2011, methodology): “To adequately capture the nonlinear structure of the dynamic expression space while still enabling realtime performance, we represent the prior term p ( x , X n ) as a Mixtures of Probabilistic Principal Component Analyzers (MPPCA) [Tipping and Bishop 1999b].”
Local distance preservation in the GP-LVM through back constraints (2006, methodology): “More recently, PCA has also been motivated as the maximum likelihood solution to a linear Gaussian latent variable model (Tipping & Bishop, 1999).”
Model-Based Clustering (2016, background): “Tipping and Bishop (1997, 1999) introduce the closely related mixture of probabilistic principal component analyzers (MPPCA) model, where theΨg matrix in each component is isotropic, i.e., Ψg = ψgIp, so that Σg = ΛgΛ′g + ψgIp.”
Principal Manifolds and Probabilistic Subspaces for Visual Recognition (2002, methodology): “More sophisticated techniques for subspace modeling of disjoint manifolds exist [30], [ 43 ], [4] which would, for example, be required if variations in pose and lighting were to modeled.”
An overview of deep learning based methods for unsupervised and semi-supervised anomaly detection in videos (2018, methodology): “A reﬁned version was implemented and evaluated in [37] which evaluated the atomic movement patterns using a probabilistic PCA [38], over rectangular regions over the image domain.”
Advanced Lectures on Machine Learning (2004, methodology): “rank(A) = rank(A ) = rank(AA ) = rank(A A) ≡ k [12].”
Recognizing faces with PCA and ICA (2003, methodology): “Although they have not yet been applied to face recognition, Tipping and Bishop provide an EM algorithm for optimizing mixture models of PCA subspaces [ 39 ], and Lee et al. provide a similar algorithm for optimizing mixtures of ICA subspaces [28].”
A tutorial on task-parameterized movement learning and retrieval (2015, methodology): “The corresponding examples for standard mixture models can also be found in demo MFA01.m and demo MPPCA01.m .”
Inferring 3D structure with a statistical image-based shape model (2003, methodology): “As described below, we rely on the mixture of probabilistic principal components analyzers (PPCA) formulation of [15] to model prior densities.”
SMEM Algorithm for Mixture Models (1998, methodology): “Recently, more sophisticated mixture density models such as mixtures of latent variable models (e.g., probabilistic PCA and factor analysis) have been proposed to approximate the underlying data manifold (Hinton, Dayan, & Revow, 1997; Tipping & Bishop, 1997; Ghahramani & Hinton, 1997).,Note that a”
Products of Gaussians and Probabilistic Minor Component Analysis (2002, methodology): “…a mixture of products of gaussian pancakes), permits using PoGP in classiﬁcation tasks (if each PoGP model deﬁnes a class-conditional density), and leads to a number of other advantages over nonprobabilistic MCA models (see the discussion of advantages of PPCA over PCA in Tipping & Bishop, 1999).”