Multilinear subspace analysis of image ensembles

By M. Alex O. Vasilescu, Demetri Terzopoulos. 2003

460 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

In Computational Mechanics

In Signal Processing

Citations in the corpus

Tensor representation in high-frequency financial data for price change prediction (2017, methodology): “With advances in mathematical tools and algorithms dealing with tensor input, many multilinear discriminant techniques as well as tensor regression have been proposed for image and video classiﬁcation problems such as [18], [19], [20], [21], [22], [23], [24], [25], [26], [27].”
Multilinear Discriminant Analysis for Face Recognition (2007, methodology): “In the real world, the extracted feature of an object often has some specialized structures and such structures are in the form of second or even higher order tensors [23].”
Discriminant Locally Linear Embedding With High-Order Tensor Data (2008, methodology): “technique and its extensions [40]–[43].”
Learning a Spatially Smooth Subspace for Face Recognition (2007, methodology): “Vasilescu and Terzopoulos have proposed a novel face representation algorithm called Tensorface [ 25 ].”
A randomized algorithm for a tensor-based generalization of the singular value decomposition (2007, methodology): “In addition, tensors provide a natural way to represent many large and complex data sets [34,33,24,27,36,45,5,46,47].”
A Newton-Grassmann Method for Computing the Best Multilinear Rank-(r1, r2, r3) Approximation of a Tensor (2009, background): “The Hessian (4.21) is still given in a coordinate-free form.”
Locality Preserving Projections (2003, methodology): “Vasilescu and Terzopoulos have proposed a novel face representation algorithm called Tensorface [76].”
General Tensor Discriminant Analysis and Gabor Features for Gait Recognition (2007, methodology): “One solution is to reduce the dimensionality of the feature space by using the principal components analysis (PCA) [26], [16] or the multilinear subspace analysis (MSA) [ 39 ], but unfortunately, some discriminant information is discarded by PCA and MSA.”
Unsupervised Multiway Data Analysis: A Literature Survey (2009, methodology): “and N-mode Orthogonal Iteration in [51].”
Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification (2014, methodology): “Index Terms—Linear discriminant analysis (LDA), multilinear discriminant analysis (MDA), direct general tensor discriminant analysis (DGTDA), constrained multilinear discriminant analysis (CMDA), pattern classification, higher-order tensor Ç”
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors (2009, background): “In part to illustrate the efficiency of these algorithms, this paper also addresses the following two related problems about the multilinear approximations of tensors and symmetric tensors, which are also important problems in their own right with various applications in analytical chemistry [52], b”
Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme (2011, background): “Fields of application of higher-order tensors also include chemometrics [42], biomedical signal processing [31, 15, 16, 4], telecommunications [40, 41, 10], scientific computing [7, 6, 20, 35], and image processing [48].”
A Survey of Face Recognition Techniques (2009, methodology): “Some recent advances in PCA-based algorithms include multi-linear subspace analysis [90], symmetrical PCA [91], two-dimensional PCA [92, 93], eigenbands [94], adaptively weighted sub-pattern PCA [95], weighted modular PCA [96], Kernel PCA [97, 98] and diagonal PCA [99].”
Tensor Decompositions and Applications (2009, background): “Alternatively, the k th frontal slice of a third-order tensor, X :: k , may be denoted more compactly as X k .”
Audio-driven facial animation by joint end-to-end learning of pose and emotion (2017, background): “This was later generalized in closely related topics to multilinear [Vasilescu and Terzopoulos 2003; Wampler et al. 2007] and non-linear models [Elgammal and Lee 2004], as well as independent component analysis [Cao et al. 2003].”
Discriminant analysis with tensor representation (2005, methodology): “Before describing the Discriminant Tensor Criterion, we review the terminologies on tensor operations [3][4][11][12].”