Generalized Low Rank Approximations of Matrices

By Jieping Ye. Machine-mediated learning, 2004

605 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/6152a4d175af3f58a80f34e3e5d9963ff0f9bb60

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In Computational Mechanics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography (2013, background): “As mentioned before, low-rank modeling is an important tool not only for compressing [50] and analyzing [30], [51] large data sets but also for regularization and the incorporation of prior information [9], [52].”
Image Denoising Using the Higher Order Singular Value Decomposition (2013, neutral): “The solution is given by an iterative minimization (starting from random initial conditions) presented in [26], [39].”
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction (2007, methodology): “2DPCA [29] is a simplified second-order tensorization of PCA and only optimizes one projection direction, while [30] and [25] are full formulations of the second-order tensorization of PCA.”
MPCA: Multilinear Principal Component Analysis of Tensor Objects (2008, methodology): “[22] and thus they can be considered special cases of MPCA when second-order tensors are considered.”
Multilinear Discriminant Analysis for Face Recognition (2007, methodology): “[27], [28] presented more general forms of 2-D PCA and 2-D LDA by simultaneously computing two subspaces.”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, background): “Several basic two-dimensional subspace formulations can be found in literature such as two-dimensional PCA (2dPCA) [421], two-dimensional SVD (2dSVD) [82], two-dimensional LDA (2dLDA) [433], two-directional two-dimensional PCA ((2d)2PCA) [442], and Generalized Low Rank Approximations of Matrices (GL”
Factor models for matrix-valued high-dimensional time series (2016, methodology): “Similar models as model (1) have been proposed and studied when conducting principal component analysis on matrix-valued data (e.g. Paatero and Tapper, 1994; Yang et al., 2004; Ye, 2005; Ding and Ye, 2005; Zhang and Zhou, 2005; Crainiceanu et al., 2011; Wang et al., 2016).”
Latent Semantic Tensor Indexing for Community-based Question Answering (2013, background): “They regard documents as matrices, or the second order tensors to generate a low rank approximations of matrices (Ye, 2005).”
Unsupervised Multiway Data Analysis: A Literature Survey (2009, background): “[76], which indeed corresponds to a Tucker2 model [13].”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “In our whole network compression scheme, we apply Tucker-2 decomposition, which is also known as GLRAM (Ye, 2005), from the second convolutional layer to the ﬁrst fully connected layers.”
Beyond streams and graphs: dynamic tensor analysis (2006, background): “Ding and Ye [7] proposed an approximation of [31].”
A survey of multilinear subspace learning for tensor data (2011, methodology): “Other MSL applications include handwritten digit recognition [27, 57], image compression [1, 27, 64], image/video retrieval [1, 87], and object categorization and recognition [46].”
Collaborative matrix factorization with multiple similarities for predicting drug-target interactions (2013, background): “First, under no regularization terms, several variants of SVD, such as the generalized low-rank approximation model (GLRAM) [30] and the probabilistic matrix factorization (PMF) model [21], are proposed, being applied to information retrieval, particularly recommender systems [17].”
Salient Object Detection via Structured Matrix Decomposition (2017, methodology): “Finally, we estimate the rank of the feature matrix, denoted by r̂, according to [72], [73]:”
Discriminant Locally Linear Embedding With High-Order Tensor Data (2008, methodology): “4) As in other previous work [6], [10]–[12], [29], [37], [53], [54], several parameters need to be decided beforehand.”