Two-Dimensional Linear Discriminant Analysis

By Jieping Ye, Ravi Janardan, Qi Li. 2004

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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].”
Subspace Learning Based on Tensor Analysis (2005, methodology): “Recently, multilinear algebra, the algebra of higher-order tensors, was applied for analyzing the multifactor structure of image ensembles [10, 11, 12].”
Maximum Neighborhood Margin Discriminant Projection for Classification (2014, methodology): “Among the DR techniques, principal component analysis (PCA) [2, 3], linear discriminant analysis (LDA) [3, 4], locality preserving projection (LPP) [5, 6], and their kernelized and tensorized variants [7–18] are the most representative and well-known algorithms.”
Tensor Subspace Analysis (2005, methodology): “Recently, multilinear algebr a, the algebra of higher-order tensors, was applied for analyzing the multifactor structu re of image ensembles [9], [11], [12].”
Linear discriminant analysis: A detailed tutorial (2017, unknown): “As shown, the dimension of the original data matrix ( X ∈ R N × M ) is reduced by projecting it onto the lower dimensional space of LDA ( V k ∈ R M × k ) as denoted in Equation (9) [81].”
Learning Discriminant Face Descriptor (2014, methodology): “As indicated in [39], one loop of iteration is Fig.”
Asymmetric Transitivity Preserving Graph Embedding (2016, background): “Besides, there are many other graph embedding algorithms for dimensionality reduction, including non-linear [33, 27], linear [15, 6], kernlized [28] and tensorized [36] algorithms.”
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.”
Matrix variate regressions and envelope models (2016, background): “E( Y )= µ + # 1 X # T 2 = µ +( # 2 # # 1 )vec( X ). This rank-one formulation and its variants have been studied in recent work for modeling a univariate response with matrix-valued predictors (e.g., Ye et al., 2004; Hung and Wang, 2013; Zhou et al., 2013). Our approach encompasses the univariate re”
Analysis of Dimensionality Reduction Techniques on Big Data (2020, unknown): “LDA is another popular dimensionality reduction approach for pre-processing step in data mining and machine learning applications [39].”
A survey of multilinear subspace learning for tensor data (2011, unknown): “Like GLRAM and GPCA, the 2D LDA (2DLDA) introduced in [65] solves for two linear transformations that project an image to a low-dimensional matrix, but with a different objective criterion.”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, unknown): “To reduce the overlap between models of sub-classes, Wan et al. [150] proposed Separability-oriented SDA (SSDA) that uses hierarchical clustering for dividing a class into separability-oriented criteria.”
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”
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction (2007, unknown): “Recently, a number of algorithms [25], [26], [27], [29], [30], [31] have been proposed to conduct dimensionality reduction on objects encoded as matrices or tensors of arbitrary order.”
Learning a Spatially Smooth Subspace for Face Recognition (2007, methodology): “Recently there have been a lot of interest in extending the ordinary vector-based subspace learning approaches to tensor space [5, 7, 13, 26, 27].”
Locality Preserving Projections (2003, methodology): “Recently, multilinear algebra, the algebra of higher-order tensors, was applied for analyzing the multifactor structure of image ensembles [76], [84], [39].”
General Tensor Discriminant Analysis and Gabor Features for Gait Recognition (2007, background): “GTDA is motivated by the successes of the twodimensional LDA (2DLDA) [43] in face recognition.”
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)(2)PCA) [442], and Generalized Low Rank Approximations of Matrices (”
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.”