Matrix Linear Discriminant Analysis

Hu, Wei; Shen, Weining; Zhou, Hua; Kong, Dehan

doi:10.1080/00401706.2019.1610069

Cited by 19 publications

(13 citation statements)

References 24 publications

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“…They introduced nuclear norm penalized regression methods to estimate

M

, which can achieve parsimonious models with enhanced interpretability. The low‐rank assumption has been commonly used in neuroimaging applications; see Zhu et al (2014); Zhou & Li (2014); Kong et al (2020); Yu et al (2020); Hu et al (2020b); Hu et al (2020a) for examples. In the current article, we also assume that

M

is of low rank.…”

Section: Model Setup and Estimation Proceduresmentioning

confidence: 99%

“…However, OLS may perform suboptimally as it does not utilize the information that the entries of Y i are related, especially when both p and T diverge with the sample size n. Recently, Yuan et al (2007), and Chen, Dong, & Chan (2013) proposed reduced rank regression models by assuming the low rankness of M. They introduced nuclear norm penalized regression methods to estimate M, which can achieve parsimonious models with enhanced interpretability. The low-rank assumption has been commonly used in neuroimaging applications; see Zhu et al (2014); Zhou & Li (2014); Kong et al (2020); Yu et al (2020); Hu et al (2020b); Hu et al (2020a) for examples. In the current article, we also assume that M is of low rank.…”

Section: Introductionmentioning

confidence: 99%

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Multivariate functional response low‐rank regression with an application to brain imaging data

Ding

Zhang

et al. 2021

Can J Statistics

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We propose a multivariate functional response low-rank regression model with possible high-dimensional functional responses and scalar covariates. By expanding the slope functions on a set of sieve bases, we reconstruct the basis coefficients as a matrix. To estimate these coefficients, we propose an efficient procedure using nuclear norm regularization. We also derive error bounds for our estimates and evaluate our method using simulations. We further apply our method to the Human Connectome Project neuroimaging data to predict cortical surface motor task-evoked functional magnetic resonance imaging signals using various clinical covariates to illustrate the usefulness of our results.

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“…They introduced nuclear norm penalized regression methods to estimate

M

M

is of low rank.…”

Section: Model Setup and Estimation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate functional response low‐rank regression with an application to brain imaging data

Ding

Zhang

et al. 2021

Can J Statistics

Self Cite

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“…The proposed feature extractors are explained in detail in this subsection  2D-PCA Principal Component Analysis(PCA) [11] is widely used as a dimensionality reduction feature representation. In this paper, 2D-PCA is proposed and its implementation is explained hereafter.…”

Section: B Feature Extractionmentioning

confidence: 99%

“…According to [11], the above function can also be rewritten as shown below in equation (9). Where function (, ) denotes the matrix trace operation.…”

Section: B Feature Extractionmentioning

confidence: 99%

Performance Analysis of Robust 2D-PCA and 2D-LDA Feature Descriptors on SVM

Gupta¹

2020

IJMTST

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Facialexpressions are the most intuitive way of communicating non-verbal messages. This type of communication provides effective response and feedback from the speaker to listener and vice-versa. In this paper robust macro facial expression recognition techniques are presented. 2D-PCA and 2D-LDA are robust geometric feature descriptors presented in this paper capable of cancelling noise and extracting maximum spatial features from image samples with unstable illumination condition which leads to correct classification of results. Experiments are carried out separately on both feature descriptors using Cohn Kanade (CK+) dataset, MMI dataset, and Japanese Female Facial Expressions (JAFFE) database for analysis. The experimental results are evaluated and their performance compared using Support vector machine (SVM) classifier with three kernels; linear, polynomial and radial basis function (RBF). The results from the proposed methods are also compared with existing novel methods and it is found out that the results from the proposed methods perform significantly well.

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“…[22] developed a generalized scalar-on-image regression models via total variation regularization, which can keep the piecewise smooth nature of imaging data. [23] proposed an efficient nuclear norm penalized estimation method for matrix linear discriminant analysis.…”

Section: Introductionmentioning

confidence: 99%

Logistic regression with image covariates via the combination of L1 and Sobolev regularizations

Zhang

2020

PLoS ONE

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The use of image covariates to build a classification model has lots of impact in various fields, such as computer science, medicine, and so on. The aim of this paper is to develop an estimation method for logistic regression model with image covariates. We propose a novel regularized estimation approach, where the regularization is a combination of L 1 regularization and Sobolev norm regularization. The L 1 penalty can perform variable selection, while the Sobolev norm penalty can capture the shape edges information of image data. We develop an efficient algorithm for the optimization problem. We also establish a nonasymptotic error bound on parameter estimation. Simulated studies and a real data application demonstrate that our proposed method performs very well.

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Matrix Linear Discriminant Analysis

Cited by 19 publications

References 24 publications

Multivariate functional response low‐rank regression with an application to brain imaging data

Multivariate functional response low‐rank regression with an application to brain imaging data

Performance Analysis of Robust 2D-PCA and 2D-LDA Feature Descriptors on SVM

Logistic regression with image covariates via the combination of L1 and Sobolev regularizations

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