Related papers: Linear Discriminant Analysis with Gradient Optimiz…
In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories…
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however,…
We consider the linear discriminant analysis problem in the high-dimensional settings. In this work, we propose PANDA(PivotAl liNear Discriminant Analysis), a tuning-insensitive method in the sense that it requires very little effort to…
In this paper, we propose a new variant of Linear Discriminant Analysis to overcome underlying drawbacks of traditional LDA and other LDA variants targeting problems involving imbalanced classes. Traditional LDA sets assumptions related to…
This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix $\O$ and the difference $\de$ of the mean vectors, we…
In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
Discriminant analysis (DA) is one of the most popular methods for classification due to its conceptual simplicity, low computational cost, and often solid performance. In its standard form, DA uses the arithmetic mean and sample covariance…
We develop a novel method for training of GANs for unsupervised and class conditional generation of images, called Linear Discriminant GAN (LD-GAN). The discriminator of an LD-GAN is trained to maximize the linear separability between…
This paper investigates the robust linear discriminant analysis (LDA) problem with elliptical distributions in high-dimensional data. We propose a robust classification method, named SSLDA, that is intended to withstand heavy-tailed…
Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the classic methods in high-dimensional settings. Asymptotic optimality has been established for some of these methods in high…
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…
Quadratic discriminant analysis (QDA) is a widely used classification technique. Based on a training dataset, each class in the data is characterized by an estimate of its center and shape, which can then be used to assign unseen…
Least-squares models such as linear regression and Linear Discriminant Analysis (LDA) are amongst the most popular statistical learning techniques. However, since their computation time increases cubically with the number of features, they…
Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…
Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…
Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making…
In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…
We explore the application of linear discriminant analysis (LDA) to the features obtained in different layers of pretrained deep convolutional neural networks (CNNs). The advantage of LDA compared to other techniques in dimensionality…