投影二次判别分析

充分维数缩减中的精度矩阵正则化以改进二次判别分类

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification

针对小样本下精度矩阵估计不稳定导致分类欠佳的问题，提出多类别且与分布无关的稳定化充分维数缩减（SSDR）方法，利用精度矩阵收缩估计量稳定投影矩阵，在保留QDA分类信息下提升分类精度。

基于投影寻踪的线性判别盲估计的大样本性质

Large-Sample Properties of Blind Estimation of the Linear Discriminant Using Projection Pursuit

本文从渐近角度研究不使用类别标签的投影寻踪线性判别盲估计，针对偏度、峰度及其凸组合三种投影指标推导中心极限定理，证明其极限协方差矩阵与LDA成比例，并揭示在组间充分分离且规模平衡时投影寻踪可达到与LDA相同的效率。

多组二次判别分析 via 投影

Multi-Group Quadratic Discriminant Analysis via Projection

本文提出MGQDA方法，通过投影高维数据以实现多组分类，具有非线性和异质性协方差结构的处理能力，并在模拟和基因表达应用中展示了其优越的预测性能。

A Direct Approach for Sparse Quadratic Discriminant Analysis

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, when the dimensionality is relatively large. To address this, we propose a novel procedure named DA-QDA for QDA in analyzing high-dimensional data. Formulated in a simple and coherent framework, DA-QDA aims to directly estimate the key quantities in the Bayes discriminant function including quadratic interactions and a linear index of the variables for classif…

Sensible Functional Linear Discriminant Analysis

The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient approach to identify the optimal LDA projections in addition to managing the noninvertibility issue of the covariance operator emerging from this extension. A conditional expectation technique is employed to tackle the challenge of projecting sparse data to the LDA directions. We study the asymptotic properties of the proposed estimators and show that asymptoti…

Sparse quadratic classification rules via linear dimension reduction

We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn't require estimation of precision matrices and scales linearly with the number of measurements, making it especially attractive for the use on high-dimens…

具有CP低秩判别结构的高维张量分类

High-Dimensional Tensor Classification with CP Low-Rank Discriminant Structure

针对高维张量分类挑战，提出基于线性判别分析并利用CP低秩结构的框架，结合随机复合PCA初始化与迭代投影算法，在互相关噪声下实现全局收敛，并证明了极小化极大最优误分类率。

Robust Generalised Quadratic Discriminant Analysis

Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which generalizes the QDA and the minimum Mahalanobis distance (MMD) classifiers to discriminate between populations with underlying elliptically symmetric distributions competes quite favorably with the QDA classifier when it is optimal and performs much better when QDA fails under non-Normal underlying distributions, e.g. Cauchy distribution. However, the classifi…

Cellwise robust regularized discriminant analysis

Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in high-dimension and cover the path between the two extremes QDA and LDA have been …

高维潜因子模型中的最优判别分析

Optimal Discriminant Analysis in High-Dimensional Latent Factor Models

针对高维分类的两步投影流程，本文构建潜变量模型提供理论依据，提出数据驱动选主成分数量的高效分类器，证明其超额风险收敛速率达极小极大最优，且特征维数可超样本量，实验验证了理论与方法的有效性。

Discussion on "Random-projection ensemble classification" by T. Cannings and R. Samworth

Discussion on "Random-projection ensemble classification" by T. Cannings and R. Samworth. We believe that the proposed approach can find many applications in economics such as credit scoring (e.g. Altman (1968)) and can be extended to more general type of classifiers. In this discussion we would like to draw authors attention to the copula-based discriminant analysis (Han et al. (2013) and He et al. (2016)).

Discriminant Analysis with Adaptively Pooled Covariance

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using Bayes theorem. With LDA, we estimate a single, pooled covariance matrix, while for QDA we estimate a separate covariance matrix for each group. Rarely do we believe in a homogeneous covariance structure between groups, but often there is insufficient data to separately estimate covariance matrices. We propose L1- PDA, a regularized model which …