Robust Generalised Quadratic Discriminant Analysis

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…

A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis

In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of structural assumptions such as sparsity conditions on the discriminating direction and differential graph for the possible construction of consistent high-dimensional QDA rules. We then propose a classification algorithm called SDAR using constrained convex optimization under the sparsity assumptions. Both minimax upper and lower bounds are obtained and this cla…

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。

使用随机投影的超高维二次判别分析

Ultrahigh-dimensional Quadratic Discriminant Analysis Using Random Projections

本文提出将随机投影集成方法应用于二次判别分析，解决超高维分类中维度灾难问题，并在理论上和实验中证明其分类性能与计算效率的优势。

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 …

Discriminant functions arising from selection distributions: theory and simulation

The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of distributions indexed by skewness/shape parameters produce more exibility in the modelling of different applications. Consequently, the results show a more realistic interpretation for these problems. For these reasons, the aim of this paper is to investigate the effects of the generalisation of a discrimination function method through the class of multivariate …

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 …