Related papers: Sparse Fisher's discriminant analysis with thresho…
For the constrained LiGME model, a nonconvexly regularized least squares estimation model, we present an iterative algorithm of guaranteed convergence to its globally optimal solution. The proposed algorithm can deal with two different…
Discriminant analysis, including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), is a popular approach to classification problems. It is well known that LDA is suboptimal to analyze heteroscedastic data, for…
We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p \times p$ covariance matrix $\Sigma$ exhibits a spiked eigenvalue structure and the vector $\zeta$, given by the difference…
In large-scale few-shot learning for classification problems, often there are a large number of classes and few high-dimensional observations per class. Previous model-based methods, such as Fisher's linear discriminant analysis (LDA),…
Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally…
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…
In this study, we introduce an innovative methodology aimed at enhancing Fisher's Linear Discriminant Analysis (LDA) in the context of high-dimensional data classification scenarios, specifically addressing situations where each feature…
The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…
Quadratic discriminant analysis (QDA) is a widely used method for classification problems, particularly preferable over Linear Discriminant Analysis (LDA) for heterogeneous data. However, QDA loses its effectiveness in high-dimensional…
Fisher Discriminant Analysis (FDA) is a subspace learning method which minimizes and maximizes the intra- and inter-class scatters of data, respectively. Although, in FDA, all the pairs of classes are treated the same way, some classes are…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
In this paper, we propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples in a weighted…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
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…
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…
The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that…
Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types.…
Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…