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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…
Classification methods that leverage the strengths of data from multiple sources (multi-view data) simultaneously have enormous potential to yield more powerful findings than two step methods: association followed by classification. We…
In this paper, we introduce a unified framework, inspired by classical regularization theory, for designing and analyzing a broad class of linear regression approaches. Our framework encompasses traditional methods like least squares…
Regression tasks in computer vision, such as age estimation or counting, are often formulated into classification by quantizing the target space into classes. Yet real-world data is often imbalanced -- the majority of training samples lie…
Probabilistic linear discriminant analysis (PLDA) has broad application in open-set verification tasks, such as speaker verification. A key concern for PLDA is that the model is too simple (linear Gaussian) to deal with complicated data;…
Big data applications, such as medical imaging and genetics, typically generate datasets that consist of few observations n on many more variables p, a scenario that we denote as p>>n. Traditional data processing methods are often…
Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…
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…
A novel approach for supervised classification analysis for high dimensional and flat data (more variables than observations) is proposed. We use the information of class-membership of observations to determine groups of observations…
Pairwise difference learning (PDL) has recently been introduced as a new meta-learning technique for regression. Instead of learning a mapping from instances to outcomes in the standard way, the key idea is to learn a function that takes…
The Engineers' Salary Prediction Challenge requires classifying salary categories into three classes based on tabular data. The job description is represented as a 300-dimensional word embedding incorporated into the tabular features,…
This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized…
Domain generalization (DG) aims to incorporate knowledge from multiple source domains into a single model that could generalize well on unseen target domains. This problem is ubiquitous in practice since the distributions of the target data…
Linear Discriminant Analysis (LDA) is commonly used for dimensionality reduction in pattern recognition and statistics. It is a supervised method that aims to find the most discriminant space of reduced dimension that can be further used…
Dominance-based Rough Set Approach (DRSA), as the extension of Pawlak's Rough Set theory, is effective and fundamentally important in Multiple Criteria Decision Analysis (MCDA). In previous DRSA models, the definitions of the upper and…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
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…
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…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…