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Applications such as face recognition that deal with high-dimensional data need a mapping technique that introduces representation of low-dimensional features with enhanced discriminatory power and a proper classifier, able to classify…
Recognising detailed facial or clothing attributes in images of people is a challenging task for computer vision, especially when the training data are both in very large scale and extremely imbalanced among different attribute classes. To…
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications…
Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…
The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…
Compressed domain image classification performs classification directly on compressive measurements acquired from the single-pixel camera, bypassing the image reconstruction step. It is of great importance for extending high-speed object…
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build…
Data quality is a crucial factor in large language models training. While prior work has shown that models trained on smaller, high-quality datasets can outperform those trained on much larger but noisy or low-quality corpora, systematic…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
Causal representation learning (CRL) models aim to transform high-dimensional data into a latent space, enabling interventions to generate counterfactual samples or modify existing data based on the causal relationships among latent…
In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…
High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…
This article concerns the dimension reduction in regression for large data set. We introduce a new method based on the sliced inverse regression approach, called cluster-based regularized sliced inverse regression. Our method not only keeps…
Existing facial image super-resolution (SR) methods focus mostly on improving artificially down-sampled low-resolution (LR) imagery. Such SR models, although strong at handling artificial LR images, often suffer from significant performance…
The development of computing has made credit scoring approaches possible, with various machine learning (ML) and deep learning (DL) techniques becoming more and more valuable. While complex models yield more accurate predictions, their…
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…
Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete…
Quadratic discriminant analysis (QDA) is a simple method to classify a subject into two populations, and was proven to perform as well as the Bayes rule when the data dimension p is fixed. The main purpose of this paper is to examine the…