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In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…

Linear discriminant analysis (LDA), a traditional classification tool, suffers from limitations such as sensitivity to noise and computational challenges when dealing with non-invertible within-class scatter matrices. Traditional stepwise…

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…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

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…

Local Fisher discriminant analysis is a localized variant of Fisher discriminant analysis and it is popular for supervised dimensionality reduction method. lfda is an R package for performing local Fisher discriminant analysis, including…

Canonical Correlation Analysis (CCA) is a method for feature extraction of two views by finding maximally correlated linear projections of them. Several variants of CCA have been introduced in the literature, in particular, variants based…

We revisit vertex discriminant analysis (VDA) from the perspective of proximal distance algorithms. By specifying sparsity sets as constraints that directly control the number of active features, VDA is able to fit multiclass classifiers…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

This paper proposes a robust high-dimensional sparse canonical correlation analysis (CCA) method for investigating linear relationships between two high-dimensional random vectors, focusing on elliptical symmetric distributions. Traditional…

High-dimensional data requires scalable algorithms. We propose and analyze three scalable and related algorithms for semi-supervised discriminant analysis (SDA). These methods are based on Krylov subspace methods which exploit the data…

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…

Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned…

Quantum Machine Learning (QML) hasn't yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved…

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…

Data augmentation (DA) techniques aim to increase data variability, and thus train deep networks with better generalisation. The pioneering AutoAugment automated the search for optimal DA policies with reinforcement learning. However,…

We propose a novel statistical method for testing the results of anomaly detection (AD) under domain adaptation (DA), which we call CAD-DA -- controllable AD under DA. The distinct advantage of the CAD-DA lies in its ability to control the…

We describe a puzzle involving the interactions between an optimization of a multivariate quadratic function and a "plug-in" estimator of a spiked covariance matrix. When the largest eigenvalues (i.e., the spikes) diverge with the…

Real-world optimization often demands diverse, high-quality solutions. Quality-Diversity (QD) optimization is a multifaceted approach in evolutionary algorithms that aims to generate a set of solutions that are both high-performing and…

Transfer learning aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Since the source and the target domains are usually from different distributions, existing methods mainly focus on…