Related papers: Quadratic Discriminant Analysis by Projection

We present Learning-Driven Annealing (LDA), a framework that links individual quantum annealing evolutions into a global solution strategy to mitigate hardware constraints such as short annealing times and integrated control errors. Unlike…

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…

A lot of prognostication methodologies have been formulated for early detection of Polycystic Ovary Syndrome also known as PCOS using Machine Learning. PCOS is a binary classification problem. Dimensionality Reduction methods impact the…

We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density…

Unsupervised Domain Adaptation (UDA) aims to align the labeled source distribution with the unlabeled target distribution to obtain domain invariant predictive models. However, the application of well-known UDA approaches does not…

The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…

We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…

Recent advances show that two-dimensional linear discriminant analysis (2DLDA) is a successful matrix based dimensionality reduction method. However, 2DLDA may encounter the singularity issue theoretically and the sensitivity to outliers.…

Latent Dirichlet Allocation (LDA) is a three-level hierarchical Bayesian model for topic inference. In spite of its great success, inferring the latent topic distribution with LDA is time-consuming. Motivated by the transfer learning…

This work is a preliminary study on using Exploratory Landscape Analysis (ELA) for Quality Diversity (QD) problems. We seek to understand whether ELA features can potentially be used to characterise QD problems paving the way for automating…

Much like the classical Fisher linear discriminant analysis (LDA), the recently proposed Wasserstein discriminant analysis (WDA) is a linear dimensionality reduction method that seeks a projection matrix to maximize the dispersion of…

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and…

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified…

Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…

Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making…

Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks.…

Accurate image segmentation remains challenging, particularly in generating sharp, confident boundaries. While modern architectures have advanced the field, many of them still rely on standard loss functions like Cross-Entropy and Dice,…

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…