Related papers: Quantum Dimensionality Reduction by Linear Discrim…

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.…

In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network…

This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension $p$ is of the same order as the…

Recently proposed L2-norm linear discriminant analysis criterion via the Bhattacharyya error bound estimation (L2BLDA) is an effective improvement of linear discriminant analysis (LDA) for feature extraction. However, L2BLDA is only…

Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…

Frozen pretrained image representations are widely used for transfer learning: a backbone is kept fixed, feature vectors are extracted, and a lightweight classifier is trained on top. This pipeline usually feeds the full feature vector to…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…

This paper investigates the effectiveness of using the Random Projection Ensemble (RPE) approach in Quadratic Discriminant Analysis (QDA) for ultrahigh-dimensional classification problems. Classical methods such as Linear Discriminant…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

Finding the similarities and differences between groups of datasets is a fundamental analysis task. For high-dimensional data, dimensionality reduction (DR) methods are often used to find the characteristics of each group. However, existing…

Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…

Linear Discriminant Analysis (LDA) is a widely-used supervised dimensionality reduction method in computer vision and pattern recognition. In null space based LDA (NLDA), a well-known LDA extension, between-class distance is maximized in…

Achieving a practical quantum speedup for deep neural networks (DNNs) remains a central yet elusive goal, hindered by the dual challenges of constructing deep architectures and the prohibitive overhead of data loading and measurement. We…

Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…