Related papers: The Analysis from Nonlinear Distance Metric to Ker…

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be…

The development of data-dependent heuristics and representations for biological sequences that reflect their evolutionary distance is critical for large-scale biological research. However, popular machine learning approaches, based on…

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve…

Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…

This paper addresses to the problem of finding the (minimum) Euclidean distance between two linear varieties. This problem is, usually, solved minimising a target function. We propose a novel approach: to use the Moore-Penrose generalised…

The skeleton is an essential shape characteristic providing a compact representation of the studied shape. Its computation on the image grid raises many issues. Due to the effects of discretization, the required properties of the skeleton -…

Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…

The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…

Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…

Detecting poorly textured objects and estimating their 3D pose reliably is still a very challenging problem. We introduce a simple but powerful approach to computing descriptors for object views that efficiently capture both the object…

We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…

This paper presents a kernelized version of the t-SNE algorithm, capable of mapping high-dimensional data to a low-dimensional space while preserving the pairwise distances between the data points in a non-Euclidean metric. This can be…

Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising…

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Riemannian manifolds have been widely employed for video representations in visual classification tasks including video-based face recognition. The success mainly derives from learning a discriminant Riemannian metric which encodes the…

Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…

In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can…