Related papers: Metric/Nonmetric Elastic MDS
Multidimensional scaling (MDS) is a class of projective algorithms traditionally used in Euclidean space to produce two- or three-dimensional visualizations of datasets of multidimensional points or point distances. More recently however,…
The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
Given an undirected graph G, the effective resistance r(s,t) measures the dissimilarity of node pair s,t in G, which finds numerous applications in real-world problems, such as recommender systems, combinatorial optimization, molecular…
In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments…
Given a matrix $D$ describing the pairwise dissimilarities of a data set, a common task is to embed the data points into Euclidean space. The classical multidimensional scaling (cMDS) algorithm is a widespread method to do this. However,…
Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty,…
In the field of 3D dynamic scene reconstruction, how to balance model convergence rate and rendering quality has long been a critical challenge that urgently needs to be addressed, particularly in high-precision modeling of scenes with…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
In various industrial contexts, estimating the distribution of unobserved random vectors Xi from some noisy indirect observations H(Xi) + Ui is required. If the relation between Xi and the quantity H(Xi), measured with the error Ui, is…
In many models used in engineering and science, material properties are uncertain or spatially varying. For example, in geophysics, and porous media flow in particular, the uncertain permeability of the material is modelled as a random…
Powder of magnesium diboride was hot isostatically pressed using three qualitatively different cycles: cooling under pressure (DMCUP), "standard" cycle with pressure and temperature reduced simultaneously and isothermal presure release.…
A high-order multi-time-step (MTS) scheme for the bond-based peridynamic (PD) model, an extension of classical continuous mechanics widely used for analyzing discontinuous problems like cracks, is proposed. The MTS scheme discretizes the…
This note introduces a doubly robust (DR) estimator for regression discontinuity (RD) designs. RD designs provide a quasi-experimental framework for estimating treatment effects, where treatment assignment depends on whether a running…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
This study investigates fall risk prediction in older adults using various machine learning models trained on accelerometric, non-accelerometric, and combined data from 146 participants. Models combining both data types achieved superior…
The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS…
In this paper, the parallel multi-extended state observers (ESOs) based active disturbance rejection control approach is proposed to achieve desired tracking performance by automatically selecting the estimation values leading to the least…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…