Related papers: Metric/Nonmetric Elastic MDS

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient…

The increasing number of protein-based metamaterials demands reliable and efficient theoretical and computational methods to study the physicochemical properties they may display. In this regard, we develop a simulation strategy based on…

We present a series of statements about scaling entropy, a metric invariant of dynamical systems proposed by A. M. Vershik in the late 90's. We show that it is a metric invariant indeed and calculate it in several special cases.

In this paper, we analyze the nontrivial zeros of the Riemann zeta-function using the multidimensional scaling (MDS) algorithm and computational visualization features. The nontrivial zeros of the Riemann zeta-function as well as the…

With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…

Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…

This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures are a class of similarity measures that can compensate for…

We address the channel estimation (CE) problem in reconfigurable intelligent surface (RIS) aided orthogonal frequency-division multiplexing (OFDM) systems by proposing a dual-structure and multi-dimensional transformations (DS-MDT)…

In psychological and educational computer-based multidimensional tests, latent speed, a rate of the amount of labor performed on the items with respect to time, may also be multidimensional. To capture the multidimensionality of latent…

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number…

In very recent decades, Scale Elasticity (SE), as a quantitative characterization of Returns to Scale (RTS), has been an attractive research issue in convex DEA models. However, we show that the existing Scale Elasticity (SE) measure does…

Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…

Conventional compressed sensing (CS) algorithms typically apply a uniform sampling rate to different image blocks. A more strategic approach could be to allocate the number of measurements adaptively, based on each image block's complexity.…

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…

The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…

Establishing dense correspondences between multiple images is a fundamental task in many applications. However, finding a reliable correspondence in multi-modal or multi-spectral images still remains unsolved due to their challenging…

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDEs) with random data, where the random coefficient is parametrized by means of a countable…