Related papers: Multi-Dimensional Scaling on Groups

The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Classical multidimensional scaling (MDS) is a method for visualizing high-dimensional point clouds by mapping to low-dimensional Euclidean space. This mapping is defined in terms of eigenfunctions of a matrix of interpoint dissimilarities.…

This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…

Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods…

Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…

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)…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to generalize the standard inner product to symmetric bilinear forms…

In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…

Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…

Seismic datasets contain valuable information that originate from areas of interest in the subsurface; such seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden.…

The recent rapid growth of the dimension of many datasets means that many approaches to dimension reduction (DR) have gained significant attention. High-performance DR algorithms are required to make data analysis feasible for big and fast…

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…

The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…

The linear representation hypothesis states that language models (LMs) encode concepts as directions in their latent space, forming organized, multidimensional manifolds. Prior work has largely focused on identifying specific geometries for…

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…