Related papers: Local biplots for multi-dimensional scaling, with …

Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…

This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of…

A new family of $n$-dimensional solutions of the Jacobi identities is characterized. Such a family is very general, thus unifying in a common framework many different well-known Poisson systems seemingly unrelated. This unification is not…

The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a…

Characterization of topology and dimensionality of spectral feature spaces provides insight into information content. The objective of this study is to characterize topology and spectral dimensionality of spectral mixing spaces representing…

Large language models (LLMs) make next-token predictions based on clues present in their context, such as semantic descriptions and in-context examples. Yet, elucidating which prior tokens most strongly influence a given prediction remains…

The standard formulation of Jacobi manifolds in terms of differential operators on line bundles, although effective at capturing most of the relevant geometric features, lacks a clear algebraic interpretation similar to how Poisson algebras…

The relation between two Morse functions defined on a common domain can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the functions are aligned. Both the Jacobi set itself as…

The local histogram transform of an image is a data cube that consists of the histograms of the pixel values that lie within a fixed neighborhood of any given pixel location. Such transforms are useful in image processing applications such…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

We introduce a novel data-driven approach aimed at designing high-quality shape deformations based on a coarse localized input signal. Unlike previous data-driven methods that require a global shape encoding, we observe that…

This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…

The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…

3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…

Boxplots and related visualization methods are widely used exploratory tools for taking a first look at collections of univariate variables. In this note an extension is provided that is specifically designed to detect and display…

Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing…

In order to find previously unknown subgroups in biomedical data and generate testable hypotheses, visually guided exploratory analysis can be of tremendous importance. In this paper we propose a new dissimilarity measure that can be used…

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…