Related papers: Visualization of Manifold-Valued Elements by Multi…

Human decision-making often relies on visual information from multiple perspectives or views. In contrast, machine learning-based object recognition utilizes information from a single image of the object. However, the information conveyed…

Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…

We reexamine the the classical multidimensional scaling (MDS). We study some special cases, in particular, the exact solution for the sub-space formed by the 3 dimensional principal coordinates is derived. Also we give the extreme case when…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained…

Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…

The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…

Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…

We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…

Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…

Dimensionality Reduction (DR) techniques such as t-SNE and UMAP are popular for transforming complex datasets into simpler visual representations. However, while effective in uncovering general dataset patterns, these methods may introduce…

This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction…

Most existing person re-identification algorithms either extract robust visual features or learn discriminative metrics for person images. However, the underlying manifold which those images reside on is rarely investigated. That raises a…

In biomedical science, a set of objects or persons can often be described by multiple distinct sets of features obtained from different data sources or modalities (called "multi-view data"). Classical machine learning methods ignore the…

We explore the design of visualizations for values spanning multiple orders of magnitude; we call them Orders of Magnitude Values (OMVs). Visualization researchers have shown that separating OMVs into two components, the mantissa and the…

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…

3D city models - which represent in 3 dimensions the geometric elements of a city - are increasingly used for an intended wide range of applications. Such uses are made possible by using semantically enriched 3D city models and by…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

We propose new methodologies in multi-dimensional unfolding in dense environments, and show that incorporating auxiliary observables can significantly improve performance. Our approach builds on the ML-based OmniFold algorithm, which we…

The quest for deeper understanding of biological systems has driven the acquisition of increasingly larger multidimensional image datasets. Inspecting and manipulating data of this complexity is very challenging in traditional visualization…