Related papers: Cyclic Polygon Plots
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
Deep learning models have achieved significant success in various image related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an efficient approach that…
We propose a generalization of the method of cyclic projections, which uses the lengths of projection steps carried out in the past to learn about the geometry of the problem and decides on this basis which projections to carry out in the…
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
In this paper, we present Hi-D maps, a novel method for the visualization of multi-dimensional categorical data. Our work addresses the scarcity of techniques for visualizing a large number of data-dimensions in an effective and…
The describing function method is a useful tool for the qualitative analysis of limit cycles in the stability analysis of nonlinear systems. This method is inherently approximate; therefore, it should be used for a fast qualitative analysis…
A plethora of dimension reduction methods have been developed to visualize high-dimensional data in low dimensions. However, different dimension reduction methods often output different and possibly conflicting visualizations of the same…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…
Hypergraph visualization has many applications in network data analysis. Recently, a polygon-based representation for hypergraphs has been proposed with demonstrated benefits. However, the polygon-based layout often suffers from excessive…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Evaluating the accuracy of dimensionality reduction (DR) projections in preserving the structure of high-dimensional data is crucial for reliable visual analytics. Diverse evaluation metrics targeting different structural characteristics…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data. However, reasoning dynamically about the results of a dimensionality reduction is difficult. Dimensionality-reduction algorithms use complex…
Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for…
We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with…
In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…