相关论文: Revisiting the Nowosi\'o{\l}ka skull with RMaCzek

Inspired by the MaCzek Visual Basic program we provide an R package, RMaCzek, that produces Czekanowski's diagram. Our package permits any seriation and distance method the user provides. In this paper we focus on the OLO and QAP_2SUM…

Visualizing data through Czekanowski's diagram has as its aim the illustration of the relationships between objects. Often, obvious clusters of observations are directly visible. However, it is not straightforward to precisely delineate…

There are many distance-based methods for classification and clustering, and for data with a high number of dimensions and a lower number of observations, processing distances is computationally advantageous compared to the raw data matrix.…

Labeled Markov Chains (or LMCs for short) are useful mathematical objects to model complex probabilistic languages. A central challenge is to compare two LMCs, for example to assess the accuracy of an abstraction or to quantify the effect…

The Topological Data Analysis Ball Mapper (TDABM) algorithm of Dlotko (2019) provides a model free means to visualize multi-dimensional data. The visualizations are abstract two-dimensional representations of covers of the dataset. To…

Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…

Introduced by Callahan and Kosaraju back in 1995, the concept of well-separated pair decomposition (WSPD) has occupied a special significance in computational geometry when it comes to solving distance problems in $d$-space. We present an…

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…

A novel method for robust estimation, called Graph-Cut RANSAC, GC-RANSAC in short, is introduced. To separate inliers and outliers, it runs the graph-cut algorithm in the local optimization (LO) step which is applied when a so-far-the-best…

Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs -- a 2014 survey by Aouchiche and Hansen on…

Over the last 25 years Monte Carlo programs were being developped in Cracow in the group guided by Prof. Stanislaw Jadach. Many of those programs became standard in their application domains. In the following let us review some aspects of…

In cognitive neuroscience research, Representational Dissimilarity Matrices (RDMs) are often incomplete because pairwise similarity judgments cannot always be exhaustively collected as the number of pairs rapidly increases with the number…

Analyzing the sub-level sets of the distance to a compact sub-manifold of R d is a common method in TDA to understand its topology. The distance to measure (DTM) was introduced by Chazal, Cohen-Steiner and M{\'e}rigot in [7] to face the…

Parcellations are fundamental tools in neuroanatomy, allowing researchers to place functional imaging and molecular data within a structural context in the brain. Visualizing these parcellations is critical to guide biological understanding…

Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…

I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…

Visual defect detection plays an important role in intelligent industry. Patch based methods consider visual images as a collection of image patches according to positions, which have stronger discriminative ability for small defects in…

We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…

Reduced ordering based vector filters have proved successful in removing long-tailed noise from color images while preserving edges and fine image details. These filters commonly utilize variants of the Minkowski distance to order the color…

Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…