Related papers: Characteristics of Distance Matrices, the Second L…

Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…

In the present paper we focus on the coherence properties of general random Euclidean distance matrices, which are very closely related to the respective matrix completion problem. This problem is of great interest in several applications…

Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…

ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction…

In this paper, we give a characterization of distance matrices of distance-regular graphs to be invertible.

In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex…

The theory of graphons comes with the so-called cut norm and the derived cut distance. The cut norm is finer than the weak* topology (when considering the predual of $L^{1}$-functions). Dole\v{z}al and Hladk\'y [J. Combin. Theory Ser. B 137…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…

Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains were introduced as an expansion of time series motifs to identify the continuous evolving patterns…

Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions…

Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…

We study the problem of linear feature selection when features are highly correlated. Such settings pose two fundamental challenges. First, how should model similarity be defined? Simply counting features in common can be misleading: two…

The rigidity of a matrix describes the minimal number of entries one has to change to reduce matrix's rank to r. We give very simple combinatorial proof of the lower bound for the rigidity of Sylvester (special case of Hadamard) matrix that…

The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…

Determining the distance between a controllable system to the set of uncontrollable systems, namely, the controllability radius problem, has been extensively studied in the past. However, the opposite direction, that is, determining the…

Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…