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Recently, clustering moving object trajectories kept gaining interest from both the data mining and machine learning communities. This problem, however, was studied mainly and extensively in the setting where moving objects can move freely…
The statement in the title was proved in \cite{Cao23} by introducing dominant sets of seeds, which are analogs of torsion classes in representation theory. In this note, we observe a short proof by the existence of consistent cluster…
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…
Recursive max-linear vectors model causal dependence between node variables by a structural equation model, expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph (DAG) and some exogenous…
Without any assumptions about data generation, multiple causal models may explain our observations equally well. To avoid selecting a single arbitrary model that could result in unsafe decisions if it does not match reality, it is therefore…
We explore if it is possible to learn a directed acyclic graph (DAG) from data without imposing explicitly the acyclicity constraint. In particular, for Gaussian distributions, we frame structural learning as a sparse matrix factorization…
Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…
This manuscript studies nodal clustering in graphs having multivariate attributes at each node. The framework includes node-specific priors for low-dimensional representations, coupled with a neural decoder that bridges observed attributes…
Let $G$ be a generalized dicyclic group with identity $1$. An inverse closed subset $S$ of $G\setminus\{1\}$ is called minimal if $\langle S\rangle=G$ and there exists some $s\in S$ such that $\langle S\setminus\{s,s^{-1}\} \rangle\neq G$.…
Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been…
Let $lct(G)$ be the minimum cardinality of a set of vertices that intersects every longest cycle of a 2-connected graph $G$. We show that $lct(G)\leq k-1$ if $G$ is a partial $k$-tree and that $lct(G)\leq \max \{1, {\omega(G){-}3}\}$ if $G$…
The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In…
The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge…
Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures…
Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample…
Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…
Although many algorithms have been designed to construct Bayesian network structures using different approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function…
Most single-molecule transport experiments produce large and stochastic datasets containing a wide range of behaviors, presenting both a challenge to their analysis, but also an opportunity for discovering new physical insights. Recently,…
Social science theories often postulate causal relationships among a set of variables or events. Although directed acyclic graphs (DAGs) are increasingly used to represent these theories, their full potential has not yet been realized in…
We propose an alternative proof concerning necessary and sufficient conditions to split the problem of searching for d-separators and building the skeleton of a DAG into small problems for every node of a separation tree T. The proof is…