Related papers: A Combinatorial Necessary and Sufficient Condition…
Our goal is to find a necessary and sufficient condition on the consensus over a random network, generated by i.i.d. stochastic matrices. We show that the consensus problem in three different convergence modes (almost surely, in…
We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices…
This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…
A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…
A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…
Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…
Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units.…
The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…
This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite-dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest…
This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…
Many community detection algorithms are inherently stochastic, leading to variations in their output depending on input parameters and random seeds. This variability makes the results of a single run of these algorithms less reliable.…
We show that the limiting state vector in the differential model of consensus seeking with an arbitrary communication digraph is obtained by multiplying the eigenprojection of the Laplacian matrix of the model by the vector of initial…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first…
The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in…