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We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
The persistence probability is a statistical index that has been proposed to detect one or more communities embedded in a network. Even though its definition is straightforward, e.g, the probability that a random walker remains in a group…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Graph clustering has been popularly studied in recent years. However, most existing graph clustering methods focus on node-level clustering, i.e., grouping nodes in a single graph into clusters. In contrast, graph-level clustering, i.e.,…
Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…
The well-known clustering algorithm of Miller, Peng, and Xu (SPAA 2013) is useful for many applications, including low-diameter decomposition and low-energy distributed algorithms. One nice property of their clustering, shown in previous…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…
In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal…
One way of getting a better view of data is using frequent patterns. In this paper frequent patterns are subsets that occur a minimal number of times in a stream of itemsets. However, the discovery of frequent patterns in streams has always…
We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental statistics and the drive to compete with the…
Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one…
We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…
In the last two decades many random graph models have been proposed to extract knowledge from networks. Most of them look for communities or, more generally, clusters of vertices with homogeneous connection profiles. While the first models…
Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the…
Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…
Easy access and vast amount of data, especially from long period of time, allows to divide social network into timeframes and create temporal social network. Such network enables to analyse its dynamics. One aspect of the dynamics is…
We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…
We propose a novel reduced-order methodology to describe complex multi-frequency fluid dynamics from time-resolved snapshot data. Starting point is the Cluster-based Network Model (CNM) thanks to its fully automatable development and human…
When a category $\mathcal{C}$ satisfies certain conditions, we define the notion of rank invariant for arbitrary poset-indexed functors $F:\mathbf{P} \rightarrow \mathcal{C}$ from a category theory perspective. This generalizes the standard…