Related papers: Frequency Based Index Estimating the Subclusters' …
The Sen index and Sen-Shorrocks-Thon (SST) index are widely used measures of poverty indices. Developing reliable inference for these measures enables us to compare these measures in different populations of interest in an effective way. It…
We study the problem of testing for community structure in networks using relations between the observed frequencies of small subgraphs. We propose a simple test for the existence of communities based only on the frequencies of three-node…
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…
We study the problem of testing for structure in networks using relations between the observed frequencies of small subgraphs. We consider the statistics \begin{align*} T_3 & =(\text{edge frequency})^3 - \text{triangle frequency}\\ T_2 &…
The increasing penetration of renewable energy leads to a continuous reduction in system inertia, for which conventional synchronization criteria based solely on frequency consistency can no longer accurately capture the coupled dynamics of…
Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…
Co-clustering is a specific type of clustering that addresses the problem of finding groups of objects without necessarily considering all attributes. This technique has shown to have more consistent results in high-dimensional sparse data…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is…
Coherent groups of generators, i.e., machines with perfectly correlated rotor angles, play an important role in power system stability analysis. This paper introduces a real-time methodology based on hierarchical clustering techniques for…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In…
Simplets, constituting elementary units within simplicial complexes (SCs), serve as foundational elements for the structural analysis of SCs. Previous efforts have focused on the exact count or approximation of simplet count rather than…
We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…
The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-fit tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing…
Cognitive radio that supports a secondary and opportunistic access to licensed spectrum shows great potential to dramatically improve spectrum utilization. Spectrum sensing performed by secondary users to detect unoccupied spectrum bands,…
In network analysis, developing a unified theoretical framework that can compare methods under different models is an interesting problem. This paper proposes a partial solution to this problem. We summarize the idea of using separation…
In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network density and degree heterogeneity under…
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general…