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Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
In network data analysis, summary statistics of a network can provide us with meaningful insight into the structure of the network. The average clustering coefficient is one of the most popular and widely used network statistics. In this…
Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
Real-world networks often come with side information that can help to improve the performance of network analysis tasks such as clustering. Despite a large number of empirical and theoretical studies conducted on network clustering methods…
Community detection in weighted networks has been a popular topic in recent years. However, while there exist several flexible methods for estimating communities in weighted networks, these methods usually assume that the number of…
Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible,…
For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description…
Graph clustering is essential in graph analysis for revealing structural patterns and node communities. Despite recent advances in self-supervised contrastive learning that have improved clustering via structural and attribute signals,…
The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with…
In this paper, we propose a self-learning mutual selection model to characterize weighted evolving networks. By introducing the self-learning probability $p$ and the general mutual selection mechanism, which is controlled by the parameter…
One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…
We propose efficient algorithms for two key tasks in the analysis of large nonuniform networks: uniform node sampling and cluster detection. Our sampling technique is based on augmenting a simple, but slowly mixing uniform MCMC sampler with…
We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large…
Complex-valued neural networks (CVNNs) are nonlinear filters used in the digital signal processing of complex-domain data. Compared with real-valued neural networks~(RVNNs), CVNNs can directly handle complex-valued input and output signals…
Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…
Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…