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We investigate statistical properties of Cluster-Weighted Modeling, which is a framework for supervised learning originally developed in order to recreate a digital violin with traditional inputs and realistic sound. The analysis is carried…

The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show…

The idea underlying the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. This correspondence between clusters and dense regions…

The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barab{\'a}si-Albert network, and the neuronal network of the C. elegans. Through the use of a…

Weight-sharing quantization has emerged as a technique to reduce energy expenditure during inference in large neural networks by constraining their weights to a limited set of values. However, existing methods for weight-sharing…

Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…

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 learned weights of a neural network have often been considered devoid of scrutable internal structure. In this paper, however, we look for structure in the form of clusterability: how well a network can be divided into groups of neurons…

Performing analytic of household load curves (LCs) has significant value in predicting individual electricity consumption patterns, and hence facilitate developing demand-response strategy, and finally achieve energy efficiency improvement…

We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…

The cluster-weighted model (CWM) is a mixture model with random covariates which allows for flexible clustering and density estimation of a random vector composed by a response variable and by a set of covariates. In this class of models,…

Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…

Network data are observed in various applications where the individual entities of the system interact with or are connected to each other, and often these interactions are defined by their associated strength or importance. Clustering is a…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…

The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…

The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this…

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…