Related papers: Spectral methods and cluster structure in correlat…

In this brief review, we critically examine the recent work done on correlation-based networks in financial systems. The structure of empirical correlation matrices constructed from the financial market data changes as the individual stock…

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…

In many applications, weighted networks are constructed based on time series data: each time series is associated to a vertex and edge weights are given by pairwise correlations. The result is a network whose edge dependency structure…

Neural networks have been used successfully in a variety of fields, which has led to a great deal of interest in developing a theoretical understanding of how they store the information needed to perform a particular task. We study the…

We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including…

We study correlations of a set of stocks selected from both the New York and London stock exchanges. Results are displayed using both Random Matrix Theory approach and the graphical visualisation of the Minimal Spanning Tree. For the set of…

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often…

The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust…

We propose a flexible framework for defining the 1-Laplacian of a hypergraph that incorporates edge-dependent vertex weights. These weights are able to reflect varying importance of vertices within a hyperedge, thus conferring the…

We investigated the topological properties of stock networks through a comparison of the original stock network with the estimated stock network from the correlation matrix created by the random matrix theory (RMT). We used individual…

Trained attention layers exhibit striking and reproducible spectral structure of the weights, including low-rank collapse, bulk deformation, and isolated spectral outliers, yet the origin of these phenomena and their implications for…

Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices,…

A number of recent works have concentrated on a few statistical properties of complex networks, such as the clustering, the right-skewed degree distribution and the community, which are common to many real world networks. In this paper, we…

We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal)…

We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…

In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis. We present a set of concentration inequalities…

A dynamic factor model with a mixture distribution of the loadings is introduced and studied for multivariate, possibly high-dimensional time series. The correlation matrix of the model exhibits a block structure, reminiscent of correlation…