Related papers: Spectral methods and cluster structure in correlat…
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…
Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena,…
Financial markets are complex adaptive systems characterized by collective behavior and abrupt regime shifts, particularly during crises. This paper studies time-varying dependencies in Nordic equity markets and examines whether…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
We investigate serial correlation, periodic, aperiodic and scaling behaviour of eigenmodes, i.e. daily price fluctuation time-series derived from eigenvectors, of correlation matrices of shares listed on the Johannesburg Stock Exchange…
The time proximity of trades across stocks reveals interesting topological structures of the equity market in the United States. In this article, we investigate how such concurrent cross-stock trading behaviors, which we denote as…
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…
This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all…
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance.…
The study on architecture and parameter characteristics remains the hot topic in the research of large language models. In this paper we concern with the characteristics of weight which are used to analyze the correlations and differences…
Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
The eigendecomposition of the coupling matrix of large biological networks is central to the study of the dynamics of these networks. For neural networks, this matrix should reflect the topology of the network and conform with Dale's law…
Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and…
We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…
Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no…
Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for different thresholds and diverse periods of time, so that it is then possible to analyze how…
With the random matrix theory, we study the spatial structure of the Chinese stock market, American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation…