Related papers: Spectral methods and cluster structure in correlat…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
In this paper, we explore the detection of clusters of stocks that are in synergy in the Indian Stock Market and understand their behaviour in different circumstances. We have based our study on high frequency data for the year 2014. This…
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the…
To construct dispersion relations for diffusion or oscillation processes on random networks, it is necessary to obtain effective length scales for the eigenvectors of a graph Laplacian matrix, whose eigenvalues represent inverse time…
In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter $\beta>1$, of the basic Toeplitz matrix-sequence…
Understanding non-linear relationships among financial instruments has various applications in investment processes ranging from risk management, portfolio construction and trading strategies. Here, we focus on interconnectedness among…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
This article investigates the correlation structure of the global crude oil market using the daily returns of 71 oil price time series across the world from 1992 to 2012. We identify from the correlation matrix six clusters of time series…
Ownership concentration is not a scalar. For a normalized investor-stock matrix $A$, it has three irreducible layers: concentration across investors, concentration across stocks, and dependence in the joint assignment of investors to…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…
Multi-view Spectral Clustering (MvSC) attracts increasing attention due to diverse data sources. However, most existing works are prohibited in out-of-sample predictions and overlook model interpretability and exploration of clustering…
The spectrum of the non-backtracking matrix plays a crucial role in determining various structural and dynamical properties of networked systems, ranging from the threshold in bond percolation and non-recurrent epidemic processes, to…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in…
We study the properties of correlation matrices widely used in the characterisation of vibrational modes in colloidal materials. We show that the eigenvectors in the middle of the spectrum are strongly mixed, but that at both the top and…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
We apply random matrix theory to compare correlation matrix estimators C obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg Stock Exchange (JSE)…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…