A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994--95 (ii) 30-min returns of 881 US stock…
New method estimates node community memberships in networks.
We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 stocks listed on the Shanghai and Shenzhen stock exchanges. Both raw correlation matrix and partial correlation matrix with respect to the ma…
We study the dynamic evolution of cross-correlations in the Chinese stock market mainly based on the random matrix theory (RMT). The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving …
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 has to be estimated using a relatively small sample of monthly returns data which…
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…
Random matrix analysis reveals that neural network weights are mostly random, with some indicating learned information.
Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both th…
This study analyzes the correlation structure of global agricultural futures markets using RMT.
We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the BSE index for the three-year period 2000-2002. Random matrix analysis is carried out us…
We investigate the problem of estimating a given real symmetric signal matrix from a noisy observation matrix in the limit of large dimension. We consider the case where the noisy measurement comes either from an arbitrary additive or multiplicative rotational invariant perturbati…
Study eigenvector overlaps in large Gaussian matrices, simplifying for GOE.
Study shows how many samples are needed for eigenvector/eigenvalue accuracy.
Machine learning models perform better with location coordinates alone, not Moran Eigenvectors.
Paper addresses eigenvector perturbation in small eigen-gap scenarios.
We calculate eigenvector overlaps between intersecting time periods of covariance matrices.
In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that prespecified target region. For example, one might be interested in the clusteri…
New methods find eigenvectors faster than Lanczos's method.
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the leading eigenvectors. The last step is sometimes referred to as rounding, where one ne…
We study the problem asking if one can embed manifolds into finite dimensional Euclidean spaces by taking finite number of eigenvector fields of the connection Laplacian. This problem is essential for the dimension reduction problem in massive data analysis. Singer-Wu proposed the vector diffusion map which embeds mani…
New metric tensor field on symmetric matrices simplifies eigenvector computation.
Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.
Housing markets play a crucial role in economies and the collapse of a real-estate bubble usually destabilizes the financial system and causes economic recessions. We investigate the systemic risk and spatiotemporal dynamics of the US housing market (1975-2011) at the state level based on the Random Matrix Theory (RMT)…
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
New algorithm updates eigenvectors of evolving graphs efficiently.
New algorithm consistently orients eigenvectors for machine learning.
A new algorithm reduces online eigenvector computation time while maintaining optimal performance.
New theory for eigenvectors of generalized Laplacian matrices, addressing dependency issues.
Fast algorithm recovers principal eigenvector from noisy matrices.
The paper explores how kernel eigenalignments affect generalization in KRR.
New method improves subspace iteration for eigenvectors in machine learning.
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a comp…
A new method approximates Laplacian eigenvectors for RL efficiently.
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a maximization problem, existing approaches formulate this problem by adding a penalty te…
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
Improved spectral clustering with fewer eigenvectors performs better.
New insights into spectral clustering reveal strong connections within eigenvectors.
The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy image. The algorithm relies on the following two observations: (1) the low-index e…
This paper proves the convergence rate of Krasulina's estimator for least eigenvalue and eigenvector.
Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.
We characterize the contractions that are similar to the backward shift in the Hardy space . This characterization is given in terms of the geometry of the eigenvector bundles of the operators.
We provide new examples of diffusion operators in dimension 2 and 3 which have orthogonal polynomials as eigenvectors. Their construction rely on the finite subgroups of O(3) and their invariant polynomials.
Study eigenvalues and eigenvectors in neural networks, focusing on signal propagation.
The paper tackles learning symmetries in data without expert knowledge.
New method improves covariance estimation for weighted samples.
Eigenvalue and eigenvector estimation improves with asymmetric data.
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) from January 1993 to December 2002. We test the spectral properties of C against ra…
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …