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 calculate eigenvector overlaps between intersecting time periods of covariance matrices.
New metric tensor field on symmetric matrices simplifies eigenvector computation.
New method improves subspace iteration for eigenvectors in machine learning.
Study eigenvector overlaps in large Gaussian matrices, simplifying for GOE.
New method improves covariance estimation for weighted samples.
Paper addresses eigenvector perturbation in small eigen-gap scenarios.
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistica…
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 algorithm updates eigenvectors of evolving graphs efficiently.
Lower bounds show linear complexity for linear regression.
New algorithm consistently orients eigenvectors for machine learning.
We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods a…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue decompositions. Several algorithms have been proposed in the recent past to accelerate spec…
Biological neurons learn tensor decompositions of higher-order correlations using nonlinear Hebbian plasticity.
The online problem of computing the top eigenvector is fundamental to machine learning. In both adversarial and stochastic settings, previous results (such as matrix multiplicative weight update, follow the regularized leader, follow the compressed leader, block power method) either achieve optimal regret but run slow,…
We consider a situation in which we see samples in drawn i.i.d. from some distribution with mean zero and unknown covariance A. We wish to compute the top eigenvector of A in an incremental fashion - with an algorithm that maintains an estimate of the top eigenvector in O(d) space, and incrementally adju…
Study on signal recovery from low-rank matrix with sparse noise.
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension and a newly introduced algorithm based on random projections. Previous work has c…
Paper proposes a distributed method to estimate principal eigenvector from high-rate streaming data.
A new method for streaming PCA provides confidence intervals for eigenvector entries.
Machine learning models perform better with location coordinates alone, not Moran Eigenvectors.
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse…
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…
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…
Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
A new algorithm improves Wasserstein discriminant analysis for better data classification.
How many samples are sufficient to guarantee that the eigenvectors and eigenvalues of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and distributions supported in a centered Euclidean ball, we prove …
We propose a general framework to study the stability of the subspace spanned by consecutive eigenvectors of a generic symmetric matrix , when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation ( is then the Hamiltonian) and financial ris…
In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative correlation, i.e., ones that can generate a "diverse" sample from a set of items.…
A new algorithm reduces data dimensionality and decorrelation in a distributed setting.
A new method for spectral barycentre of graph datasets.
SGD benefits from a directional bias in kernel regression models.
ELD compares graphs by their embedded Laplacian eigenvectors, resolving ambiguities.
New theory for eigenvectors of generalized Laplacian matrices, addressing dependency issues.
Fast algorithm recovers principal eigenvector from noisy matrices.
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…
The paper explores how kernel eigenalignments affect generalization in KRR.
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 these algorithms' success and their Achilles heel: forming a graph and computin…
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…
Improved spectral clustering with fewer eigenvectors performs better.
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
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 considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and scientific computing with numerous applications in machine learning and statistics (…
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.
Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.