Related papers: Spectral Methods for Data Science: A Statistical P…

Spectral densities encode non-perturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics,…

Due to its high spatial and spectral information content, hyperspectral imaging opens up new possibilities for a better understanding of data and scenes in a wide variety of applications. An essential part of this process of understanding…

Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…

The paper introduces the software Spectangular for spectral disentangling via singular value decomposition with global optimisation of the orbital parameters of the stellar system or radial velocities of the individual observations. We will…

Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is…

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…

Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…

The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…

Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…

As machine learning models are increasingly considered for high-stakes domains, effective explanation methods are crucial to ensure that their prediction strategies are transparent to the user. Over the years, numerous metrics have been…

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving…

Two-dimensional electronic spectroscopy has become one of the main experimental tools for analyzing the dynamics of excitonic energy transfer in large molecular complexes. Simplified theoretical models are usually employed to extract model…

We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses any such stationary functional time series, whether linear…

We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to…

Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct…

The ideal spectral averaging method depends on one's science goals and the available information about one's data. Including low-quality data in the average can decrease the signal-to-noise ratio (SNR), which may necessitate an optimization…

We develop a novel method to separate the components of a diffuse emission process based on an association with the energy spectra. Most of the existing methods use some information about the spatial distribution of components, e.g.,…

Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation…

Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…