相关论文: Manifold-regularised Large-Margin $\ell_p$-SVDD fo…

With the increasing volume of astronomical data generated by modern survey telescopes, automated pipelines and machine learning techniques have become crucial for analyzing and extracting knowledge from these datasets. Anomaly detection,…

Randomized singular value decomposition (RSVD) is a class of computationally efficient algorithms for computing the truncated SVD of large data matrices. Given an $m \times n$ matrix $\widehat{{\mathbf M}}$, the prototypical RSVD algorithm…

In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…

A novel approach to detecting anomalies in time series data is presented in this paper. This approach is pivotal in domains such as data centers, sensor networks, and finance. Traditional methods often struggle with manual parameter tuning…

Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients…

This paper presents a new approach, based on polynomial optimization and the method of moments, to the problem of anomaly detection. The proposed technique only requires information about the statistical moments of the normal-state…

Data-driven anomaly detection methods suffer from the drawback of detecting all instances that are statistically rare, irrespective of whether the detected instances have real-world significance or not. In this paper, we are interested in…

This paper and its follow-up arXiv:2508.11109 are concerned with the well-posedness and $\mathrm{L}^p$-based Sobolev regularity for appropriate weak formulations of a family of prototypical PDEs posed on manifolds of minimal regularity. In…

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…

Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…

In this paper we investigate the generalization error of gradient descent (GD) applied to an $\ell_2$-regularized OLS objective function in the linear model. Based on our analysis we develop new methodology for computationally tractable and…

This paper proposes a new method for anomaly detection in time-series data by incorporating the concept of difference subspace into the singular spectrum analysis (SSA). The key idea is to monitor slight temporal variations of the…

Video Anomaly Detection (VAD) aims to identify and locate deviations from normal patterns in video sequences. Traditional methods often struggle with substantial computational demands and a reliance on extensive labeled datasets, thereby…

Anomaly subsequence detection is to detect inconsistent data, which always contains important information, among time series. Due to the high dimensionality of the time series, traditional anomaly detection often requires a large time…

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These…

In this paper we consider nonlinear parabolic systems with elliptic part which can be also degenerate. We prove optimal error estimates for smooth enough solutions. The main novelty, with respect to previous results, is that we obtain the…

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…