Related papers: LC-SVD-DLinear: A low-cost physics-based hybrid ma…

In this paper, we present a class of high order methods to approximate the singular value decomposition of a given complex matrix (SVD). To the best of our knowledge, only methods up to order three appear in the the literature. A first part…

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…

In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…

This work presents an analysis of Higher Order Singular Value Decomposition (HO-SVD) applied to lossy compression of 3D mesh animations. We describe strategies for choosing a number of preserved spatial and temporal components after tensor…

Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…

The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…

Interfacial fluctuations in a two-phase binary fluid mixture reveal signatures of underlying physical processes that occur within each phase and on a range of spatial and temporal scales. In this study, we investigate a model binary fluid…

To solve deep neural network (DNN)'s huge training dataset and its high computation issue, so-called teacher-student (T-S) DNN which transfers the knowledge of T-DNN to S-DNN has been proposed. However, the existing T-S-DNN has limited…

Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…

A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method…

Vision-language models (VLMs) like CLIP have shown impressive zero-shot and few-shot learning capabilities across diverse applications. However, adapting these models to new fine-grained domains remains difficult due to reliance on prompt…

Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…

Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to…

With the rapid development of science and technology, the problem of energy load monitoring and decomposition of electrical equipment has been receiving widespread attention from academia and industry. For the purpose of improving the…

We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Owing to its minimal pollution and efficient energy use, wind energy has become one of the most widely exploited renewable energy resources. The successful integration of wind power into the grid system is contingent upon accurate wind…

A common machine learning task is to discriminate between normal and anomalous data points. In practice, it is not always sufficient to reach high accuracy at this task, one also would like to understand why a given data point has been…

Forecasting the short-term ridership among origin-destination pairs (OD matrix) of a metro system is crucial in real-time metro operation. However, this problem is notoriously difficult due to the high-dimensional, sparse, noisy, and skewed…