Related papers: A Kernelizable Primal-Dual Formulation of the Mult…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…

This thesis gives an overview of the state-of-the-art randomized linear algebra algorithms for singular value decomposition (SVD), including the presentation of existing pseudo-codes and theoretical error analysis. Our main focus is on…

This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under…

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…

Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

SVD (singular value decomposition) is one of the basic tools of machine learning, allowing to optimize basis for a given matrix. However, sometimes we have a set of matrices $\{A_k\}_k$ instead, and would like to optimize a single common…

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first…

In this paper we propose a multi-task linear classifier learning problem called D-SVM (Dictionary SVM). D-SVM uses a dictionary of parameter covariance shared by all tasks to do multi-task knowledge transfer among different tasks. We…

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…

Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on…

This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version…

Deep learning methods achieve great success recently on many computer vision problems, with image classification and object detection as the prominent examples. In spite of these practical successes, optimization of deep networks remains an…

The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the…

As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks:…

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

The availability of large amounts of data and compelling computation power have made deep learning models much popular for text classification and sentiment analysis. Deep neural networks have achieved competitive performance on the above…

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…