相关论文: TDSVD: A Way to Get The Single Solution From TR-Sp…

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…

Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…

Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data…

We obtain a class of exact solutions of a Bessel-type differential equation, which is a six-parameter linear ordinary differential equation of the second order with irregular (essential) singularity at the origin. The solutions are obtained…

Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…

In the field of medical imaging, AI-assisted techniques such as object detection, segmentation, and classification are widely employed to alleviate the workload of physicians and doctors. However, single-task models are predominantly used,…

From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have…

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…

We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…

The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…

When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in…

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,…

Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear…

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…

We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…

This is an introductory survey, from a geometric perspective, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view to tensors, we define the singular space of…

Transport phenomena-describing the movement of particles, energy, or other physical quantities-are fundamental in various scientific disciplines, including nuclear physics, plasma physics, astrophysics, engineering, and the natural…

orthoDr is a package in R that solves dimension reduction problems using orthogonality constrained optimization approach. The package serves as a unified framework for many regression and survival analysis dimension reduction models that…

A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful tool that is the workhorse of many methods both in…

Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…