arXiv research

We analyzed SVD and variants for eigenpair computation, comparing their time and space complexities.

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization prob…

Due to the iterative nature of most nonnegative matrix factorization (\textsc{NMF}) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many initialization schemes have been proposed for NMF, among which one of the most popular class of methods…

Paper proposes a new optimization framework for learning eigenfunctions of operators.

The paper updates SVD of evolving matrices using projection techniques.

Physics-inspired methods optimize SVD compression of LLMs.

We show that given an estimate $\widehat{A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $A$ in spectral norm (i.e., $\|\widehat{A}-A\|_2 \leq δ$), the simple truncated SVD of $\widehat{A}$ produces a multiplicative approximation of $A$ in Frobenius norm. This observation leads to many inte…

A new algorithm reduces communication in distributed SVD by $p$ factors.

New algorithm approximates conditional expectations with fast convergence.

The paper analyzes how random perturbations affect RSVD and its applications.

Study uses random matrix theory to improve tensor approximation accuracy.

Sparse Singular Value Decomposition (SVD) models have been proposed for biclustering high dimensional gene expression data to identify block patterns with similar expressions. However, these models do not take into account prior group effects upon variable selection. To this end, we first propose group-sparse SVD model…

Two multifidelity trust-region methods use low-fidelity models for efficient optimization.

New K-SVD framework speeds up image denoising with active set algorithm.

Randomized SVD shows phase transitions in noisy data.

New estimator reduces bias and variance in tensor and matrix denoising.

New insights into choosing between two data integration methods based on SVD.

Efficient SVD algorithm robust to outliers.

A neural network, IHT-Net, improves DOA estimation with sparse arrays.

The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users' ratings on items based on their latent factors. However, current Matrix Factorization models p…

This paper improves SVD for recommender systems using block-based matrix factorization.

This paper improves K-SVD for image denoising using deep learning.

SVD training reduces DNN rank and computation load without SVD per step.

Ranky solves SVD for large sparse matrices in distributed systems.

New method uses SVD entropy to price artworks.

Study of logarithms in SVD-closed subgroups of unitary group.

Unified framework for structured principal subspace estimation with bounds and rates.

Formula for complex SVD backpropagation developed.

Improved SVD for shifted matrices without explicit matrix construction.

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern recognition, artificial intelligence, computer vision, signal processing, etc. In recen…

Generalizes randomized SVD for better matrix approximations using Gaussian vectors.

This paper examines the impact of centering in PCA and SVD.

Unified SVD compression fails in practical tasks, highlighting the importance of per layer activation reconstruction.

GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.

Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and rescaling the coordinate axes (by a predefined function of the singular value). Howe…

The power of randomized algorithms in numerical methods have led to fast solutions which use the Singular Value Decomposition (SVD) as a core routine. However, given the large data size of modern and the modest runtime of SVD, most practical algorithms would require some form of approximation, such as sketching, when r…

Paper develops a bootstrap method for estimating sketched SVD errors.

Paper improves tensor completion using unitary transforms.

A new method for efficiently updating large-scale matrices in real-time.

This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast …

SVD-RND detects blurred images better than conventional methods.

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure featu…

EarlyStopping package helps prevent overfitting in iterative learning procedures.

New asymmetric kernel methods improve feature learning.

New method tackles non-smooth tensor data for better recovery.

Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this factorization one can derive notion of tensor rank, referred to as the tensor tubal…

Singular Value Decomposition (SVD) has been used successfully in recent years in the area of recommender systems. In this paper we present how this model can be extended to consider both user ratings and information from Wikipedia. By mapping items to Wikipedia pages and quantifying their similarity, we are able to use…