Related papers: Low-Rank Matrix Factorizations with Volume-based C…
Low-rank regularization is an effective technique for addressing ill-posed inverse problems when the unknown variable exhibits low-rank characteristics. However, global low-rank assumptions do not always hold for seismic wavefields; in many…
Effective representation learning from text has been an active area of research in the fields of NLP and text mining. Attention mechanisms have been at the forefront in order to learn contextual sentence representations. Current…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative $n \times m$ matrix $M$ into a product of a nonnegative $n \times d$ matrix $W$ and a nonnegative $d \times m$ matrix $H$. Restricted NMF requires in…
Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Principal component analysis and factor analysis are fundamental multivariate analysis methods. In this paper a unified framework to connect them is introduced. Under a general latent variable model, we present matrix optimization problems…
Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services…
The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem…
Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these…
High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this…
Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified value. This generalizes the problem of finding a nearest…
Large language models (LLMs) contain billions of parameters, yet many exact values are not essential. We show that what matters most is the relative rank of weights-whether one connection is stronger or weaker than another-rather than…
Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…
Foundation models have achieved remarkable success, yet their growing parameter counts pose significant computational and memory challenges. Low-rank factorization offers a promising route to reduce training and inference costs, but the…
Factorization machines (FMs) are machine learning predictive models based on second-order feature interactions and FMs with sparse regularization are called sparse FMs. Such regularizations enable feature selection, which selects the most…