Related papers: Low-Rank Matrix Factorizations with Volume-based C…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…
Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…
Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…
With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan…
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…
Low-rank matrix recovery is a fundamental problem in signal processing and machine learning. A recent very popular approach to recovering a low-rank matrix X is to factorize it as a product of two smaller matrices, i.e., X = UV^T, and then…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…
Low rank matrix factorisation is often used in recommender systems as a way of extracting latent features. When dealing with large and sparse datasets, traditional recommendation algorithms face the problem of acquiring large, unrestrained,…
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…
Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method…
Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…