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Matrix completion has attracted attention in many fields, including statistics, applied mathematics, and electrical engineering. Most of the works focus on the independent sampling models under which the observed entries are sampled…

With the huge influx of various data nowadays, extracting knowledge from them has become an interesting but tedious task among data scientists, particularly when the data come in heterogeneous form and have missing information. Many data…

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under…

We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…

The noisy matrix completion problem, which aims to recover a low-rank matrix $\mathbf{X}$ from a partial, noisy observation of its entries, arises in many statistical, machine learning, and engineering applications. In this paper, we…

Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender…

The clustering method based on graph models has garnered increased attention for its widespread applicability across various knowledge domains. Its adaptability to integrate seamlessly with other relevant applications endows the graph…

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…

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion…

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…

Coded caching provides significant gains over conventional uncoded caching by creating multicasting opportunities among distinct requests. Massive multiple-input multiple-output (MIMO) systems require downlink channel state information…

The need for multimodal data integration arises naturally when multiple complementary sets of features are measured on the same sample. Under a dependent multifactor model, we develop a fully data-driven orchestrated approximate message…

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack…