Related papers: Mixture Matrix Completion
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…
The Nystrom method is an efficient technique to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
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…
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
The low-rank matrix completion (LRMC) technology has achieved remarkable results in low-level visual tasks. There is an underlying assumption that the real-world matrix data is low-rank in LRMC. However, the real matrix data does not…
We call a matrix completely mixable if the entries in its columns can be permuted so that all row sums are equal. If it is not completely mixable, we want to determine the smallest maximal and largest minimal row sum attainable. These…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
Multiclass classification (MCC) is a fundamental machine learning problem of classifying each instance into one of a predefined set of classes. In the deep learning era, extensive efforts have been spent on developing more powerful neural…
This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix…
Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general low rank setting. For positive data, we achieve results…
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…