Related papers: A two-dimensional decomposition approach for matri…

In this paper, we propose novel gossip algorithms for the low-rank decentralized matrix completion problem. The proposed approach is on the Riemannian Grassmann manifold that allows local matrix completion by different agents while…

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…

Learning big data by matrix decomposition always suffers from expensive computation, mixing of complicated structures and noise. In this paper, we study more adaptive models and efficient algorithms that decompose a data matrix as the sum…

In this paper, we focus on subspace learning problems on the Grassmann manifold. Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others. Motivated by privacy…

We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

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…

We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…

Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has…

The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…