相关论文: Algebraic Algorithms for Fractional Linear Matroid…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
We propose an efficient matrix rank reduction method for non-negative matrices, whose time complexity is quadratic in the number of rows or columns of a matrix. Our key insight is to formulate rank reduction as a mean-field approximation by…
We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs.…
In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…
This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…