相关论文: One-sided Matrix Completion from Two Observations …

We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target…

The item response theory obtains the estimates and their confidence intervals for parameters of abilities of examinees and difficulties of problems by using the observed item response matrix consisting of 0/1 value elements. Many papers…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools. However, in many practical applications such as…

We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…

The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…

A matrix completion problem, which aims to recover a complete matrix from its partial observations, is one of the important problems in the machine learning field and has been studied actively. However, there is a discrepancy between the…

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…

Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…

Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…

Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most…

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…

In this paper, we introduce the first method that (1) can complete kernel matrices with completely missing rows and columns as opposed to individual missing kernel values, (2) does not require any of the kernels to be complete a priori, and…