Statistical inference based on robust low-rank data matrix approximation

Robust Weighted Low-Rank Matrix Approximation

The calculation of a low-rank approximation to a matrix is fundamental to many algorithms in computer vision and other fields. One of the primary tools used for calculating such low-rank approximations is the Singular Value Decomposition, but this method is not applicable in the case where there are outliers or missing elements in the data. Unfortunately this is often the case in practice. We p...

Practical low-rank matrix approximation under robust L1-norm

A great variety of computer vision tasks, such as rigid/nonrigid structure from motion and photometric stereo, can be unified into the problem of approximating a lowrank data matrix in the presence of missing data and outliers. To improve robustness, the L1-norm measurement has long been recommended. Unfortunately, existing methods usually fail to minimize the L1-based nonconvex objective funct...

Local Low-Rank Matrix Approximation

Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is locally of low-rank, leading to a representation of the observed matrix as a weighted sum of low...

CLRMA: Compact Low Rank Matrix Approximation for Data Compression

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse lowrank matrix approximation (SLRMA), an effective computational tool for data compression. SLRMA extends the conventional LRMA by exploring both the intraand i...

Complex data analytics via sparse, low-rank matrix approximation