Wednesday, January 06, 2016

A Review on Low-Rank Models in Signal and Data Analysis / An overview of low-rank matrix recovery from incomplete observations

Today we have two reviews on low rank matrices from slightly diferent perspectives. I should soon include them in the Advanced Matrix factorization Jungle.


Nowadays we are in the big data era. The high-dimensionality of signal and data imposes big challenge on how to process them effectively and efficiently. Fortunately, in practice signals and data are not unstructured. Their samples usually lie around low-dimensional manifolds and have high correlation among them. Such characteristics can be effectively depicted by low rankness. As an extension to the sparsity of first order signals, such as voices, low rankness is also an effective measure for the sparsity of second order signals, such as images. In this paper, I review the representative theories, algorithms and applications of the low rank subspace recovery models in signal and dataprocessing 

An overview of low-rank matrix recovery from incomplete observations by Mark Davenport and Justin Romberg

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and one encounters the problem of recovering the matrix given only incomplete and indirect observations. This paper provides an overview of modern techniques for exploiting low-rank structure to perform matrix recovery in these settings, providing a survey of recent advances in this rapidly-developing field. Specific attention is paid to the algorithms most commonly used in practice, the existing theoretical guarantees for these algorithms, and representative practical applications of these techniques.

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