Reducing the effects of motion artifacts in fMRI: A structured matrix completion approach

Author(s):  
Arvind Balachandrasekaran ◽  
Alexander L. Cohen ◽  
Onur Afacan ◽  
Simon K. Warfield ◽  
Ali Gholipour
2017 ◽  
Vol 43 ◽  
pp. 88-94 ◽  
Author(s):  
Mark Bydder ◽  
Stanislas Rapacchi ◽  
Olivier Girard ◽  
Maxime Guye ◽  
Jean-Philippe Ranjeva

Author(s):  
Emanuele Bugliarello ◽  
Swayambhoo Jain ◽  
Vineeth Rakesh

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approach: first, we transform this task into a constrained matrix completion problem with entries bounded in the unit interval [0,1]; second, we propose two novel matrix factorization models that leverage our knowledge of the VFX environment. Our first approach, expertise matrix factorization (EMF), is an interpretable method that structures the latent factors as weighted user-item interplay. The second one, survival matrix factorization (SMF), is instead a probabilistic model for the underlying process defining employees' efficiencies. We show the effectiveness of our proposed models by extensive numerical tests on our VFX dataset and two additional datasets with values that are also bounded in the [0,1] interval.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Henry Adams ◽  
Lara Kassab ◽  
Deanna Needell

<p style='text-indent:20px;'>The task of predicting missing entries of a matrix, from a subset of known entries, is known as <i>matrix completion</i>. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step. Structured matrix completion includes any setting in which data is not missing uniformly at random. In recent work, a modification to the standard nuclear norm minimization (NNM) for matrix completion has been developed to take into account <i>sparsity-based</i> structure in the missing entries. This notion of structure is motivated in many settings including recommender systems, where the probability that an entry is observed depends on the value of the entry. We propose adjusting an Iteratively Reweighted Least Squares (IRLS) algorithm for low-rank matrix completion to take into account sparsity-based structure in the missing entries. We also present an iterative gradient-projection-based implementation of the algorithm that can handle large-scale matrices. Finally, we present a robust array of numerical experiments on matrices of varying sizes, ranks, and level of structure. We show that our proposed method is comparable with the adjusted NNM on small-sized matrices, and often outperforms the IRLS algorithm in structured settings on matrices up to size <inline-formula><tex-math id="M1">\begin{document}$ 1000 \times 1000 $\end{document}</tex-math></inline-formula>.</p>


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