Matrix completion via local density loss optimization

Hui Fang; Yunbin Wang; Zhaojiong Chen

doi:10.1117/12.2623455

16 February 2022 Matrix completion via local density loss optimization

Hui Fang, Yunbin Wang, Zhaojiong Chen

Author Affiliations +

Proceedings Volume 12083, Thirteenth International Conference on Graphics and Image Processing (ICGIP 2021); 120830P (2022) https://doi.org/10.1117/12.2623455
Event: Thirteenth International Conference on Graphics and Image Processing (ICGIP 2021), 2021, Kunming, China

Abstract

One of the main methods for dealing with low-rank problems is the matrix completion, which attempts to recover incomplete values in an incomplete matrix. It has been employed in a large number of real-world applications like recommender systems and image recovery. When the data is highly sparse, many practical problems of recommender systems and image recovery are hard to solve. Therefore, we use the fully connected neural networks for the matrix completion to avoid problems caused by sparse matrices. In this paper, we utilize the local density loss function to measure the difference of the matrix completion results, where trainable parameters are updated via calculating the derivatives according to the influence function. The local density loss function effectively measures the deviation between the predicted value and the real value, and the convergence of the model is guaranteed. So as to validate the effectiveness of the proposed method, we conduct substantial experiments in terms of image recovery and recommender systems. In addition, we employ three metrics, including root mean square error and peak signal-to-noise ratio and structure similarity, to measure the recovery accuracy of missing matrix. Experimental results demonstrate that this framework is superior to other state-of-the-art methods in running time and learning performance.

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Hui Fang, Yunbin Wang, and Zhaojiong Chen "Matrix completion via local density loss optimization", Proc. SPIE 12083, Thirteenth International Conference on Graphics and Image Processing (ICGIP 2021), 120830P (16 February 2022); https://doi.org/10.1117/12.2623455

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KEYWORDS

Image restoration

Neural networks

Matrices

Image quality

Precision measurement

Signal to noise ratio

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