# Transduction with Matrix Completion Using Smoothed Rank Function

arXiv: https://arxiv.org/abs/1805.07561 · HTML: https://mlsanity.com/paper/1805.07561/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2018.

## Built on by (most cited first, 3 of 3)

- [Two-way Spectrum Pursuit for CUR Decomposition and Its Application in Joint Column/Row Subset Selection](https://mlsanity.com/paper/2106.06983/) (2021)
- [Transductive Matrix Completion with Calibration for Multi-Task Learning](https://mlsanity.com/paper/2302.09834/) (2023)
- [Generative Model Adversarial Training for Deep Compressed Sensing](https://mlsanity.com/paper/2106.10696/) (2021)

## Abstract (arXiv)

In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data matrix forming a stacked matrix. Assuming the data matrix is of low rank, we propose new recommendation methods by posing the problem as a constrained minimization of the Smoothed Rank Function (SRF). We provide convergence analysis for the proposed algorithms. The simulations are conducted on real datasets in two different scenarios of randomly missing pattern with and without block loss. The results confirm that the accuracy of our proposed methods outperforms those of state-of-the-art methods even up to 10% in low observation rates for the scenario without block loss. Our accuracy in the latter scenario, is comparable to state-of-the-art methods while the complexity of the proposed algorithms are reduced up to 4 times.