# MLCTR: A Fast Scalable Coupled Tensor Completion Based on Multi-Layer Non-Linear Matrix Factorization

arXiv: https://arxiv.org/abs/2109.01773 · HTML: https://mlsanity.com/paper/2109.01773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 4 Sep 2021.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distributed Flexible Nonlinear Tensor Factorization](https://mlsanity.com/paper/1604.07928/) (2016)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages](https://mlsanity.com/paper/1407.8289/) (2014)
- [Bayesian multi-tensor factorization](https://mlsanity.com/paper/1412.4679/) (2014)

## Abstract (arXiv)

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and different levels of sparsity. Current non-linear tensor completion algorithms tend to learn noisy embedding and incur overfitting. This paper focuses on the embedding learning aspect of the tensor completion problem and proposes a new multi-layer neural network architecture for tensor factorization and completion (MLCTR). The network architecture entails multiple advantages: a series of low-rank matrix factorizations (MF) building blocks to minimize overfitting, interleaved transfer functions in each layer for non-linearity, and by-pass connections to reduce the gradient diminishing problem and increase the depths of neural networks. Furthermore, the model employs Stochastic Gradient Descent(SGD) based optimization for fast convergence in training. Our algorithm is highly efficient for imputing missing values in the EPS data. Experiments confirm that our strategy of incorporating non-linearity in factor matrices demonstrates impressive performance in embedding learning and end-to-end tensor models, and outperforms approaches with non-linearity in the phase of reconstructing tensors from factor matrices.