# Bayesian Joint Matrix Decomposition for Data Integration with Heterogeneous Noise

arXiv: https://arxiv.org/abs/1712.03337 · HTML: https://mlsanity.com/paper/1712.03337/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2017.

## Built on by (most cited first, 1 of 1)

- [Improving Noise Robustness through Abstractions and its Impact on Machine Learning](https://mlsanity.com/paper/2406.08428/) (2024)

## Abstract (arXiv)

Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of matrix decomposition methods have been extended for such multi-view data integration and pattern discovery. While only few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, we propose a joint matrix decomposition framework (BJMD), which models the heterogeneity of noise by Gaussian distribution in a Bayesian framework. We develop two algorithms to solve this model: one is a variational Bayesian inference algorithm, which makes full use of the posterior distribution; and another is a maximum a posterior algorithm, which is more scalable and can be easily paralleled. Extensive experiments on synthetic and real-world datasets demonstrate that BJMD considering the heterogeneity of noise is superior or competitive to the state-of-the-art methods.