2021.10.27 18:40 N625

Matrix factorization (MF) plays a fundamental role in data mining and machine learning. The history of using MF for data analysis dates back more than a hundred years ago when Karl Pearson invented principal component analysis (PCA) for agricultural data analysis. PCA has become a standard approach for dimension reduction and feature extraction, and has numerous applications in various fields. Tipping and Bishop connected PCA to a probabilistic framework and showed that PCA underlyingly assumes that the noise follows identical and independent distributed (IID) Gaussian distribution. However, the noise of real-world data can be complicated and the IID Gaussian distribution can be easily violated. Many researchers have devoted their efforts to develop probabilistic matrix factorization methods to handle complicated noise in real-world data. In this talk, I will briefly review the history and recent advance in probabilistic MF, including three probabilistic MF methods we proposed to model complicated noise for different settings.