Matrix Factorization With Aggregated Observations

Yoshifumi Aimoto, Hisashi Kashima

Abstract: Missing value estimation is a fundamental task in machine learning and data mining. It is not only used as a preprocessing step in data analysis, but also serves important purposes such as recommendation. Matrix factorization with low-rank assumption is a basic tool for missing value estimation. However, existing matrix factorization methods cannot be applied directly to such cases where some parts of the data are observed as aggregated values of several features in high-level categories. In this paper, we propose a new problem of restoring original micro observations from aggregated observations, and we give formulations and efficient solutions to the problem by extending the ordinary matrix factorization model. Experiments using synthetic and real data sets show that the proposed method outperforms several baseline methods.