Matrix Factorization With Aggregated Observations
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.
KeywordsSingular Value Decomposition Matrix Factorization Baseline Method Purchase Data Correspondence Matrix
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- 4.Eriksson, A., Hengel, A.V.D.: Efficient computation of robust low-rank matrix approximations in the presence of missing data using the L 1 norm. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 771–778. IEEE, San Francisco (2010)Google Scholar
- 5.Han, J., Kamber, M., Pei, J.: Data Mining: Concepts and Techniques, 3rd edn. Morgan Kaufmann (2011)Google Scholar
- 8.Lee, L., Seung, D.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems 13, pp. 556–562 (2001)Google Scholar
- 9.Little, R.J., Rubin, D.B.: Statistical Analysis with Missing Data. Wiley (1987)Google Scholar
- 10.Singh, A.P., Gordon, G.J.: Relational learning via collective matrix factorization. In: ACM SIGKDD, Las Vegas, USA, pp. 650–658 (2008)Google Scholar
- 11.Srebro, N., Rennie, J., Jaakkola, T.: Maximum-margin matrix factorization. In: Advances in Neural Information Processing Systems 17 (2005)Google Scholar