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PSDBoost: Matrix-generation linear programming for positive semidefinite matrices learning

Conference Paper


Abstract


  • In this work, we consider the problem of learning a positive semidefinite matrix. The critical issue is how to preserve positive semidefiniteness during the course of learning. Our algorithm is mainly inspired by LPBoost [1] and the general greedy convex optimization framework of Zhang [2]. We demonstrate the essence of the algorithm, termed PSDBoost (positive semidefinite Boosting), by focusing on a few different applications in machine learning. The proposed PSDBoost algorithm extends traditional Boosting algorithms in that its parameter is a positive semidefinite matrix with trace being one instead of a classifier. PSDBoost is based on the observation that any trace-one positive semidefinite matrix can be decomposed into linear convex combinations of trace-one rank-one matrices, which serve as base learners of PSDBoost. Numerical experiments are presented.

Publication Date


  • 2009

Citation


  • Shen, C., Welsh, A., & Wang, L. (2009). PSDBoost: Matrix-generation linear programming for positive semidefinite matrices learning. In Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference (pp. 1473-1480).

Scopus Eid


  • 2-s2.0-84863362632

Web Of Science Accession Number


Start Page


  • 1473

End Page


  • 1480

Abstract


  • In this work, we consider the problem of learning a positive semidefinite matrix. The critical issue is how to preserve positive semidefiniteness during the course of learning. Our algorithm is mainly inspired by LPBoost [1] and the general greedy convex optimization framework of Zhang [2]. We demonstrate the essence of the algorithm, termed PSDBoost (positive semidefinite Boosting), by focusing on a few different applications in machine learning. The proposed PSDBoost algorithm extends traditional Boosting algorithms in that its parameter is a positive semidefinite matrix with trace being one instead of a classifier. PSDBoost is based on the observation that any trace-one positive semidefinite matrix can be decomposed into linear convex combinations of trace-one rank-one matrices, which serve as base learners of PSDBoost. Numerical experiments are presented.

Publication Date


  • 2009

Citation


  • Shen, C., Welsh, A., & Wang, L. (2009). PSDBoost: Matrix-generation linear programming for positive semidefinite matrices learning. In Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference (pp. 1473-1480).

Scopus Eid


  • 2-s2.0-84863362632

Web Of Science Accession Number


Start Page


  • 1473

End Page


  • 1480