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PSDBoost: Matrix-Generation Linear Programming for Positive Semidefinite Matrices Learning
Chunhua Shen · Alan Welsh · Lei Wang

Mon Dec 08 08:45 PM -- 12:00 AM (PST) @ None #None

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 semidefinitematrix can be decomposed into linear convex combinations of trace-one rank-one matrices, which serve as base learners of PSDBoost. Numerical experiments are presented.

Author Information

Chunhua Shen (University of Adelaide)
Alan Welsh
Lei Wang (University of Wollongong)

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