On The Projection Operator to A Threeview Cardinality Constrained Set
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:38713880, 2017.
Abstract
The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NPhard in general when there exist multiple overlapped cardinality constraints. In this paper, we consider the scenario where the overlapped cardinality constraints satisfy a Threeview Cardinality Structure (TVCS), which reflects the natural restriction in many applications, such as identification of gene regulatory networks and taskworker assignment problem. We cast the projection into a linear programming, and show that for TVCS, the vertex solution of this linear programming is the solution for the original projection problem. We further prove that such solution can be found with the complexity proportional to the number of variables and constraints. We finally use synthetic experiments and two interesting applications in bioinformatics and crowdsourcing to validate the proposed TVCS model and method.
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