  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 NP-hard in general when there exist multiple overlapped cardinality
constraints. In this paper, we consider the scenario where the overlapped
cardinality constraints satisfy a Three-view Cardinality Structure (TVCS),
which reflects the natural restriction in many applications, such as
identification of gene regulatory networks and task-worker 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.
