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Finding the largest cardinality feasible subset of an infeasible set oflinear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solvingthis problem is crucial in a wide range of applications such as machinelearning and compressive sensing. Although MAX FS is NP-hard, useful heuristicalgorithms exist, but these can be slow for large problems. We extend theexisting heuristics for the case of dense constraint matrices to greatlyincrease their speed while preserving or improving solution quality. We testthe extended algorithms on two applications that have dense constraintmatrices: binary classification, and sparse recovery in compressive sensing. Inboth cases, speed is greatly increased with no loss of accuracy.

Faster Maximum Feasible Subsystem Solutions for Dense Constraint Matrices