Randomized Subspace Newton Convex Method Applied to Data-Driven Sensor Selection Problem

The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the update variables are selected to be the present best sensor candidates is also considered. In the converged solution, almost the same results are obtained by original and randomized-subspace-Newton convex methods. As expected, the randomized-subspace-Newton methods require more computational steps while they reduce the total amount of the computational time because the computational time for one step is significantly reduced by the cubic of the ratio of numbers of randomly updating variables to all the variables. The customized method shows superior performance to the straightforward implementation in terms of the quality of sensors and the computational time.

Automated summary

This study proposes randomized subspace Newton convex methods for sensor selection problem, where a customized approach is used to select update variables for improved performance. The results show that the randomized subspace Newton methods yield almost identical results in the converged solution compared to the original method. Furthermore, while requiring more computational steps, the randomized subspace Newton methods reduce total computational time significantly.