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

TL;DR

This paper introduces randomized subspace Newton convex methods for sensor selection, demonstrating that they reduce computational time per step while maintaining solution quality, with a customized approach outperforming standard methods.

Contribution

The paper proposes a novel randomized subspace Newton convex algorithm and a customized variant for sensor selection, improving computational efficiency and sensor quality.

Findings

Randomized methods reduce computational time per step.

Customized method outperforms standard in sensor quality and time.

Solutions are comparable between original and randomized methods.

Abstract

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.