  The randomized group-greedy method and its customized method for large-scale
sensor selection problems are proposed. The randomized greedy sensor selection
algorithm is applied straightforwardly to the group-greedy method, and a
customized method is also considered. In the customized method, a part of the
compressed sensor candidates is selected using the common greedy method or
other low-cost methods. This strategy compensates for the deterioration of the
solution due to compressed sensor candidates. The proposed methods are
implemented based on the D- and E-optimal design of experiments, and numerical
experiments are conducted using randomly generated sensor candidate matrices
with potential sensor locations of 10,000--1,000,000. The proposed method can
provide better optimization results than those obtained by the original
group-greedy method when a similar computational cost is spent as for the
original group-greedy method. This is because the group size for the
group-greedy method can be increased as a result of the compressed sensor
candidates by the randomized algorithm. Similar results were also obtained in
the real dataset. The proposed method is effective for the E-optimality
criterion, in which the objective function that the optimization by the common
greedy method is difficult due to the absence of submodularity of the objective
function. The idea of the present method can improve the performance of all
optimizations using a greedy algorithm.
