  Reservoir computing, a recurrent neural network paradigm in which only the
output layer is trained, has demonstrated remarkable performance on tasks such
as prediction and control of nonlinear systems. Recently, it was demonstrated
that adding time-shifts to the signals generated by a reservoir can provide
large improvements in performance accuracy. In this work, we present a
technique to choose the time-shifts by maximizing the rank of the reservoir
matrix using a rank-revealing QR algorithm. This technique, which is not task
dependent, does not require a model of the system, and therefore is directly
applicable to analog hardware reservoir computers. We demonstrate our
time-shift selection technique on two types of reservoir computer: one based on
an opto-electronic oscillator and the traditional recurrent network with a
$tanh$ activation function. We find that our technique provides improved
accuracy over random time-shift selection in essentially all cases.
