  Although largely different concepts, echo state networks and compressed
sensing models both rely on collections of random weights; as the reservoir
dynamics for echo state networks, and the sensing coefficients in compressed
sensing. Several methods for generating the random matrices and metrics to
indicate desirable performance are well-studied in compressed sensing, but less
so for echo state networks. This work explores any overlap in these compressed
sensing methods and metrics for application to echo state networks. Several
methods for generating the random reservoir weights are considered, and a new
metric, inspired by the restricted isometry property for compressed sensing, is
proposed for echo state networks. The methods and metrics are investigated
theoretically and experimentally, with results suggesting that the same types
of random matrices work well for both echo state network and compressed sensing
scenarios, and that echo state network classification accuracy is improved when
the proposed restricted isometry-like constants are close to 1.
