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Regular echo state networks: simple and accurate reservoir models to real-world applications

Reservoir computing is a computational paradigm derived from recurrent neural network models. One of its most representative technique is the Echo State Network (ESN), which is usually composed by two salient components: reservoir and readout. The former is responsible by mapping temporal (or sequential) inputs into a high-dimensional space and the latter aims at learning the patterns in such a new space. Despite ESN has attracted a lot of attention nowadays, most works in the literature are focused on the development of additional features to the model, while there is a considerable lack of investigations related to understand and evaluate some of its inherent concepts as well as their relationships. In this paper we address such a limitation by investigating ESN components related to the reservoir structure and readout layer. To be specific, we evaluate regular and small-world network models besides the extensively adopted random one, and also analyze a total of eight classification techniques instead of considering just the few techniques largely adopted in the literature (mostly linear ones). In order to consistently evaluate the alternative ESN methods, we analyzed a wide range of parameters in both reservoir and readout layers through of several experiments with five real-world data sets. The results revealed that some problems can be considerably benefited from some level of organization in the reservoir, such as those provided by regular or small-world network models; and that the non-linear support vector machine classifier achieved the best predictive performance, although it was statistically comparable with the k-nearest neighbors one, which has much smaller time complexity. Interestingly, such findings may make the adoption of ESN methods more efficient from the point of view of embedded systems and large scale problems.