|In Reservoir Computing, signals or sequences are fed into a set of interconnected non-linear units (neurons) with capabilities for storing information (reservoir). The reservoir generates an expanded representation of the input, which is subsequently mapped onto the desired output using a trained output layer (readout). However, despite their success in various experimental tasks, the dynamics of the reservoir are not yet well understood. In this paper we introduce a new technique, based on the well known Singular Value Decomposition (SVD), to obtain the main dynamic modes of the reservoir when excited with an input signal. We conduct experiments using Echo State Networks (ESN) to demonstrate the technique's potential and its ability to decompose input signals into Principal Component Modes as expanded by the reservoir. We expect that this approach will open new possibilities in its application to the field of visual analytics in process state visualisation, determination of attribute vectors, and detection of novelties. Furthermore, this technique could serve as a foundation for a better understanding of the reservoir's dynamic state that could help in other areas of research, such as domain shift or continual learning.
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