The horizontal visibility algorithm has been recently introduced as a mapping
between time series and networks. The challenge lies in characterizing the
structure of time series (and the processes that generated those series) using
the powerful tools of graph theory. Recent works have shown that the visibility
graphs inherit several degrees of correlations from their associated series,
and therefore such graph theoretical characterization is in principle possible.
However, both the mathematical grounding of this promising theory and its
applications are on its infancy. Following this line, here we address the
question of detecting hidden periodicity in series polluted with a certain
amount of noise. We first put forward some generic properties of horizontal
visibility graphs which allow us to define a (graph theoretical) noise
reduction filter. Accordingly, we evaluate its performance for the task of
calculating the period of noisy periodic signals, and compare our results with
standard time domain (autocorrelation) methods. Finally, potentials,
limitations and applications are discussed.Comment: To be published in International Journal of Bifurcation and Chao
