  Approximate entropy (ApEn) has been widely used as an estimator of regularity
in many scientific fields. It has proved to be a useful tool because of its
ability to distinguish different system's dynamics when there is only available
short-length noisy data. Incorrect parameter selection (embedding dimension
$m$, threshold $r$ and data length $N$) and the presence of noise in the signal
can undermine the ApEn discrimination capacity. In this work we show that
$r_{max}$ ($ApEn(m,r_{max},N)=ApEn_{max}$) can also be used as a feature to
discern between dynamics. Moreover, the combined use of $ApEn_{max}$ and
$r_{max}$ allows a better discrimination capacity to be accomplished, even in
the presence of noise. We conducted our studies using real physiological time
series and simulated signals corresponding to both low- and high-dimensional
systems. When $ApEn_{max}$ is incapable of discerning between different
dynamics because of the noise presence, our results suggest that $r_{max}$
provides additional information that can be useful for classification purposes.
Based on cross-validation tests, we conclude that, for short length noisy
signals, the joint use of $ApEn_{max}$ and $r_{max}$ can significantly decrease
the misclassification rate of a linear classifier in comparison with their
isolated use.
