Belief Rényi Divergence of Divergence and its Application in Time Series Classification

Time series data contains the amount of information to reflect the development process and state of a subject. Especially, the complexity is a valuable factor to illustrate the feature of the time series. However, it is still an open issue to measure the complexity of sophisticated time series due to its uncertainty. In this study, based on the belief R
$\acute{e}$
nyi divergence, a novel time series complexity measurement algorithm, called belief R
$\acute{e}$
nyi divergence of divergence (BR
$\acute{e}$
DOD), is proposed. Specifically, the BR
$\acute{e}$
DOD algorithm takes the boundaries of time series value into account. What is more, according to the Dempster-Shafer (D-S) evidence theory, the time series is converted to the basic probability assignments (BPAs) and it measures the divergence of a divergence sequence. Then, the secondary divergence of the time series is figured out to represent the complexity of the time series. In addition, the BR
$\acute{e}$
DOD algorithm is applied to sets of cardiac inter-beat interval time series, which shows the superiority of the proposed method over classical machine learning methods and recent well-known works.