Forbidden ordinal patterns are ordinal patterns (or ‘rank blocks’) that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L0, it has forbidden patterns of any length L ≥ L0 and their number grows superexponentially with L. Using recent results on...

For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d = 2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns indicating changes between up and down into the monotonic relation to H, one obtains the Zero Crossing (ZC) estimator of the Hurst parameter which has found consid...

The recognition of all main features of a healthy heart rhythm (the so-called sinus rhythm) is still one of the biggest challenges in contemporary cardiology. Recently the interesting physiological phenomenon of heart rate asymmetry has been observed. This phenomenon is related to unbalanced contributions of heart rate decelerations and accelerations to heart rate variability. In this paper we ...

A reliable personal recognition based on ear biometrics is highly in demand due to its vast application in automated surveillance, law enforcement etc. In this paper a robust ear recognition system is proposed using gradient ordinal relationship pattern. A reference point based normalization is proposed along with a novel ear transformation over normalized ear, to obtain robust ear representati...

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of the time series and robust against small perturbations or measurement errors. Ordinal pattern dependence can be characterized by four parameters. We propose ...

We introduce the concept of ordinal pattern dependence between time series and show in an explorative study that both types of this dependence show up in real world financial data.

U. Parlitz, H. Suetani, and S. Luther 1 Max-Planck-Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany 2 Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany 3 Department of Physics and Astronomy, Graduate School of Science and Engineering, Kagoshima University, 1-21-35 Korimto Kagoshima 890-0065, Japan 4...

Tackling missing data is one of the fundamental data pre-processing steps. Data analysis and pattern extraction are affected due to the underlying differences between instances with and without missing data. This is a particular problem with ordinal data, where for example a sample of a population may have all failed to answer a specific question in a questionnaire. The existing methods such as...

Palmprint-based personal identification, as a new member in the biometrics family, has become an active research topic in recent years. Although great progress has been made, how to represent palmprint for effective classification is still an open problem. In this paper, we present a novel palmprint representation —— ordinal measure, which unifies several main palmprint algorithms into a genera...

Ordinal classification refers to classification problems in which the classes have a natural order imposed on them because of the nature of the concept studied. Some ordinal classification approaches perform a projection from the input space to one-dimensional (latent) space that is partitioned into a sequence of intervals (one for each class). Class identity of a novel input pattern is then de...