论文标题
Rao-Burbea质心应用于时间序列和图像的统计表征通过序数模式
Rao-Burbea centroids applied to the statistical characterisation of time series and images through ordinal patterns
论文作者
论文摘要
概率分布之间的分歧或相似性度量已成为研究统计对象的不同方面（例如时间序列，网络和图像）的非常有用的工具。值得注意的是，当应用于同一问题时，每个差异都不会提供相同的结果。因此，将最广泛的差异集用于研究的问题很方便。除此之外，对每个统计对象的分析中的一个重要步骤是将其代表值的每个代表值映射到方便选择的符号的字母中。在这项工作中，我们攻击了这两个问题，即，选择分歧的家族以及将地图分解为符号序列的方法。为了在第一个任务中晋升，我们与称为Burbea-Rao Centroids（BRC）的差异家族合作，在第二个差异中，我们通过使用序数模式将原始对象映射到符号序列中来进行。最后，我们将建议应用于分析模拟和实时序列以及真实的纹理图像。我们工作的主要结论是，至少在研究的情况下，最好的BRC是Jensen Shannon Divergence，除了它验证了一些有趣的正式属性。
Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects such as time series, networks and images. Notably not every divergence provides identical results when applied to the same problem. Therefore it is convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work we attack both problems, that is, the choice of a family of divergences and the way to do the map into a symbolic sequence. For advancing in the first task we work with the family of divergences known as the Burbea-Rao centroids (BRC) and for the second one we proceed by mapping the original object into a symbolic sequence through the use of ordinal patterns. Finally we apply our proposals to analyse simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen Shannon divergence, besides the fact that it verifies some interesting formal properties.
