函数型数据的形状异常检测与可视化：异常图
Shape Outlier Detection and Visualization for Functional Data: the Outliergram
摘要：
提出了一种新的曲线形状异常点的可视化和检测方法。在函数数据分析中，我们观察定义在给定实区间上的曲线，形状异常值是那些表现出与样本其余部分不同形状的曲线。虽然幅度异常值，即在某些点或整个区间上表现出极高或极低值的曲线，通常很容易识别，但形状异常值通常被掩盖在其余曲线中，因此难以检测。在这篇文章中，我们利用函数数据的两个深度之间的关系，以帮助可视化曲线的形状，并开发一个算法的形状离群检测。我们说明了使用的可视化工具，outliergram，通过几个例子和评估的性能的算法上的模拟研究。我们将它们应用于儿童生长数据集中的异常值检测，其中女孩样本被男孩曲线污染，反之亦然。
英文摘要：
We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis we observe curves defined over a given real interval and shape outliers are those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that exhibit atypically high or low values at some points or across the whole interval, are in general easy to identify, shape outliers are often masked among the rest of the curves and thus difficult to detect. In this article we exploit the relation between two depths for functional data to help visualizing curves in terms of shape and to develop an algorithm for shape outlier detection. We illustrate the use of the visualization tool, the outliergram, through several examples and asses the performance of the algorithm on a simulation study. We apply them to the detection of outliers in a children growth dataset in which the girls sample is contaminated with boys curves and viceversa.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
