Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The object shape is easy to compute and interpret, owing to its intuitive interpretation as interpolation between two extreme forms of symmetry. As one major part of this work, we apply object shape in various metric spaces and show that it manages to unify several pre-existing, classical forms of symmetry. We also propose a new visualization tool called the peeling plot, which allows using the object shape for outlier detection and principal component analysis of object data.

翻译：对象数据分析关注的是数据集元素位于任意非特定度量空间中的统计方法。本文提出了一种针对对象数据的新型形状/对称性度量——对象形状。由于该度量被直观地解释为两种极端对称形式之间的插值，因此易于计算和解释。作为本文的核心部分，我们将对象形状应用于多种度量空间，并证明其能够统一多种已有的经典对称形式。我们还提出了一种名为剥离图的可视化新工具，该工具可利用对象形状进行对象数据的异常值检测和主成分分析。