Shapes: Their Clustering and Evolution

将相似对象分组为互斥的组是知识发现最基本的方法之一。在现代之前，对世界的研究主要是定性的，定性的分组被用来从宇宙中提取知识。例如，亚里士多德将生物体分为两组：植物和动物，并根据动物的运动方式将动物分为三组：行走、飞行或游泳。伽利略利用恒星群运动的相似性，发现它们位于同一个星系，今天被称为银河系。门捷列夫通过将具有相似化学特征的元素分组而发现了元素周期表。达尔文通过对生物体进行分组来研究物种的进化。

Grouping similar objects into mutually exclusive groups is one of the most fundamental methods of knowledge discovery. Before the modern era the world was studied mostly qualitatively, and qualitative grouping was used to extract knowledge from the universe. For example, Aristotle divided living organisms into two groups, plants and animals, and divided animals into three groups according to how they moved: walking, flying, or swimming. Galileo used the similarity of movement of groups of stars and discovered that they are positioned in the same galaxy, which today is called the Milky Way. Mendeleev discovered the periodic table by grouping elements having similar chemical characteristics. Darwin studied the evolution of species by grouping biological bodies.