Shapes: Their Clustering and Evolution

将相似的对象划分为互斥的组是知识发现的最基本方法之一。在现代之前，世界主要是定性研究，定性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类，植物和动物，并根据动物的运动方式将其分为三类：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，即今天的银河系。门捷列夫通过对具有相似化学特性的元素进行分组发现了元素周期表。达尔文通过对生物体进行分类来研究物种的进化。

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.