概念空间中超球的大小
The Size of a Hyperball in a Conceptual Space
摘要：
概念空间的认知框架[3]提供了表示知识的几何手段。概念空间是一个高维空间，其维度被划分为所谓的域。在每个域中，欧几里得度量用于计算距离。通过将曼哈顿度量应用于域内距离来计算整个空间中的距离。在这个空间中，空间被表示为点，概念被表示为区域。本文在概念空间的组合度量下，导出了超球的大小公式。我们可以把这样一个超球看作是所有与超球中心具有某种最小相似性的点的集合。
英文摘要：
The cognitive framework of conceptual spaces [3] provides geometric means for representing knowledge. A conceptual space is a high-dimensional space whose dimensions are partitioned into so-called domains. Within each domain, the Euclidean metric is used to compute distances. Distances in the overall space are computed by applying the Manhattan metric to the intra-domain distances. Instances are represented as points in this space and concepts are represented by regions. In this paper, we derive a formula for the size of a hyperball under the combined metric of a conceptual space. One can think of such a hyperball as the set of all points having a certain minimal similarity to the hyperball's center.
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。
