Inertial Entropy and External Validation of Clusterings  

作　　者：Dan Simovici Joshua Yee 

机构地区：[1]Computer Science Deptartment,University of Massachusetts Boston,Boston 02125,USA

出　　处：《Journal of Harbin Institute of Technology(New Series)》2024年第5期41-54,共14页哈尔滨工业大学学报（英文版）

摘　　要：Axiomatization of Shannon entropy is a subject that has received lots of attention in the information theory literature.While Shannon entropy is defined on probability distribution,we define a new type of entropy on the set of partitions of finite subsets of metric spaces,which has a rich algebraic structure as a partially ordered set.We propose an axiomatization of an entropy-like measure of partitions of sets of objects located in metric spaces,and we derive an analytic expression of this new type of entropy referred to as inertial entropy.This approach starts with the notion of inertia of a partition and includes a study of the behavior of the sum of square errors of a partition.In this context,we characterize the chain of partitions produced by the Ward hierarchical clustering method.Starting from inertial entropies of partitions,we introduce conditional entropies which,in turn,generate metrics on partitions of finite sets.These metrics are used as external validation tools for clusterings of labeled data sets.The metric generated by inertial entropy can be used to validate data clustering for labeled data sets.This type of validation aims to determine to what extend labeling of the data coincides with the clustering obtained algorithmically,and we obtain a high degree of consistency of the data labeling with the results of several hierarchical clusterings.

关 键 词：PARTITION INERTIA hierarchical clustering generalized entropy 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论]