An Algebra Description for Hard Clustering

Abstract

Hard clustering algorithm partitions data set into several distinct regions. Clustering result offers a kind of characterization for the distribution of data relied on concentration. At the same time, the cluster structure can be regarded as a representation of knowledge in the form of data. However, as a sort of unsupervised learning task, due to a lack of overall criterion for evaluating the effect of clustering algorithms, different clustering algorithms lead to different results based on different considerations. Because of this uncertainty of single clustering result, by virtue of algebra tools, this paper tries to obtain a more reasonable cluster structure by combining various hard clustering results. Furthermore, based on the algebra representation and topological description of clustering, lattice theory and latticized topology can be employed, which allows us to define algebra operations and discuss topology property on clustering results.