Generalizations and Unification of Centroid-based Clustering Methods

k-means;data mining;cluster analysis

Canas, Daniel Alberto ; Dr. Robert Funderlic, Committee Chair,Dr, Jon Doyle, Committee Member,Dr. Steffen Heber, Committee Member,Canas, Daniel Alberto ; Dr. Robert Funderlic ; Committee Chair ; Dr ; Jon Doyle ; Committee Member ; Dr. Steffen Heber ; Committee Member

University:North Carolina State University

关键词: k-means;    data mining;    cluster analysis;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/1203/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

There are many clustering methods that are referred to as k-means-like.We give the minimal necessary and sufficient components for the mechanism of the k-means (iterative and partitional) clustering method of a finite set of objects, X.Thus k-means is generalized and the methods that mimic k-means are unified.We name these k-center clustering methods.The fundamental mechanism of k-center methods exposes the usual misconceptions of k-means such as (a) "distance" satisfies some of properties of a mathematical metric, (b) there is a need to measure "distance" between objects in X, and (c)the centers of clusters have the same nature as the objects of X.Moreover, k-center methods have a common formula to choose or calculate centers of clusters.We characterize the convergent common objective function by expressing it in terms of(a) a distance measure for closeness between center objects and the objects in X and (b) the coherence of clusters. We give a three object example to demonstrate the components of the formal mechanism of a k-center method. We then give examples of various known methods that belong to the class ofk-center methods.We exhibit an extensive and thorough comparison of the qualitative k-modes and the numerical spherical k-means. Included are paradigm applications, a matrix environment, an understanding of the duality of a dissimilarity and similarity measure, and an understanding of normalized X and the normalized centers of subsets of X.