CAJ | 학술논문

用于发现数据集类簇数 k 的常用内部评价指标 DB（Davies Bouldin）和 BWP（Between-within Proportion）等需要先确定一个搜索范围 kmax ，使数据集的类簇数满足 k≤kmax，但如何确定 k max尚无理论指导。针对这一问题，提出一个新 F 统计量 Fr ，将 Fr 作为新聚类有效性准则，以判断聚类算法收敛与否，自适应地确定数据集类簇数；将 Fr 应用于快速 K-medoids 算法的收敛性判断，并以基于最小生成树的测地距离，即样本对在最小生成树上的路径长度，代替其间的直接欧氏距离度量样本相似性，得到一种自适应的快速 K-medoids 聚类算法，解决了 K-medoids 算法需要人为给定类簇数和不能发现任意形状簇的问题。UCI 机器学习数据库数据集和人工模拟数据集实验测试表明，本文提出的Fr 指标是一种有效的聚类算法评价指标，基于该指标和测地距离的 K-medoids 算法不仅能发现任意形状的簇，还可以自适应地确定数据集的类簇数，且对噪音数据有很好的鲁棒性。
용우발현수거집류족수 k 적상용내부평개지표 DB（Davies Bouldin）화 BWP（Between-within Proportion）등수요선학정일개수색범위 kmax ，사수거집적류족수만족 k≤kmax，단여하학정 k max상무이론지도。침대저일문제，제출일개신 F 통계량 Fr ，장 Fr 작위신취류유효성준칙，이판단취류산법수렴여부，자괄응지학정수거집류족수；장 Fr 응용우쾌속 K-medoids 산법적수렴성판단，병이기우최소생성수적측지거리，즉양본대재최소생성수상적로경장도，대체기간적직접구씨거리도량양본상사성，득도일충자괄응적쾌속 K-medoids 취류산법，해결료 K-medoids 산법수요인위급정류족수화불능발현임의형상족적문제。UCI 궤기학습수거고수거집화인공모의수거집실험측시표명，본문제출적Fr 지표시일충유효적취류산법평개지표，기우해지표화측지거리적 K-medoids 산법불부능발현임의형상적족，환가이자괄응지학정수거집적류족수，차대조음수거유흔호적로봉성。
The internal evaluation criteria,such as DB and BWP et al,need the upper bound of k max to be given in advance when these criteria are used to determine the number of clusters of a dataset,so that the number of clusters of k in a dataset satisfies k≤k max.However,there is not so far a theory about how to find the upper bound of k max .Aiming at this problem,a new F-sta-tistics Fr is proposed in this paper.Fr can be used as a new criterion to judge whether a clustering algorithm is converged or not,so that the number of clusters of a dataset can be found automati-cally without the upper bound of k max to be given in advance.In addition,F r is applied to the fast K-medoids clustering algorithm as its criterion to judge whether its iterations continues or not, and the geodesic distance between samples on the minimum spanning tree (MST),that is the length of the path between samples on MST,is introduced to instead of the direct Euclidean dis-tance between them to measure their similarities,so that an adaptive fast K-medoids algorithm is obtained.The adaptive K-medoids algorithm avoids the deficiencies of the available K-medoids al-gorithms which need the number of clusters to be given in advance and cannot detect the clusters with any arbitrary shape.The power of the proposed criterion Fr and the power of the adaptive fast K-medoids algorithm are tested in real world datasets from UCI machine learning repository and in the synthetic datasets.All the experimental results demonstrate that our proposed criteri-on Fr is a valid clustering criterion,and the adaptive fast K-medoids algorithm based on the F r and geodesic distance can recognize the clusters with arbitrary shape,and can detect the number of clusters automatically,and is robust to noises as well.