关键词: 聚类分析, 后验概率, 贝叶斯信息准则, 判别分析

Abstract:

Clustering analysis is to determine the intrinsic grouping in a set of unlabeled data. A cluster is a collection of objects which are similar between them and are dissimilar to the objects belonging to other clusters. However, the current clustering techniques have not addressed all the requirements adequately. For instance, dealing with large number of dimensions and large number of data can be problematic because of time complexity. The effectiveness of the distance-based clustering methods depends on the definition of distance; if an obvious distance measure doesn’t exist we must define it, which is not always easy, especially in multi-dimensional spaces. In addition, the choice of the optimal number of clusters in practice is impossible. Thus, choosing the correct number of clusters and the best clustering method is still a question open to discussion. In order to solve these problems, in this paper, we introduced a maximum likelihood-based dynamic clustering method, which combined the conventional dynamic clustering and discrimination analysis. The parameters of different clusters were estimated by the maximum likelihood method implemented via expectation-maximization (EM) algorithm and the objects were classified by the Bayesian posterior probability. This classified idea could increase the posterior confidence of classified individuals. The results of simulation studies showed that the proposed method not only unbiasedly estimated the corresponding cluster parameters but also differentiated the optimum clustering numbers by Bayesian information criterion (BIC). Compared with the K-means method and the minimum square sum within groups (MinSSw) method, the proposed method was more robustness and had almost the same clustering accuracy as K-means and MinSSw methods. Moreover, the misclassified rate (MR) could be reduced by enhancing the discrimination criterion. However, the unclassified rate (UR) would be increased by enhancing the discrimination criterion. Thus, an eclectic discrimination criterion could be given by the user in order to decrease both MR and UR. The result indicated that the proposed method had a significant advantage on clustering accuracy compared to the K-means and MinSSw methods. An example of the plant height and the number of tiller of F₂ population in rice cross Duonieai×Zhonghua 11 was used in the illustration. The results listed in Table 6 indicated that the genetic difference of these two traits in this cross involves only one pleiotropic major gene. The additive effect and dominance effect of the major gene were estimated as －24.57 cm and 57.12 cm on plant height, and 23.01 and －25.89 on number of tiller, respectively. The major gene shows overdominance for plant height and near complete dominance for number of tillers.

Key words: Cluster analysis, Posterior probability, Bayesian information criterion, Discrimination analysis