一种基于似然极大的动态聚类方法及其应用

A Maximum Likelihood-Based Dynamic Clustering Method and Its Application

将传统的动态聚类分析和判别分析相结合,引出一种基于似然极大的动态聚类方法,该方法以EM算法实现的极大似然估计进行类参数估计,以相应的贝叶斯后验概率判别个体的归类。模拟研究表明,该方法通常既可无偏估计类参数,又可判别最佳分类个数。与重心法动态聚类和最小组内平方和法动态聚类相比,稳健性较高。同时通过提高判别标准,可以降低误判率。用Fisher的Iris试验数据验证了方法的可行性,并将之成功应用于一个水稻F2群体的个体的主基因基因型鉴别。

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 miselassified 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 method was validated by a real dataset and 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 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 em 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 eomplete dominance for number of tillers.