This paper introduces a new evidential clustering algorithm based on finding the “cumulative belief peaks” and evidential $K$-nearest neighbor rule. The basic assumption of this algorithm is that a cluster center has the highest cumulative possibility of becoming a cluster center among its neighborhood and size of its neighborhood is relatively large. To measure such cumulative possibility, a new notion of cumulative belief is proposed in the framework of belief functions. By maximizing an objective function, an appropriate size of the relatively large neighborhood is determined. Then, the objects with highest cumulative belief among their own neighborhood of this size are automatically detected as cluster centers. Finally, a credal partition is derived by evidential $K$-nearest neighbor rule with the fixed cluster center. Experimental results show that the proposed evidential clustering algorithm can automatically detect cluster centers and well reveal the data structure in form of a credal partition in tolerable time, when tackling datasets with small number of data objects and dimensions. As the sizes of datasets increase, running time of such new clustering algorithm increases sharply and this reduces the practicability of it. Simulations on synthetic and real-world datasets validate our conclusions.

本文在发现“累积置信峰值”和证据的基础上，提出了一种新的证据聚类算法。 $ķ$-最近邻居规则。该算法的基本假设是，聚类中心在其邻域中成为聚类中心的累积可能性最高，并且其邻域的大小相对较大。为了测量这种累积可能性，在信念函数框架内提出了一种新的累积信念概念。通过最大化目标函数，确定相对较大邻域的适当大小。然后，在其自己的这种大小的邻域中具有最高累积置信度的对象将自动检测为聚类中心。最后，根据证据推导出一个credal分区$ķ$-使用固定群集中心的最近邻居规则。实验结果表明，提出的证据聚类算法在处理数据对象和维数较少的数据集时，可以在可忍受的时间内自动检测聚类中心并以credal分区的形式很好地揭示数据结构。随着数据集大小的增加，这种新的聚类算法的运行时间急剧增加，这降低了其实用性。在合成和真实数据集上进行的仿真验证了我们的结论。