基于密度峰值的混合型数据聚类算法设计

针对k-prototypes算法无法自动识别簇数以及无法发现任意形状的簇的问题，提出一种针对混合型数据的新方法：寻找密度峰值的聚类算法。首先，把CFSFDP（Clustering by Fast Search and Find of Density Peaks）聚类算法扩展到混合型数据集，定义混合型数据对象之间的距离后利用CFSFDP算法确定出簇中心，这样也就自动确定了簇的个数，然后其余的点按照密度从大到小的顺序进行分配。其次，研究了该算法中阈值（截断距离）及权值的选取问题：对于密度公式中的阈值，通过计算数据场中的势熵来自动提取；对于距离公式中的权值，利用度量数值型数据集和分类型数据集聚类趋势的统计量来定义。最后通过在三个实际混合型数据集上的测试发现：与传统k-prototypes算法相比，寻找密度峰值的聚类算法能有效提高聚类的精度。

Design of mixed data clustering algorithm based on density peak

Focusing on the issue that k-prototypes algorithm is incapable of identifying automatically the number of clusters and discovering clusters with arbitrary shape, a mixed data clustering algorithm based on searching for density peaks was proposed. Firstly, CFSFDP (Clustering by fast Search and Find of Density Peaks) clustering algorithm was extended to mixed datasets in which the distances between mixed data objects were calculated to determine the cluster centers by using CFSFDP algorithm, that is, the number of clusters was determined automatically. The rest points were then assigned to the cluster in order of their density from large to small. Secondly, the selection method of threshold and weight in the proposed algorithm was introduced. In the density formula, the threshold (cutoff distance) was extracted automatically by calculating potential entropy of data field; in the distance formula, the weight was defined through certain statistic which can measure clustering tendency of numeric datasets and categorical datasets. Finally, experimental results on three real mixed datasets show that compared with k-prototypes algorithm, the proposed algorithm can effectively improve the accuracy of clustering.