Abstract: The dissimilarity measure and clustering approach about the heterogeneous dataset are studied，and a Weighted Mahalanobis Distance-based Quantum Clustering（WMDQC） algorithm is presented in this paper.Data often do appear in homogeneous groups，the WMDQC utilizes the structural information to improve the clustering accuracy.Unlike the numeric data，categorical data are often unbalancedly distributed，whose distribution are often unrelated with their distance measure.These characteristics are very similar to the particle world in quantum mechanism，so the WMDQC ascertains the clustering centers by the rewriting quantum potential.Further，a WMDQC-based method WMDQCM is proposed，the WMDQCM mines the structural clue by the agglomerative hierarchical clustering AHC algorithm to construct the weight matrix.By presenting the above to the WMDQC，the final clustering results are obtained.The new WMDQCM exhibits its robustness to initialization and clustering capability to heterogeneous dataset.Experimental results compared with other methods demonstrate that the proposed method has promising performance.

Key words: heterogeneous data, dissimilarity measure, Mahalanobis distance, quantum potential, clustering algorithm

摘要： 研究了异构属性数据的聚类问题。通过挖掘样本中的结构信息，用加权的Mahalanobis距离来度量异构样本的相异性；根据分类属性数据的分布与粒子在量子势能场中的分布不平衡的相似性，重写量子势能公式为距离量子势能的形式，提出了一种新的异构属性数据量子聚类WMDQC算法。通过进一步集成该算法和AHC算法为WMDQCM聚类方法，用AHC算法更高效地挖掘样本中有利于聚类的结构线索。实验结果表明，方法具有比较优势，显著地改善了聚类性能，具有一定的实用价值。

关键词: 异构数据, 相异性度量, Mahalanobis距离, 量子势能, 聚类算法