The selection of a proper distance function is crucial for analyzing the data efficiently. To find an appropriate distance for clustering algorithm is an unsolved problem as of now. The purpose of this study is to introduce an adaptive fused distance. The S-distance is integrated with the Euclidean distance with the help of a statistical coefficient that depends on density variance of a dataset. We afterward propose a modified $k$-means clustering algorithm using the novel distance in order to achieve improvement in clustering by finding out the natural and obscure patterns in the data. Some useful properties of the novel distance metrics are elaborated. Theoretical convergence analysis of the proposed clustering is addressed. All the experiments are performed on fourteen datasets. Empirical results using five clustering evaluation metrics on fourteen datasets illustrate that the proposed clustering algorithm defeats seven state-of-the-art clustering methods before and after adding noisy features. It is also proved that the proposed clustering algorithm is statistically significant.

选择合适的距离函数对于有效分析数据至关重要。到目前为止，为聚类算法找到合适的距离是一个尚未解决的问题。本研究的目的是介绍自适应融合距离。在取决于数据集密度方差的统计系数的帮助下，S距离与欧几里得距离相结合。我们随后提出修改的建议$ķ$-均值聚类算法使用新颖的距离，以便通过找出数据中的自然和模糊模式来实现聚类的改进。阐述了新颖距离度量的一些有用属性。提出的聚类的理论收敛分析得到解决。所有实验均在14个数据集上进行。在14个数据集上使用5个聚类评估指标的经验结果表明，所提出的聚类算法在添加噪声特征之前和之后均击败了7种最新的聚类方法。还证明了所提出的聚类算法具有统计意义。