The applications of clustering in biomedical is pervasive and ubiquitous. A typical example is gene expression data analysis, where clustering is emerging as a powerful solution for uncovering cancer-related insights. Neutrosophic -means (NCM) clustering has advantages over other conventional clustering methods in characterizing the uncertainty and imprecision caused by cluster overlap and identifying outliers. Nonetheless, NCM and its derivatives equally treat the contribution of each attribute to the cluster. In biomedical applications, genes ( attributes) should take different importance in identifying different clusters. In this paper, we first propose a self-adaptive attribute-weighted neutrosophic -means (AWNCM) clustering method to overcome the above defects. Moreover, a new objective function is designed to obtain optimal neutrosophic partition, cluster centers and attribute weights. Since AWNCM tends to be more effective against spherical data, we further develop a kernelized version of AWNCM, called KAWNCM, in order to better satisfy the clustering of some complex data ( non-spherical data). We employ the iterative optimization strategy to obtain the optimal solutions for AWNCM and KAWNCM. The advantage of AWNCM and KAWNCM is to improve performance by learning the importance of each attribute to the cluster while maintaining an efficient solution to cluster overlap and outliers. Extensive experimental results using synthetic data and gene expression data demonstrate the feasibility and effectiveness of the proposed methods.

中文翻译：

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用于生物医学应用的自适应属性加权中智c均值聚类

聚类在生物医学中的应用是普遍且无处不在的。一个典型的例子是基因表达数据分析，其中聚类正在成为揭示癌症相关见解的强大解决方案。中智均值（NCM）聚类在表征聚类重叠引起的不确定性和不精确性以及识别异常值方面比其他传统聚类方法具有优势。尽管如此，NCM 及其衍生产品同等对待每个属性对集群的贡献。在生物医学应用中，基因（属性）在识别不同簇时应具有不同的重要性。在本文中，我们首先提出了一种自适应属性加权中智均值（AWNCM）聚类方法来克服上述缺陷。此外，设计了新的目标函数以获得最优的中智分区、聚类中心和属性权重。由于AWNCM往往对球形数据更有效，因此我们进一步开发了AWNCM的内核化版本，称为KAWNCM，以便更好地满足一些复杂数据（非球形数据）的聚类。我们采用迭代优化策略来获得 AWNCM 和 KAWNCM 的最优解。 AWNCM 和 KAWNCM 的优点是通过了解每个属性对集群的重要性来提高性能，同时保持对集群重叠和异常值的有效解决方案。使用合成数据和基因表达数据的大量实验结果证明了所提出方法的可行性和有效性。