Abstract Traditional partition-based clustering algorithms, hard or fuzzy version of C-means, could not deal with high-dimensional data sets effectively as redundant features may impact the computation of distances and local spatial structures among patterns are rarely considered. High dimensionality of space gives rise to so-called concentration effect that is detrimental. In this paper, a novel locality preserving based fuzzy C-means (LPFCM) clustering method and its optimization are presented. An orthogonally projected space, which preserves the locality of structural properties, can be generated in LPFCM, thus enhancing the capability of fuzzy C-means (FCM) for handling high-dimensional data. It is the first time to introduce projection techniques to the FCM optimization objective function directly, and the ideas of fuzzy clustering, geometric structure preservation and feature extraction are seamlessly integrated. LPFCM is also regarded as a unified model that combines two separate stages of spectral clustering. Experimental results on some benchmark data sets show the effectiveness of LPFCM in comparison with FCM and some state-of-the-art methods.

中文翻译：

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具有局部性保留的投影模糊 C 均值聚类

摘要 传统的基于分区的聚类算法，C-means 的硬或模糊版本，无法有效处理高维数据集，因为冗余特征可能影响距离的计算，并且很少考虑模式之间的局部空间结构。空间的高维会产生有害的所谓集中效应。在本文中，提出了一种新的基于局部保持的模糊 C 均值 (LPFCM) 聚类方法及其优化。在 LPFCM 中可以生成保留结构特性局部性的正交投影空间，从而增强模糊 C 均值 (FCM) 处理高维数据的能力。首次将投影技术直接引入FCM优化目标函数，模糊聚类的思想，几何结构保存和特征提取无缝集成。LPFCM 也被认为是一个统一的模型，它结合了光谱聚类的两个独立阶段。在一些基准数据集上的实验结果表明，与 FCM 和一些最先进的方法相比，LPFCM 的有效性。