Many clustering methods may have poor performance when the data structure is complex (i.e., the data has an aspheric shape or non-linear relationship). Inspired by this view, we proposed a clustering model which combines kernel function and Locality Preserving Projections (LPP) together. Specifically, we map original data into the high-dimensional feature space according to the idea of kernel function. Secondly, it is feasible to explore the local structure of data in clustering tasks. LPP is used to preserve the original local structure information of data to improve the validity of the clustering model. Finally, some outliers are often included in real data, so we embedded sparse regularization items in the model to adjust feature weights and remove outliers. In addition, we design a simple iterative optimization method to solve the final objective function and show the convergence of the optimization method in the experimental part. The experimental analysis of ten public data sets showed that our proposed method has better efficiency and performance in clustering tasks than existing clustering methods.

当数据结构复杂（即数据具有非球面形状或非线性关系）时，许多聚类方法的性能可能会很差。受此观点启发，我们提出了一个聚类模型，该模型将内核功能和局部性保留投影（LPP）结合在一起。具体来说，我们根据核函数的思想将原始数据映射到高维特征空间。其次，在聚类任务中探索数据的局部结构是可行的。LPP用于保留数据的原始局部结构信息，以提高聚类模型的有效性。最后，实际数据中经常包含一些离群值，因此我们将稀疏正则化项嵌入模型中以调整特征权重并删除离群值。此外，我们设计了一种简单的迭代优化方法来求解最终目标函数，并在实验部分展示了该优化方法的收敛性。对十个公共数据集的实验分析表明，与现有聚类方法相比，本文提出的方法在聚类任务中具有更高的效率和性能。