Current clustering algorithms solved a few of the issues around clustering such as similarity measure learning, or the cluster number estimation. For instance, some clustering algorithms can learn the data similarity matrix, but to do so they need to know the cluster number beforehand. On the other hand, some clustering algorithms estimate the cluster number, but to do so they need the similarity matrix as an input. Real-world data often contains redundant features and outliers, which many algorithms are susceptive to. None of the current clustering algorithms are able to learn the data similarity measure and the cluster number simultaneously, and at the same time reduce the influence of outliers and redundant features. Here we propose a joint feature selection with dynamic spectral clustering (FSDS) algorithm that not only learns the cluster number k and data similarity measure simultaneously, but also employs the \( {\text{L}}_{2,1} \)-norm to reduce the influence of outliers and redundant features. The optimal performance could be reached when all the separated stages are combined in a unified way. Experimental results on eight real-world benchmark datasets show that our FSDS clustering algorithm outperformed the comparison clustering algorithms in terms of two evaluation metrics for clustering algorithms including ACC and Purity.

当前的聚类算法解决了围绕聚类的一些问题，例如相似性度量学习或聚类数估计。例如，某些聚类算法可以学习数据相似性矩阵，但要这样做，他们需要事先知道聚类编号。另一方面，某些聚类算法会估计聚类数，但要这样做，它们需要相似度矩阵作为输入。现实世界中的数据通常包含冗余特征和离群值，许多算法对此很敏感。当前的聚类算法均无法同时学习数据相似性度量和聚类数，同时还可以减少离群值和冗余特征的影响。k和数据相似度同时进行度量，但也使用\（{\ text {L}} _ {2,1} \）-范数来减少离群值和冗余特征的影响。当所有分离的阶段以统一的方式组合时，可以达到最佳性能。在八个真实基准数据集上的实验结果表明，就两个聚类算法（包括ACC和Purity）的评估指标而言，我们的FSDS聚类算法优于比较聚类算法。