The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for optimization, leading to limitations in the clustering effect due to the introduced hyperparameters and the initialization of clustering centers. Moreover, maintaining class balance during clustering remains challenging. To overcome these issues, we propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework. Specifically, we establish a connection between K-means and the manifold structure, allowing us to perform K-means without explicitly defining centroids. Additionally, we use this centroid-free K-means to generate labels in low-dimensional space and subsequently utilize the label information to determine the similarity between samples. This approach ensures consistency between the manifold structure and the labels. Our model effectively achieves one-step clustering without the need for redundant balancing hyperparameters. Notably, we have discovered that maximizing the $\ell_{2,1}$-norm naturally maintains class balance during clustering, a result that we have theoretically proven. Finally, experiments on multiple datasets demonstrate that the clustering results of Our-LPP and Our-MFA exhibit excellent and reliable performance.

本研究针对传统K均值聚类中的维度诅咒和类不平衡问题，提出了一种自监督图嵌入框架，通过将流形学习与K均值聚类相结合，以实现无中心的聚类。该方法不仅避免了超参数的影响，还通过最大化$\ell_{2,1}$-范数来自然维护类平衡。实验结果表明，该方法在多个数据集上表现出色且可靠。

自监督图嵌入聚类