Although spectral clustering is capable of identifying clusters of arbitrary shapes, its high time and space complexity poses limitations in large-scale data clustering applications. To tackle this problem, researchers have proposed using anchor points to construct the similarity matrix, thereby reducing time and space complexity. However, current methods for generating anchor points do not fit the data well and are limited in approach. To improve upon existing anchor points generation methods, we proposes a pseudo-label-based anchor points generation approach and develops a fast spectral clustering algorithm for large-scale data, named FSC-PLGB. The algorithm first randomly selects r points as an initial granular-ball, applies K-Means on these points to obtain pseudo-labels, calculates the pseudo-purity of the granular-ball based on these pseudo labels, and then performs granular-ball division based on these pseudo-purity to generate anchor points. A similarity matrix is constructed between all sample points and anchor points, and finally, spectral clustering is applied to obtain the clustering results. The experimental results demonstrate that our proposed algorithm exhibits exceptional efficiency and significant superiority on large-scale datasets. The source code is available at https://github.com/DongdongCheng/FSC-PLGB.

With the swift advancement of information technology, vast amounts of high-dimensional data have accumulated across various domains. Clustering such data presents a significant challenge, as existing methods often suffer from slow execution speeds and reduced clustering accuracy. To tackle these issues, we introduce the granular-ball approach, which aims to decrease the number of sample points and enhance processing speed, while also improving clustering accuracy through feature selection. Granular-ball computing, a coarse-grained data representation technique, has demonstrated its advantages in enhancing classification and clustering models in recent studies. However, current granular-ball division techniques are inadequate for high-dimensional data. To confront the complexities arising from clustering high-dimensional data and improve upon existing granular-ball methods, this paper proposes a novel granular-ball division approach that leverages pseudo-labels and feature selection. This new method enables the identification of anchor points through an improved granular-ball division process, leading to the development of a fast spectral clustering algorithm for high-dimensional data, termed PLGB-FSC. Specifically, we initially employ weighted K-Means for feature to generate pseudo-labels. Subsequently, we conduct a primary stage of feature selection by utilizing the mutual information between pseudo-labels and features, thereby eliminating the interference caused by irrelevant features. We further refine the feature selection by combining standard deviation and pearson correlation coefficients to choose mutually independent features. Using these pseudo-labels, we then perform granular-ball division to obtain anchor points. Lastly, we construct a similarity matrix between all sample points and the anchor points, and leveraging spectral clustering for definitive clustering outcomes. Experimental evaluations reveal that PLGB-FSC surpasses state-of-the-art algorithms such as W-KMeans, WGB, GB-USC, RC-PCA-SC, GLUFC, FGOC, SFESA, SPCAFS, and LLSRFS, and it achieves higher accuracy and faster execution speed. The source code is available at https://github.com/DongdongCheng/PLGB-FSC.