Granular-ball computing-based manifold clustering algorithms for ultra-scalable data

Manifold learning is essential for analyzing high-dimensional data, but it suffers from high time complexity. To address this, researchers proposed using anchors and constructing a similarity matrix to expedite eigen decomposition and reduce sparse consumption. However, randomly selected anchors fail to represent the data well, and using K-means for anchor generation is time-consuming. In this paper, we introduce Granular-ball (GB) into unsupervised manifold learning, presenting GB-USC and GB-USEC. By employing a coarse-to-fine approach, we generate high-quality anchors aligned with the data distribution. A bipartite graph is constructed between data points and anchors, enabling low-dimensional manifold embedding using transfer cut. GB-USEC combines multiple GB-USC clusters, generating consistent low-dimensional embeddings across dimensions and determining clustering results through voting. The experimental results show that compared with the state-of-the-art algorithm U-SPEC, GB-USC achieves the similar performance with the average running time of GB-USC is 33.96% less than that of U-SPEC for several million-level datasets. Additionally, our ensemble algorithm improves the clustering efficiency by an average of 29.19% compared with U-SENC.