Spectral clustering and embedding with inter-class topology-preserving

Spectral clustering and embedding are critical in data mining and rely heavily on pre-computed graph structure quality. Some methods simultaneously learn graph structures and low-dimensional embeddings to achieve high-quality graph structures with separable categories. However, existing approaches prioritize inter-class separability while overlooking the inter-class topological structure. Consequently, the learned low-dimensional manifold representations may fail to capture inter-class semantic information, causing the learned graph structures to represent categories partitioning inaccurately. To address these issues, we come up with the inter-class topology and utilize category anchors to indicate class locations in low-dimensional space. The inter-class topology reflects the elaborate structural neighbor information of class, which makes the neighbor classes rationally separable and helps to learn better low-dimensional embedding representations. The spectral embedded clustering method and some variants are proposed to preserve inter-class topology while making categories separable. Furthermore, we ensure intra-class sample compactness in low-dimensional space by assigning sample embeddings near the anchors. We analyze the importance of inter-class topology preserving and intra-class compactness learning. Extensive experiments on publicly available datasets demonstrate that our method is competitive with popular graph clustering and embedding baselines and effectively captures the inter-class topology.