Block diagonal representation learning with local invariance for face clustering

Facial data under non-rigid deformation are often assumed lying on a highly non-linear manifold. The conventional subspace clustering methods, such as Block Diagonal Representation (BDR), can only handle the high-dimensionality of facial data, ignoring the useful non-linear property embedded in data. Yet, discovering the local invariance in facial data remains a critical issue for face clustering. To this end, we propose a novel Block Diagonal Representation via Manifold learning (BDRM) in this paper. To be concrete, the manifold information within facial data can be learned by Locally Linear Embedding (LLE). Then manifold structure and block diagonal representation are considered jointly to uncover the intrinsic structure of facial data, which leads to a better representation for subsequent clustering task. Furthermore, the diffusion process is adopted to derive the final affinity matrix with context-sensitive, by which the learned affinity matrix can be spread and re-evaluated to enhance the connectivity of data belonging to the same intra-subspace. The extensive experimental results show that our proposed approach achieves a superior clustering performance against the state-of-the-art methods on both synthetic data and real-world facial data. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.