Deep spectral clustering by integrating local structure and prior information

The traditional spectral clustering (SC) is an effective clustering method that can handle data with complex structure. SC essentially embeds data in another feature space with time-consuming spectral embedding before clustering, and has to re-embed the whole data when unseen data arrive, lacking the so-called out-of-sample-extension capability. SpectralNet (Shaham et al., 2018) is a pioneer attempt to resolve these two problems by training with random mini-batches to scale to large-scale data and by an orthogonal transformation layer to ensure orthogonality of embeddings and remove redundancy in features. However, the randomly selected data in each mini-batch might be far away from each other and fail to convey local structural information; the orthogonal transformation can only ensure orthogonality for each mini-batch instead of the whole data. In this paper, we propose a novel approach to address these two problems. By improving data selection for batches with batch augmentation using neighboring information, it helps the network to better capture local structural information. By devising core point guidance to exploit the spectral embeddings of representative points as prior information, it guides the network to learn embeddings that can better maintain the overall structures of data points. Empirical results show that our method resolves the two problems of SpectralNet and exhibits superior clustering performance to SpectralNet and other state-of-the-art deep clustering algorithms, while being able to generalize the embedding to unseen data.