Learning Structure Aware Deep Spectral Embedding
This addresses a limitation in spectral embedding for clustering real-world data with non-linear structures, representing an incremental improvement over existing subspace clustering methods.
The paper tackles the problem of spectral embedding not preserving subspace structure when data lies on non-linear manifolds, proposing a structure-aware deep spectral embedding that combines spectral embedding loss with structure preservation loss using attention-based self-expression learning, achieving excellent clustering performance on six real-world datasets compared to state-of-the-art methods.
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original space is not preserved in the embedding space. To address this issue subspace clustering has been proposed by replacing the SE graph affinity with a self-expression matrix. It works well if the data lies in a union of linear subspaces however, the performance may degrade in real-world applications where data often spans non-linear manifolds. To address this problem we propose a novel structure-aware deep spectral embedding by combining a spectral embedding loss and a structure preservation loss. To this end, a deep neural network architecture is proposed that simultaneously encodes both types of information and aims to generate structure-aware spectral embedding. The subspace structure of the input data is encoded by using attention-based self-expression learning. The proposed algorithm is evaluated on six publicly available real-world datasets. The results demonstrate the excellent clustering performance of the proposed algorithm compared to the existing state-of-the-art methods. The proposed algorithm has also exhibited better generalization to unseen data points and it is scalable to larger datasets without requiring significant computational resources.