Adaptively Topological Tensor Network for Multi-View Subspace Clustering

Multi-view subspace clustering employs learned self-representation from multiple tensor decompositions to exploit the low-rank information. However, the data structures embedded with self-representation tensors may vary in different multi-view datasets. Therefore, a pre-defined decomposition may not fully exploit low-rank information from various data, resulting in sub-optimal multi-view clustering performance. To alleviate this, we proposed the adaptively topological tensor network (ATTN). ATTN can learn a suitable decomposition structure that can represent the low-rank structure and high-order correlation of the self-representation tensors better in a data-driven way, which can capture the intra-view and inter-view information better. Firstly, instead of connecting the tensor network blindly, ATTN utilizes the correlation between adjacent factors to prune redundant connections from the fully connected tensor network, making the tensor network more expressive. Furthermore, a greedy adaptive rank-increasing strategy is applied to optimize the pruned tensor network structure, which improves the capacity of capturing low-rank structure. We apply ATTN on a multi-view subspace clustering task and utilize the alternating direction method of multipliers(ADMM) method to optimize it. Experiments show that multi-view subspace clustering based on ATTN has better performance on nine multi-view datasets.