Auto-weighted exponential tensor nuclear norm minimization for multi-attribute low-dimensional subspace clustering

Subspace clustering (SC) is a commonly used clustering method for handling high-dimensional data. However, most existing SC algorithms ignore the multi-attribute information in the original data. In addition, they do not fully utilize the inherent low-dimensional consensus information implied in the original data, resulting in the loss of important data features during the dimensionality reduction process. To solve these issues, we propose the auto-weighted exponential tensor nuclear norm minimization for multi-attribute low-dimensional subspace clustering (MALDSC). Specifically, firstly, we design a triple matrix factorization method to find the inherent low-dimensional consensus information and obtain the corresponding multi-attribute features. Secondly, we utilize the self-expressive property of the multi-attribute features to obtain self-expressive matrices. Thirdly, to harness the complete structural information embedded within the self-expressive matrix, we tack them into a tensor, which is regulated by the auto-weighted exponential tensor nuclear norm (AWETNN), serving as a more effective substitute for the tensor rank. The AWETNN takes full account of the physical differences among singular values through a non-convex penalty function, thus more accurately representing the high-order correlation between multiple attributes. Finally, the augmented Lagrange multiplier method (ALM) is utilized to unify the above three steps into one framework. The experimental results obtained from multiple datasets demonstrate that the MALDSC algorithm outperforms the state-of-the-art algorithms in terms of performance. The code is publicly available at https://github.com/TongWuahpu/MALDSC.