Fast subspace clustering by learning projective block diagonal representation *

Block Diagonal Representation (BDR) has attracted massive attention in subspace clustering, yet the high computational cost limits its widespread application. To address this issue, we propose a novel approach called Projective Block Diagonal Representation (PBDR), which rapidly pursues a representation matrix with the block diagonal structure. Firstly, an effective sampling strategy is utilized to select a small subset of the original large-scale data. Then, we learn a projection mapping to match the block diagonal representation matrix on the selected subset. After training, we employ the learned projection mapping to quickly generate the representation matrix with an ideal block diagonal structure for the original largescale data. Additionally, we further extend the proposed PBDR model ( i.e. , PBDR c 1 and PBDR *) by capturing the global or local structure of the data to enhance block diagonal coding capability. This paper also proves the effectiveness of the proposed model theoretically. Especially, this is the first work to directly learn a representation matrix with a block diagonal structure to handle the large-scale subspace clustering problem. Finally, experimental results on publicly available datasets show that our approaches achieve faster and more accurate clustering results compared to the state-of-the-art block diagonal-based subspace clustering approaches, which demonstrates its practical usefulness. (c) 2022 Elsevier Ltd. All rights reserved.