Manifold Enhanced 2-D Fuzzy Subspace Clustering for Image Data

Many fuzzy subspace clustering methods have been proposed for high-dimensional image data with rich structural information. However, since these methods do not fully exploit the subspace information in each cluster, their performance on image clustering is still not promising. In this work, we propose to find soft partitions directly based on the construction of subspaces. For each cluster, we use a bilinear orthogonal subspace to represent it. Then, through the reconstruction error of a sample in the subspace corresponding to a cluster, a new membership measure for the sample to the cluster is established. Furthermore, the graph regularization is imposed on these bilinear subspaces to preserve the local relational or manifold information of the image data in the original space. Altogether, we get a clustering model considering not only the subspace information but also the manifold information in image data. An efficient optimization algorithm is proposed to our model, and its theoretical convergence and time complexity are presented correspondingly. The proposed method is a one-stage clustering model that does not require vectorized image data, thereby reducing the computational burden while maintaining the structural relationship between pixels in the image. Competitive experimental results on benchmark datasets show that our model can converge quickly with strong clustering performance, which confirms the efficiency and superiority of the proposed method compared to other state-of-the-art fuzzy clustering methods.