Deep subspace clustering uses latent features instead of raw images to construct the self-expression coefficient matrix. Existing methods primarily focus on optimizing the self-expression coefficient matrix, often neglecting the impact of latent features. However, better latent features are more in line with the self-representation assumption and results in a better self-expression coefficient matrix, which construct a chain relationship. Based on the chain relationship, this paper proposes a Class Relation Constraint (CRC) induced Deep Subspace Clustering (DSC) method to improve the representation ability of latent features. First, an intra- and inter-class weighted constraint is proposed to enhance latent data separability in subspaces. Then, to further remove negative samples inside a subspace, a contrastive loss function is introduced within the diagonal blocks of the self-expression coefficient matrix, i.e. the same subspace, under the guidance of spectral clustering results. Along with the enhanced representation ability on latent features and corresponding diagonal blocks, the self-expression coefficient matrix can provide more accurate data relationships for spectral clustering. Experimental results on multiple benchmark datasets have validated the effectiveness of the proposed DSCCRC method, particularly in handling small samples and complex datasets.

Image feature representation is a key factor influencing the accuracy of clustering. Traditional point-based feature spaces represent spectral features of an image independently and introduce spatial relationships of pixels in the image domain to enhance the contextual information expression ability. Mapping-based feature spaces aim to preserve the structure information, but the complex computation and the unexplainability of image features have a great impact on their applications. To this end, we propose an explicit feature space called Riemannian manifold feature space (RMFS) to present the contextual information in a unified way. First, the Gaussian probability distribution function (pdf) is introduced to characterize the features of a pixel in its neighborhood system in the image domain. Then, the feature-related pdfs are mapped to a Riemannian manifold, which constructs the proposed RMFS. In RMFS, a point can express the complex contextual information of corresponding pixel in the image domain, and pixels representing the same object are linearly distributed. This gives us a chance to convert nonlinear image segmentation problems to linear computation. To verify the superiority of the expression ability of the proposed RMFS, a linear clustering algorithm and a fuzzy linear clustering algorithm are proposed. Experimental results show that the proposed RMFS-based algorithms outperform their counterparts in the spectral feature space and the RMFS-based ones without the linear distribution characteristics. This indicates that the RMFS can better express features of an image than spectral feature space, and the expressed features can be easily used to construct linear segmentation models.

Synthetic aperture radar (SAR) image segmentation is a challenge due to its inherent speckle. Gamma distribution is believed to be an appropriate statistical model to describe the characteristics of speckle in SAR images. In this letter, a fuzzy clustering algorithm based on gamma distribution for SAR image segmentation is proposed, in which the Stirling equation is used to approach the gamma function in the dominator of gamma distribution under the assumption of mean field theory to make the shape parameter$\alpha $derivable. Then, the value range of the estimated$\alpha $is demonstrated to meet the requirement of gamma distribution by Jensen’s inequality. Experimental results show that the proposed method gives promising results in SAR image (including large area SAR image) segmentation and effectively suppresses the influence of speckle.