Region detection and image clustering via sparse Kronecker product decomposition

Image clustering is usually conducted by vectorizing image pixels, treating them as independent, and applying classical clustering approaches to the obtained features. However, as image data is often of high-dimensional and contains rich spatial information, such treatment is far from satisfactory. For medical image data, another important characteristic is the region-wise sparseness in signals. That is to say, there are only a few unknown regions in the medical image that differentiate the images associated with different groups of patients, while other regions are uninformative. Accurately detecting these informative regions would not only improve clustering accuracy, more importantly, it would also provide interpretations for the rationale behind them. Motivated by the need to identify significant regions of interest, we propose a general framework named Image Clustering via Sparse Kronecker Product Decomposition (IC-SKPD). This framework aims to simultaneously divide samples into clusters and detect regions that are informative for clustering. Our framework is general in the sense that it provides a unified treatment for matrix and tensor-valued samples. An iterative hard-thresholded singular value decomposition approach is developed to solve this model. Theoretically, the IC-SKPD enjoys guarantees for clustering accuracy and region detection consistency under mild conditions on the minimum signals. Comprehensive simulations along with real data analysis further validate the superior performance of IC-SKPD on clustering and region detection.