Medical imaging technology has made tremendous progress in recent decades and is playing a more and more crucial role in contemporary medical analysis. The growth of medical imaging data facilitates the integration of medicine and machine learning methods, which is bringing medicine into the era of big data. Compared to general images, medical imaging data has its own properties, including but not limited to two aspects: i) data is usually of high dimension while low sample size and ii) model interpretation is more concerned. Traditional machine learning methods have difficulty addressing these characters. Therefore, this thesis proposed three novel statistical machine learning methods, aiming at regression and clustering tasks. Based on Kronecker product decomposition, one regression method and one clustering method are studied for both matrix and tensor valued data. The regression method named Deep Kronecker Network models the coefficients through consecutive Kronecker product, which significantly reduces the dimension while capturing important regions associated with the response. Notably, it not only connects with another tensor regression framework, but also can be viewed as a special convolutional neural network. The clustering method, named Image Clustering via Sparse Kronecker Product Decomposition, supposes region-wise sparseness in signals. It would simultaneously divide samples into clusters and detect regions that are informative for clustering. In addition, considering the heterogeneity of data, an individualized regression model is proposed for the purpose of personalized treatment. It starts with the vector correlation, modelling the coefficients by internal relations within samples themselves. The proposed method is referred to as Attention boosted Individualized Regression due to its close connections with the self-attention mechanism. Each method is solved by the developed algorithm and theoretical guarantees of computed results are provided. Comprehensive simulation studies are conducted to show their superior performances. Besides, they are applied to real brain MRI data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) which demonstrates their applicability.