Aging subjects with neurodegenerative conditions have multiple contributors and pathology progression patterns that result in heterogeneous disease biology and different disease phenotypes. Clinical data play a crucial role in disentangling such disease heterogeneity, but they are usually by noise, which can result in errors in clustering leading to spurious non-clinically relevant clusters. A limitation of conventional neuroimaging clustering methods is neglecting the potential bias caused by noise. To remove noise, we introduce adaptive regularization based on coefficient distribution modeling in transform domain. Different from traditional sparsity techniques that assume zero expectation of the coefficients, we use the data of interest to form the Laplace distributions so that they can depict the statistical characteristics more accurately. Furthermore, we use feature clusters to provide weak supervision for enhanced clustering of subjects. To this end, we employ nonnegative matrix tri-factorization to collaboratively cluster subjects and features. Experimental results on synthetic data and the real-life clinical dataset PRVENT-AD demonstrate superior effectiveness of the proposed approach.