Recent studies on Alzheimer's Disease (AD) or its prodromal stage, Mild Cognitive Impairment (MCI), diagnosis presented that the tasks of identifying brain disease status and predicting clinical scores based on neuroimaging features were highly related to each other. However, these tasks were often conducted independently in the previous studies. Regarding the feature selection, to our best knowledge, most of the previous work considered a loss function defined as an element-wise difference between the target values and the predicted ones. In this paper, we consider the problems of joint regression and classification for AD/MCI diagnosis and propose a novel matrix-similarity based loss function that uses high-level information inherent in the target response matrix and imposes the information to be preserved in the predicted response matrix. The newly devised loss function is combined with a group lasso method for joint feature selection across tasks, i.e., clinical scores prediction and disease status identification. We conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and showed that the newly devised loss function was effective to enhance the performances of both clinical score prediction and disease status identification, outperforming the state-of-the-art methods.