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Alzheimer's disease (AD) is a neurodegenerative disorder with slow onset, which could result in the deterioration of the duration of persistent neurological dysfunction. How to identify the informative longitudinal phenotypic neuroimaging markers and predict cognitive measures are crucial to recognize AD at early stage. Many existing models related imaging measures to cognitive status using regression models, but they did not take full consideration of the interaction between cognitive scores. In this paper, we propose a robust low-rank structured sparse regression method (RLSR) to address this issue. The proposed model simultaneously selects effective features and learns the underlying structure between cognitive scores by utilizing novel mixed structured sparsity inducing norms and low-rank approximation. In addition, an efficient algorithm is derived to solve the proposed non-smooth objective function with proved convergence. Empirical studies on cognitive data of the ADNI cohort demonstrate the superior performance of the proposed method.

Support Vector Machine (SVM) is originally proposed as a binary classification model, and it has already achieved great success in different applications. In reality, it is more often to solve a problem which has more than two classes. So, it is natural to extend SVM to a multi-class classifier. There have been many works proposed to construct a multi-class classifier based on binary SVM, such as one versus all strategy, one versus one strategy and Weston's multi-class SVM. One versus all strategy and one versus one strategy split the multi-class problem to multiple binary classification subproblems, and we need to train multiple binary classifiers. Weston's multi-class SVM is formed by ensuring risk constraints and imposing a specific regularization, like Frobenius norm. It is not derived by maximizing the margin between hyperplane and training data which is the motivation in SVM. In this paper, we propose a multi-class SVM model from the perspective of maximizing margin between training points and hyperplane, and analyze the relation between our model and other related methods. In the experiment, it shows that our model can get better or compared results when comparing with other related methods.

The low-rank matrix recovery is an important machine learning research topic with various scientific applications. Most existing low-rank matrix recovery methods relax the rank minimization problem via the trace norm minimization. However, such a relaxation makes the solution seriously deviate from the original one. Meanwhile, most matrix recovery methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix recovery model to address the above two challenges. The joint capped trace norm and capped $\ell_1$-norm are used to tightly approximate the rank minimization and enhance the robustness to outliers. The evaluation experiments are performed on both synthetic data and real world applications in collaborative filtering and social network link prediction. All empirical results show our new method outperforms the existing matrix recovery methods.