Optimal Margin Distribution Ridge Regression

Ridge regression (RR) has been one of the most classical machine learning algorithms in many real applications such as face detection, cell prediction, etc. The ridge regression has many advantages such as convex optimization objection, closed-form solution, strong interpretability, easy to kernelization and so on. But the optimization objection of ridge regression doesn’t consider the structural relationship between instances. Supervised manifold regularized (MR) method has been one of the most representative and successful ridge regression regularized methods, which considers the instance structural relationship inter each class by minimizing each class’s variance. But considering the structural relationship interclasses alone is not a very comprehensive idea. Based on the recent principle of optimal margin distribution machine (ODM) learning with a novel view, we find the optimization object of ODM can include the local structural relationship and the global structural relationship by optimizing the margin variance interclasses and the margin variance intraclasses. In this thesis, we propose a ridge regression algorithm called optimal margin distribution machine ridge regression (ODMRR) which fully considers the structural character of the instance. Besides, this algorithm can still contain all the advantages of ridge regression and manifold regularized ridge regression. Finally, the experiments validate the effectiveness of our algorithm.