最优间隔分布脊回归

Optimal Margin Distribution Ridge Regression

脊回归(ridge regression,RR)是经典的机器学习算法之一,广泛应用于人脸识别、基因工程等诸多领域.其具有优化目标凸、存在闭合解、可解释性强以及易于核化等优点,但是脊回归的优化目标并没有考虑样本之间的结构关系.监督流形正则化学习是最具代表性的、最成功的脊回归正则化方法之一,其通过最小化每类类内方差来考虑样本之间的类内结构关系,可是单纯地只考虑类内结构仍然不够全面.以一种全新的视角重新审视最近提出的"最优间隔分布学习"原理,发现了最优间隔分布的目标可以同时优化类内间隔方差和类间间隔方差,从而同时优化了局部的类内结构和全局的类间结构.基于此提出了一种充分考虑数据结构化特征的脊回归算法——最优间隔分布脊回归(optimal margin distributionmachine ridge regression,ODMRR)算法,该算法具有RR以及MRRR(manifold regularization ridge regression)的各种优势.最后通过实验验证了该方法具有优越的性能.

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.