Online learning for supervised dimension reduction

Online learning has attracted great attention due to the increasingdemand for systems that have the ability of learning and evolving. When thedata to be processed is also high dimensional and dimension reduction is necessary for visualization or prediction enhancement, online dimension reductionwill play an essential role. The purpose of this paper is to propose a new onlinelearning approach for supervised dimension reduction. Our algorithm is motivated by adapting the sliced inverse regression (SIR), a pioneer and effectivealgorithm for supervised dimension reduction, and making it implementable inan incremental manner. The new algorithm, called incremental sliced inverseregression (ISIR), is able to update the subspace of significant factors with intrinsic lower dimensionality fast and efficiently when new observations come in.We also refine the algorithm by using an overlapping technique and develop anincremental overlapping sliced inverse regression (IOSIR) algorithm. We verifythe effectiveness and efficiency of both algorithms by simulations and real dataapplications.