Semi-Parametric Polynomial Inverse Regression For Dimension Reduction And Its Application

Modern advances in computing power have greatly widened our scope in gathering information from more variables, which might have been ignored in the past.Yet to effectively scan a large pool of variables is not a easy task,and high-dimension independent variables also challenge the traditional nonparametric methods.At the same time,as the development of the gene microarray technology,the contradiction between number of genes and sample size has become more apparent.In this article,we propose a new method for dimension reduction,Semi-Parametric Polynomial Inverse Regression ,based on sliced inverse regression.In order to gather the information we need about y,according to the model y = f(β₁^T x,β₂^Tx,…,β_K^Tx,ε), we regress x against y.Under such inverse regression,the data matrix X is modified to a new one X^*,which include the information we want,and then conduct a principal component analysis for X^*.(β₁,…,β_K), which is the dimension reduction component,has nothing to do with structural form of f.By simulation,we demonstrate how SPPIR can reduce the dimension of the input variables effectively without information loss,and fix the number of the dimension reduction component.In the end of article,we conduct SPPIR and discrimination analysis for a tumor gene microarray data,and then effectiveness of the dimension reduction methods can be seen by comparing with other methods.