Dimensionality Reducing Based On Sliced Inverse Regression

Dimension reduction arises more attention. It is convenient to data analysis and application. Recently, advanced technique has made a great deal progress, particular biotechnology, so three are a great many high dimension data with which is needed to deal. Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high dimensional data analysis. It is of great interest both in theory and in practice.In this thesis, we review background on reducing dimension and introduce sliced inverse regression methods for reducing dimension. We propose a regularized least square algorithm on sliced inverse regression. We apply kernel into sliced inverse re-gression, in this case, some nonlinear problems are converted into linear problems, which brings a lot convenience. Local sliced inverse regression apply sliced inverse regression into semi-supervised sample data.We organize the thesis as follows:In Chapter1, we present a quick overview of background on sliced inverse regres-sion and sliced inverse regression algorithms.In Chapter2, we give regularized sliced inverse regression and kernel sliced in-verse regression. Tikhonov presented regularization method in1963. In this article, we use least square regularization. Kernel sliced inverse regression usually use Gaussian kernel.In Chapter3, we discuss local sliced inverse regression, in deed, a lot of sample data are not labeled. Aiming at the problem, we propose a local sliced inverse regres-sion, to promote its use scope.In Chapter4, we test the effectiveness of the kernel sliced inverse regression al-gorithm, and compare the slice inverse regression with kernel slice inverse regression algorithm.Finally, in Chapter5, we summarize the paper and give expectations in the future.