A New RKHS-based Approach To Nonlinear Kernel Dimension Reduction

Due to the continuous development of science and technology, especially the rapid development of computer technology, high-dimensional data continue to emerge in many areas, such as large Internet data, socioeconomic data, biomedical data. High-dimensional data bring in greater amount of information, but also bring the advent of the "curse of dimensionality" problem. How to effectively solve the "curse of dimen-sionality" has become a pressing issue. Study dimension reduction becomes significant. Kenji Fukumizu, who proposed the use of conditional covariance based on reproducing kernel Hilbert space (RKHS) theory of operator to obtain a new dimension reduction. The method utilizes the nature of RKHS, with the conditional covariance operator to characterize SDR. In this paper, on the basis of its promotion to the nonlinear case, so that the method can process data model with nonlinear structure. The advantage of this approach is that less assumptions, strong adaptability and stability. By data simulation and empirical analysis, we can see that the method of nonlinear dimensionality reduc-tion problem on a good performance, while the use of the classification issue which also has a good performance. At the same time, this method also has some areas for further research, such as the speed of the algorithm to be further enhanced, in theory, the progressive nature of further study.