In this chapter, we discussed dimension reduction methods for data analysis. First, PCA methods were explained for the linear method. Then, projection pursuit methods were described. For nonlinear methods, GPCA algebraic curve fitting methods and principal curves were introduced. Finally, we explained sliced inverse regression for the reduction of the dimension of explanatory variable space.
These methods are not only useful for data analysis, but also effective for preprocessing when carrying out another data analysis. In particular, they are indispensable for the analysis of enormous amounts of and complex data, e.g. microarray data, log data on the Internet, etc. Research in this field will continue to evolve in the future.