Stochastic simulation of patterns using ISOMAP for dimensionality reduction of training images.

Most data in the real world are normally nonlinear or difficult to determine whether they are linear or not beforehand. Some linear dimensionality reduction algorithms, e.g., principal component analysis (PCA) and multi-dimensional scaling (MDS) are only suitable for linear dimensionality reduction of spatial data. The patterns extracted from training images (TIs) used in MPS simulation mostly are probably nonlinear, so for some MPS simulation methods based on dimensionality reduction, e.g., FILTERSIM using some filters created via the idea of PCA and DisPAT using MDS as a tool of dimensionality reduction, those linear methods for dimensionality reduction are not appropriate when realizing the dimensionality reduction of nonlinear data of patterns. Therefore, isometric mapping (ISOMAP) working as a nonlinear dimensionality reduction method used in manifold learning is introduced to map those patterns, regardless of being linear or nonlinear, into low-dimensional space. However, because the original ISOMAP has some disadvantages in computing speed and accuracy, landmark points of patterns are selected to improve the speed and neighborhoods of patterns are set to guarantee the quality of dimensionality reduction. Next, the sequential simulation similar to FILTERSIM is performed after low-dimensional data of patterns are classified by a density-based clustering algorithm. The comparisons with FILTERSIM and DisPAT show the improvement of pattern reproductivity and computing speed of our method for both continuous and categorical variables. [ABSTRACT FROM AUTHOR]