Image Dimensionality Reduction Based on the Intrinsic Dimension and Parallel Genetic Algorithm

2. Commonly Used Methods For Image Dimension Reduction

Web Image Dimensional Reduction has a basic principle, that is, the sample is mapped to a low-dimensional space from the input space via a linear or nonlinear mode, and thus to obtain a compact low-dimensional expression on the original data sets. Traditional linear dimensionality reduction methods are featured with simplicity, easiness to explain and extendibility, etc., making it a major research direction in high-dimensional data processing. The existing linear dimension reduction methods include Principal Component Analysis (PCA) (Banerjee, 2009; Zhu, 2009; Zhang, 2009; Fan, 2008), Independent Component Analysis (ICA) (Rahman, 2009; Wang, 2009; Müller, 2009), Fisher Discriminated Analysis (FDA) (Zachary, 2000), Principal Curves, Projection Pursuit (PP), Local Linear Projection (LLP), as well as Self-Organizing Map (SOM) that is based on neural networks (Xiao, 2007). These methods are actually ways to find the best linear model under different optimization criteria, and this is also common to linear dimension reduction methods. However, with the advent of the information age, especially in the Web environment, a large number of high-dimensional nonlinear data will inevitably come along. Traditional linear dimension reduction methods are difficult to directly be used to analyze high-dimensional and non-linear data sourced from the real world. This may attribute to the following main reasons: the dimension of expansion leading to a rapid increase in computational complexity; high-dimensional may lead to a relatively small sample size, causing the statistical damage on some of the asymptotic properties; traditional methods in dealing with high dimensional data cannot meet the robustness requirements. Therefore, the study of high-dimensional nonlinear data confronts many difficulties. This is mainly because that high-dimensional factor may bring about the sparse data, and the curse of dimensionality, while the non-linear feature makes the rapid maturing of the existing linear model that no longer applies.