Most of the complex real-world systems involve more than three dimensions and it may be difficult to model these higher dimensional data related to their inputoutput relationships, mathematically. Moreover, the mathematical modeling may become computationally expensive for the said systems. A human being can visualize only up to three dimensions (3-D). So, any system involving more than 3-D cannot be visualized. To overcome this difficulty, higher dimensional data are generally mapped into either 2-D or 3-D, for visualization and ease of modeling. Dimensionality reduction techniques are nothing but the mapping methods, with the help of which the higher dimensional data can be mapped into the lower dimension after ensuring a reasonable accuracy. It is to be noted that the precision of modeling depends on the said accuracy in mapping. Thus, it is worthy to study the dimensionality reduction techniques.
In this section, the principles of some of the non-linear dimensionality reduction techniques have been explained.