Chapter 4: Linear Dimensionality Reduction
Bastian Bohn, Jochen Garcke, Michael Griebel · Society for Industrial and Applied Mathematics eBooks · 2024
One encounters large and nominally high-dimensional data sets in many real-world applications. However, the information in such data sets is often redundant in the sense that the different coordinates of a data set, stemming, e.g., from different physical measurements, are typically not independent but correlated. Thus, the high-dimensional representation of the data is not in a compact form. To determine a more effective representation of the data, we need to find a mapping into a lower-dimensional representation space that preserves the relevant information. But relevant can be understood in different ways, e.g., as preserving pairwise distances between data points or as allowing for almost lossless reconstruction of the original data set. The process of determining such a low-dimensional representation of the data is known as dimensionality reduction; see also Section 1.2.