Multidimensional Scaling

Multidimensional scaling (MDS) is a technique used for dimensionality reduction.

MDS is employed when the input data is not linearly arranged or it is unknown whether a linear relationship exists. It is typically used in fields like psychology, marketing, and bioinformatics to visualize the level of similarity of individual cases of a dataset.

MDS works by iteratively minimizing the difference between the distances of pairs of points in the original high-dimensional space and the distances between the corresponding pairs of points in the lower-dimensional space. The goal is to preserve the relative distances as much as possible.

For example, consider a dataset of different types of fruits characterized by multiple attributes such as color, size, and taste. MDS can be used to project this high-dimensional data into a two-dimensional space, where similar fruits are placed closer together, making it easier to visualize their similarities and differences.

Sammon mapping or Sammon projection is the mathematical procedure that is most commonly employed to achieve this.