Multidimensional Scaling

Synonyms

MDS

Definition

Multidimensional scaling (MDS) is a mathematical dimension reduction technique that best preserves the interpoint distances by analyzing gram matrix. Given any two points p_i and p_j in a dataset P, MSD aims to minimize the following objective function:

$$ \mathrm{Error}=\sum \left[d\left( pi, pj\right)-{d}^{\prime}\left( pi, pj\right)\right]2 $$

where d(pi, pj)d(pi, pj) and d′(pi, pj)d′(pi, pj) represent the distance between points p_i and p_j in original space and the lower dimensional subspace, respectively.

Key Points

Multidimensional scaling (MDS) is a set of related statistical techniques often used in data visualization and analysis for exploring similarities or dissimilarities in data. An MDS algorithm starts with a matrix of point-point (dis)similarities and then assigns a location of each point in a low-dimensional space. The points are arranged in this subspace so that the distances between pairs of points have their original distance maximally retained....