Technique that renders observed or computed (dis)similarities among objects into distances in a low-dimensional space (usually Euclidean). It thus constructs dimensions for the data; the objects can be plotted and conceptualized in those dimensions
The goal of multidimensional scaling (MDS) is, given pairwise dissimilarities (i.e. a matrix of distances $D = (d_{ij})$), find coordinates $x_i, x_j$ such that:
$$d_{ij} \approx ||x_i - x_j||_2$$
That is, such that distances are preserved.
Distance or dissimilarity is defined for any pair of objects. A distance is a metric in the mathematical sense and satisfies certain properties.
