Multidimensional scaling with very large datasets

Multidimensional scaling has a wide range of applications when observations are not continuous but it is possible to define a distance (or dissimilarity) among them. However, standard implementations are limited when analyzing very large datasets because they rely on eigendecomposition of the full distance matrix and require very long computing times and large quantities of memory. Here, a new approach is developed based on projection of the observations in a space defined by a subset of the full dataset. The method is easily implemented. A simulation study showed that its performance are satisfactory in different situations and can be run in a short time when the standard method takes a very long time or cannot be run because of memory requirements