Notes: Most often the approaches are an average less complicated. For MDS-like approaches, the complexity depends very much on the method used and whether the data are given as vectors or proximities. The proximity space approach may generate further costs if, for example, a classification model has to be calculated for the representation. Proxy matrix approaches are very costly due to the raised optimization problem and the classical solver used. Some proxy approaches solve a similar complex optimization problem for out-of-sample extensions. For low-rank proximity matrices, the costs can often be reduced by a magnitude or more. See section 7.