A collection of entity descriptions may be conveniently represented by a set of tuples or a set of objects with appropriate attributes. The utility of relational and object databases is based on this premise. Methods of multivariate analysis can naturally be applied to such a representation. Multidimensional Scaling deserves particular attention because of its suitability for visualization. The advantage of using Multidimensional Scaling is its generality. Provided that one can judge or calculate the dissimilarity between any pair of data objects, this method can be applied. This makes it invariant to the number and types of object attributes. To take advantage of this method for visualizing large collections of data, however, its inherent computational complexity needs to be alleviated. This is particularly the case for least squares scaling, which involves numerical minimization of a loss function; on the other hand the technique gives better configurations than analytical classical scaling. Numerical optimization requires selection of a convergence criterion, i.e. deciding when to stop. A common solution is to stop after a predetermined number of iterations has been performed. Such an approach, while guaranteed to terminate, may prematurely abort the optimization. The incremental Multidimensional Scaling method presented here solves these problems. It uses cluster analysis techniques to assess the structural significance of groups of data objects. This creates an opportunity to ignore dissimilarities between closely associated objects, thus greatly reducing input size. To detect convergence it maintains a compact representation of all intermediate optimization results. This method has been applied to the analysis of database tables.
"Incremental multidimensional scaling method for database visualization", Proc. SPIE 3643, Visual Data Exploration and Analysis VI, (25 March 1999); doi: 10.1117/12.342830; https://doi.org/10.1117/12.342830