FastMap, MetricMap, and Landmark MDS are all Nystrom Algorithms

This paper unifies the mathematical foundation of three multidimen- sional scaling algorithms: FastMap, MetricMap, and Landmark MDS (LMDS). All three algorithms are based on the Nystrom approximation of the eigenvectors and eigenvalues of a matrix. LMDS is applies the basic Nystrom approximation, while FastMap and MetricMap use generaliza- tions of Nystrom, including deflation and using more points to establish an embedding. Empirical experiments on the Reuters and Corel Image Features data sets show that the basic Nystrom approximation outper- forms these generalizations: LMDS is more accurate than FastMap and MetricMap with roughly the same computation and can become even more accurate if allowed to be slower.