Multi-Core Implementation of Geometric Multidimensional Scaling For Large-Scale Data

well-known procedure for mapping data from high dimensional space to lower dimensional space is multidimensional scaling (MDS). Although MDS demonstrates great versatility, it is computationally demanding, especially when the data set is not fixed and its size is constantly growing. Conventional MDS approaches are limited when analysing very large datasets, as they require very long computation times and large amounts of memory. A way to minimize MDS stress has been developed using the ideas of Geometric MDS, where all points in a low-dimensional space change their coordinates simultaneously and independently during a single iteration of stress minimization. It is shown in this paper that Geometric MDS allows the implementation of parallel computing for the dimensionality reduction process of large-scale data using multithreaded multicore processors. We examine how the computational time expenses for data dimensionality reduction and multidimensional data visualisation varies with either the number of processor cores or the number of processor threads used.