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

A well-known and widely used technique for mapping data from high-dimensional space to lower-dimensional space is multidimensional scaling (MDS). Although MDS, as a dimensionality reduction method used for data visualization, demonstrates great versatility, it is computationally demanding, especially when the data set is not fixed and its size is constantly growing. Traditional MDS approaches are limited when analyzing very large data sets, as they require very long computation times and large amounts of memory. A way to minimize MDS stress, which can be used to reduce the dimensionality of large-scale data, 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 multi-core processors. We explore how the computational time consumption of data dimensionality reduction and multidimensional data visualization depends on the number of processor cores or processor threads used.