Fast multidimensional scaling on big geospatial data using neural networks

Abstract

This paper presents a fast approximation method for Multidimensional Scaling (MDS)-based dimensionality reduction on large cartography datasets. Since MDS preserves data point distances, it is useful in application domains where geolocation data are critical. Typical relevant tasks include smartphone user behavioral pattern extraction, animal motion tracking over long distances, or distributed sensor data monitoring. The input to MDS is a data distance matrix employed for reducing data point dimensionality under distance constraints. Similar procedures are crucial for analyzing and revealing the original hidden data structure, as well as for data visualization, feature extraction, or compression. For N data points, MDS has a computational complexity that exceeds $\varvec{O(N^{2})}$ which, may be excessive for a large $\varvec{N}$, e.g., for several hundred thousands or millions of data points. The proposed method allows fast approximate MDS calculation on million-point datasets in less than a minute on a simple laptop, by sampling a small subset of the original dataset, performing regular MDS on it and training a neural regressor to learn the desired MDS mapping. Quantitative and qualitative empirical evaluation of the proposed fast MLP-MDS algorithm on a geospatial data mapping task, i.e., on reducing 3D Earth surface points (longitude, latitude, radius) to 2D maps, has resulted in promising findings and small approximation errors. The benefits are even greater in incremental settings, where new data points are obtained and projected over time. Unlike regular MDS or competing approximations, this is trivially supported in MLP-MDS due to the latter’s model-based nature.