Spanning Trees as Approximation of Data Structures

Abstract

The connections in a graph generate a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this article, we present STAD (Simplified Topological Abstraction of Data), a parameter-free dimensionality reduction method that projects high-dimensional data into a graph. STAD generates an abstract representation of high-dimensional data by giving each data point a location in a graph which preserves the approximate distances in the original high-dimensional space. The STAD graph is built upon the Minimum Spanning Tree (MST) to which new edges are added until the correlation between the distances from the graph and the original dataset is maximized. Additionally, STAD supports the inclusion of additional functions to focus the exploration and allow the analysis of data from new perspectives, emphasizing traits in data which otherwise would remain hidden. We demonstrate the effectiveness of our method by applying it to two real-world datasets: traffic density in Barcelona and temporal measurements of air quality in Castile and León in Spain.