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The connection of edges in a graph generates a structure that is independentof a coordinate system. This visual metaphor allows creating a more flexiblerepresentation of data than a two-dimensional scatterplot. In this work, wepresent STAD (Spanning Trees as Approximation of Data), a dimensionalityreduction method to approximate the high-dimensional structure into a graphwith or without formulating prior hypotheses. STAD generates an abstractrepresentation of high-dimensional data by giving each data point a location ina graph which preserves the distances in the original high-dimensional space.The STAD graph is built upon the Minimum Spanning Tree (MST) to which new edgesare added until the correlation between the distances from the graph and theoriginal dataset is maximized. Additionally, STAD supports the inclusion ofadditional functions to focus the exploration and allow the analysis of datafrom new perspectives, emphasizing traits in data which otherwise would remainhidden. We demonstrate the effectiveness of our method by applying it to tworeal-world datasets: traffic density in Barcelona and temporal measurements ofair quality in Castile and Le\'on in Spain.

Improving the Projection of Global Structures in Data through Spanning Trees