Scatterplot Summarization by Constructing Fast and Robust Principal Graphs from Skeletons

Abstract

Principal curves are a long-standing and well-known method for summarizing large scatterplots. They are defined as self-consistent curves (or curve sets in the more general case) that locally pass through the middle of the scatterplot data. However, computing principal curves that capture well complex scatterplot topologies and are robust to noise is hard and/or slow for large scatterplots. We present a fast and robust approach for computing principal graphs (a generalization of principal curves for more complex topologies) inspired by the similarity to medial descriptors (curves locally centered in a shape). Compared to state-of-the-art methods for computing principal graphs, we outperform these in terms of computational scalability and robustness to noise and resolution. We also demonstrate the advantages of our method over other scatterplot summarization approaches.