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arXiv · 1702.05815

Compressive Embedding and Visualization using Graphs

Johan Paratte·Nathanaël Perraudin·Pierre Vandergheynst
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Abstract

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming data volumes, the scalability of such methods have become more and more important. In this work, we present a method which allows to apply any visualization or embedding algorithm on very large datasets by considering only a fraction of the data as input and then extending the information to all data points using a graph encoding its global similarity. We show that in most cases, using only $\mathcal{O}(\log(N))$ samples is sufficient to diffuse the information to all $N$ data points. In addition, we propose quantitative methods to measure the quality of embeddings and demonstrate the validity of our technique on both synthetic and real-world datasets.

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Johan Paratte, Nathanaël Perraudin, Pierre Vandergheynst. 2017-02-19. Compressive Embedding and Visualization using Graphs. https://arxiv.org/abs/1702.05815

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