Principal Graph and Structure Learning Based on Reversed Graph Embedding

Publication Type:
Journal Article
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39 (11), pp. 2227 - 2241
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© 2017 IEEE. Many scientific datasets are of high dimension, and the analysis usually requires retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are mathematically formulated by curves, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected ℓ 1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.
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