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Robust principal graphs for data approximation

Gorban, Alexander N.; Mirkes, Evgeny M.; Zinovyev, Andrei

Revealing hidden geometry and topology in noisy data sets is a challenging task. An Elo-Elastic principal graph is a computationally efficient and
flexible data approximator based on embedding a graph into the data space and minimizing the energy functional penalizing the deviation of graph nodes both from data points and from a pluri-harmonic configuration (generalization of linearity). The structure of the principal graph is learned from data by application of a topological grammar which in the simplest case leads to the construction of principal curves or trees. In order to more efficiently cope with noise and outliers, we suggest using a trimmed data approximation term to increase the robustness of the method. The modification of the method that we suggest does not affect either computational efficiency or general convergence properties of the original elastic graph method. The trimmed elastic energy functional remains a Lyapunov function for the optimization algorithm. On several examples of complex data distributions we demonstrate how the robust principal graphs learn the global data structure and show the advantage of using the trimmed data approximation term for the construction of principal graphs and other popular data approximators.

Volltext §
DOI: 10.5445/KSP/1000058749/11
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Informationswirtschaft und Marketing (IISM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2363-9881
KITopen-ID: 1000068111
Erschienen in Archives of Data Science, Series A (Online First)
Band 2
Heft 1
Seiten 16 S. online
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