Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly

05/18/2018
by   Benjamin Guedj, et al.
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When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. Principal curves act as a nonlinear generalization of PCA and the present paper proposes a novel algorithm to automatically and sequentially learn principal curves from data streams. We show that our procedure is supported by regret bounds with optimal sublinear remainder terms. A greedy local search implementation that incorporates both sleeping experts and multi-armed bandit ingredients is presented, along with its regret bound and performance on a toy example and seismic data.

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