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

Benjamin Guedj 1, 2, 3, 4 Le Li 5
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : 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 (called \texttt{slpc}, for Sequential Learning Principal Curves) that incorporates both sleeping experts and multi-armed bandit ingredients is presented, along with its regret computation and performance on synthetic and real-life data.
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https://hal.inria.fr/hal-01796011
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Submitted on : Wednesday, May 8, 2019 - 10:06:29 PM
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Benjamin Guedj, Le Li. Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly. 2019. ⟨hal-01796011v2⟩

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