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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
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille, Université de Lille, Sciences et Technologies
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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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. Entropy, MDPI, 2021, ⟨10.3390/e23111534⟩. ⟨hal-01796011v2⟩



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