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

Benjamin Guedj (1) , Le Li (2)

1 MODAL - MOdel for Data Analysis and Learning
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Mots clés: sequential learning; principal curves; data streams; regret bounds; greedy al- gorithm; sleeping experts

Domaines: Machine Learning [stat.ML]; Apprentissage [cs.LG]; Statistiques [math.ST]

Benjamin Guedj, Le Li. Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly. 2018. ⟨hal-01796011v1⟩