  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.
