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

arXiv: https://arxiv.org/abs/1805.07418 · HTML: https://mlsanity.com/paper/1805.07418/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2018.

## Built on by (most cited first, 1 of 1)

- [RestoreAI -- Pattern-based Risk Estimation Of Remaining Explosives](https://mlsanity.com/paper/2507.19873/) (2025)

## Abstract (arXiv)

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 textttslpc, 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.