This paper shows that one can be competitive with the k-means objective while operating online. In this model, the algorithm receives vectors v 1 , . . . , v n one by one in an arbitrary order. For each vector v t the algorithm outputs a cluster identifier before receiving v t+1 . Our online algorithm generates O(k log n log γn) clusters whose expected k-means cost is O(W * log n). Here, W * is the optimal k-means cost using k clusters and γ is the aspect ratio of the data. The dependence on γ is shown to be unavoidable and tight. We also show that, experimentally, it is not much worse than kmeans++ while operating in a strictly more constrained computational model.

Decomposing a complex time series into trend, seasonality, and remainder components is an important primitive that facilitates time series anomaly detection, change point detection, and forecasting. Although numerous batch algorithms are known for time series decomposition, none operate well in an online scalable setting where high throughput and real-time response are paramount. In this paper, we propose OnlineSTL, a novel online algorithm for time series decomposition which is highly scalable and is deployed for real-time metrics monitoring on high-resolution, high-ingest rate data. Experiments on different synthetic and real world time series datasets demonstrate that OnlineSTL achieves orders of magnitude speedups (100x) for large seasonalities while maintaining quality of decomposition.

No abstract

No abstract

No abstract