Derivative Delay Embedding: Online Modeling of Streaming Time Series

TL;DR

This paper introduces DDE-MGM, a novel online approach for streaming time series modeling that preserves data characteristics without assumptions on length or alignment, achieving high efficiency and accuracy.

Contribution

The paper presents a new online modeling scheme using derivative delay embedding and a non-parametric Markov model, handling streaming data without segmentation or normalization.

Findings

Outperforms state-of-the-art in online classification accuracy

Efficiently models streaming time series without data length assumptions

Maintains high performance with misaligned and variable-length data

Abstract

The staggering amount of streaming time series coming from the real world calls for more efficient and effective online modeling solution. For time series modeling, most existing works make some unrealistic assumptions such as the input data is of fixed length or well aligned, which requires extra effort on segmentation or normalization of the raw streaming data. Although some literature claim their approaches to be invariant to data length and misalignment, they are too time-consuming to model a streaming time series in an online manner. We propose a novel and more practical online modeling and classification scheme, DDE-MGM, which does not make any assumptions on the time series while maintaining high efficiency and state-of-the-art performance. The derivative delay embedding (DDE) is developed to incrementally transform time series to the embedding space, where the intrinsic characteristics of data is preserved as recursive patterns regardless of the stream length and misalignment. Then, a non-parametric Markov geographic model (MGM) is proposed to both model and classify the pattern in an online manner. Experimental results demonstrate the effectiveness and superior classification accuracy of the proposed DDE-MGM in an online setting as compared to the state-of-the-art.