You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Time series are ubiquitous in real world problems and computing distance between two time series is often required in several learning tasks. Computing similarity between time series by ignoring variations in speed or warping is often encountered and dynamic time warping (DTW) is the state of the art. However DTW is not applicable in algorithms which require kernel or vectors. In this paper, we propose a mechanism named WaRTEm to generate vector embeddings of time series such that distance measures in the embedding space exhibit resilience to warping. Therefore, WaRTEm is more widely applicable than DTW. WaRTEm is based on a twin auto-encoder architecture and a training strategy involving warping operators for generating warping resilient embeddings for time series datasets. We evaluate the performance of WaRTEm and observed more than @math improvement over DTW in multiple real-world datasets.

Cited Abstract(s):
[1]: Computing distances between examples is at the core of many learning algorithms for time series. Consequently, a great deal of work has gone into designing effective time series distance measures. We present Jiffy, a simple and scalable distance metric for multivariate time series. Our approach is to reframe the task as a representation learning problem---rather than design an elaborate distance function, we use a CNN to learn an embedding such that the Euclidean distance is effective. By aggressively max-pooling and downsampling, we are able to construct this embedding using a highly compact neural network. Experiments on a diverse set of multivariate time series datasets show that our approach consistently outperforms existing methods.

[2]: Dynamic Time Warping (DTW) is one of the best similarity measures for time series, and it has extensively been used in retrieval, classification or mining applications. It is a costly measure, and applying it to numerous and or very long times series is difficult in practice. Recently, Shapelet Transform (ST) proved to enable accurate supervised classification of time series. ST learns small subsequences that well discriminate classes, and transforms the time series into vectors lying in a metric space. In this paper, we adopt the ST framework in a novel way: we focus on learning, without class label information, shapelets such that Euclidean distances in the ST-space approximate well the true DTW. Our approach leads to an ubiquitous representation of time series in a metric space, where any machine learning method (supervised or unsupervised) and indexing system can operate efficiently.
There are two more recent methods that consider learning embeddings to approximate DTW distances. The first, called Jiffy [1] , targets the case of multi-variate time series, and proposes a convolutional neural architecture. We differ from their task setting in that we consider the univariate setting for devising our method. The second method [2] models the embedding task as one of identifying a specified number of shapelets of specified lengths (both being method parameters) that enable transforming time series data into embeddings closely approximating DTW distances. Our model is not constrained to produce shapelets, and targets to train a neural architecture that embodies the transformation within itself.