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.
There are two more recent methods that consider learning embeddings to approximate DTW distances. The first, called Jiffy @cite_4 , 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 @cite_12 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.
@cite_4 @cite_12
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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. Dynamic time warping (DTW), which finds the minimum path by providing non-linear alignments between two time series, has been widely used as a distance measure for time series classification and clustering. However, DTW does not account for the relative importance regarding the phase difference between a reference point and a testing point. This may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition. Therefore, we propose a novel distance measure, called a weighted DTW (WDTW), which is a penalty-based DTW. Our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers. The rationale underlying the proposed distance measure is demonstrated with some illustrative examples. A new weight function, called the modified logistic weight function (MLWF), is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point. By applying different weights to adjacent points, the proposed algorithm can enhance the detection of similarity between two time series. We show that some popular distance measures such as DTW and Euclidean distance are special cases of our proposed WDTW measure. We extend the proposed idea to other variants of DTW such as derivative dynamic time warping (DDTW) and propose the weighted version of DDTW. We have compared the performances of our proposed procedures with other popular approaches using public data sets available through the UCR Time Series Data Mining Archive for both time series classification and clustering problems. The experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems.