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.
@cite_8: A considerable amount of machine learning algorithms take instance-feature matrices as their inputs. As such, they cannot directly analyze time series data due to its temporal nature, usually unequal lengths, and complex properties. This is a great pity since many of these algorithms are effective, robust, efficient, and easy to use. In this paper, we bridge this gap by proposing an efficient representation learning framework that is able to convert a set of time series with equal or unequal lengths to a matrix format. In particular, we guarantee that the pairwise similarities between time series are well preserved after the transformation. The learned feature representation is particularly suitable to the class of learning problems that are sensitive to data similarities. Given a set of @math time series, we first construct an @math partially observed similarity matrix by randomly sampling @math pairs of time series and computing their pairwise similarities. We then propose an extremely efficient algorithm that solves a highly non-convex and NP-hard problem to learn new features based on the partially observed similarity matrix. We use the learned features to conduct experiments on both data classification and clustering tasks. Our extensive experimental results demonstrate that the proposed framework is both effective and efficient.
Most related to our work is a recent work @cite_8 addressing the same task as ours, that of converting a time series dataset into a set of vector embeddings. Starting from a dataset of @math time series, they build an @math matrix of pairwise similarities that is defined using DTW distances. This is done by performing @math DTW computations, and approximating the other entries in the matrix using a low-rank assumption. If a time series is of length @math , a DTW computation takes time of the order of @math . This makes just the matrix creation step a process in @math . The similarity matrix is then subject to symmetric matrix factorization so that a vector embedding matrix X is learnt such that XX @math approximates the similarity matrix well. This calls for eigen decomposition which is superlinear in @math as well. This makes it impractical for most large datasets. In contrast to this work, the method we propose is linear in both @math and @math , making our method significantly more scalable.