text: Traditionally, the automatic recognition of human activities is performed with supervised learning algorithms on limited sets of specific activities. This work proposes to recognize recurrent activity patterns, called routines, instead of precisely defined activities. The modeling of routines is defined as a metric learning problem, and an architecture, called SS2S, based on sequence-to-sequence models is proposed to learn a distance between time series. This approach only relies on inertial data and is thus non intrusive and preserves privacy. Experimental results show that a clustering algorithm provided with the learned distance is able to recover daily routines.
  @cite_26: Measuring similarities between unlabeled time series trajectories is an important problem in domains as diverse as medicine, astronomy, finance, and computer vision. It is often unclear what is the appropriate metric to use because of the complex nature of noise in the trajectories (e.g. different sampling rates or outliers). Domain experts typically hand-craft or manually select a specific metric, such as dynamic time warping (DTW), to apply on their data. In this paper, we propose Autowarp, an end-to-end algorithm that optimizes and learns a good metric given unlabeled trajectories. We define a flexible and differentiable family of warping metrics, which encompasses common metrics such as DTW, Euclidean, and edit distance. Autowarp then leverages the representation power of sequence autoencoders to optimize for a member of this warping distance family. The output is a metric which is easy to interpret and can be robustly learned from relatively few trajectories. In systematic experiments across different domains, we show that Autowarp often outperforms hand-crafted trajectory similarity metrics.
  @cite_9: In almost every scientific field, measurements are performed over time. These observations lead to a collection of organized data called time series. The purpose of time-series data mining is to try to extract all meaningful knowledge from the shape of data. Even if humans have a natural capacity to perform these tasks, it remains a complex problem for computers. In this article we intend to provide a survey of the techniques applied for time-series data mining. The first part is devoted to an overview of the tasks that have captured most of the interest of researchers. Considering that in most cases, time-series task relies on the same components for implementation, we divide the literature depending on these common aspects, namely representation techniques, distance measures, and indexing methods. The study of the relevant literature has been categorized for each individual aspects. Four types of robustness could then be formalized and any kind of distance could then be classified. Finally, the study submits various research trends and avenues that can be explored in the near future. We hope that this article can provide a broad and deep understanding of the time-series data mining research field.
  @cite_21: Many algorithms have been proposed for the problem of time series classification. However, it is clear that one-nearest-neighbor with Dynamic Time Warping (DTW) distance is exceptionally difficult to beat. This approach has one weakness, however; it is computationally too demanding for many realtime applications. One way to mitigate this problem is to speed up the DTW calculations. Nonetheless, there is a limit to how much this can help. In this work, we propose an additional technique, numerosity reduction, to speed up one-nearest-neighbor DTW. While the idea of numerosity reduction for nearest-neighbor classifiers has a long history, we show here that we can leverage off an original observation about the relationship between dataset size and DTW constraints to produce an extremely compact dataset with little or no loss in accuracy. We test our ideas with a comprehensive set of experiments, and show that it can efficiently produce extremely fast accurate classifiers.
  @cite_0: Dynamic Time Warping (DTW) has a quadratic time and space complexity that limits its use to small time series. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarser resolution and refines the projected solution. We prove the linear time and space complexity of FastDTW both theoretically and empirically. We also analyze the accuracy of FastDTW by comparing it to two other types of existing approximate DTW algorithms: constraints (such as Sakoe-Chiba Bands) and abstraction. Our results show a large improvement in accuracy over existing methods.
  @cite_5: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization is given using time-warping function. Then, two time-normalized distance definitions, called symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discussions and experimental studies. The symmetric form algorithm superiority is established. A new technique, called slope constraint, is successfully introduced, in which the warping function slope is restricted so as to improve discrimination between words in different categories. The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimental comparison with various DP-algorithms, previously applied to spoken word recognition by different research groups. The experiment shows that the present algorithm gives no more than about two-thirds errors, even compared to the best conventional algorithm.
summary: The traditional approach to compute distances between sequences (or time series, or trajectories) is to perform Dynamic Time Warping (DTW) @cite_5 which was introduced in 1978. Since then, several improvements of the algorithm have been published, notably a fast version by Salvador @cite_0 . DTW is considered one of the best metric to use for sequence classification @cite_21 combined with @math -nearest neighbors. Recently, Abid @cite_26 proposed a neural network architecture to learn the parameters of a warping distance accordingly to the euclidean distances in a projection space. However, DTW, as other shaped-based distances @cite_9 , is only able to retrieve local similarities when time series have a relatively small length and are just shifted or not well aligned.