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arXiv 1804.06352cs.LGstat.ML
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高维时间序列发生器

High Dimensional Time Series Generators

Humboldt-Universität zu Berlin(柏林洪堡大学)

Jörg P. Bachmann, Johann-Christoph Freytag

摘要:

多维时间序列是由实值向量组成的序列。它们出现在不同的领域,例如手写字符、GPS跟踪和现代虚拟现实运动控制器的手势。在这些领域中,一个共同的任务是搜索相似的时间序列。动态时间规整(DTW)是一种比较两个时间序列的常用距离函数。带实际惩罚的编辑距离(ERP)和养狗距离(DK)是时间序列上的两个距离函数。他们的行为进行了分析1维时间序列。然而,要评估它们与不断增长的维度有关的行为并不容易。出于这个原因,我们提出了两个新的数据合成器生成多维时间序列。第一个合成器扩展了众所周知的圆柱钟形漏斗(CBF)数据集的多维时间序列。这里,每个时间序列在每个维度上都有一个任意的类型(圆柱形、钟形或漏斗形),因此对于$d$维时间序列,有$3^{d}$不同的类。第二个合成器(RAM)创建时间序列,其思想来自布朗运动,这是物理学中常见的运动模型。最后,我们评估的适用性1-最近邻分类器使用DTW对我们的合成器生成的数据集。

英文摘要:

Multidimensional time series are sequences of real valued vectors. They occur in different areas, for example handwritten characters, GPS tracking, and gestures of modern virtual reality motion controllers. Within these areas, a common task is to search for similar time series. Dynamic Time Warping (DTW) is a common distance function to compare two time series. The Edit Distance with Real Penalty (ERP) and the Dog Keeper Distance (DK) are two more distance functions on time series. Their behaviour has been analyzed on 1-dimensional time series. However, it is not easy to evaluate their behaviour in relation to growing dimensionality. For this reason we propose two new data synthesizers generating multidimensional time series. The first synthesizer extends the well known cylinder-bell-funnel (CBF) dataset to multidimensional time series. Here, each time series has an arbitrary type (cylinder, bell, or funnel) in each dimension, thus for $d$-dimensional time series there are $3^{d}$ different classes. The second synthesizer (RAM) creates time series with ideas adapted from Brownian motions which is a common model of movement in physics. Finally, we evaluate the applicability of a 1-nearest neighbor classifier using DTW on datasets generated by our synthesizers.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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