Tensor algebras give rise to one of the most powerful measures of similarity
for sequences of arbitrary length called the signature kernel accompanied with
attractive theoretical guarantees from stochastic analysis. Previous algorithms
to compute the signature kernel scale quadratically in terms of the length and
the number of the sequences. To mitigate this severe computational bottleneck,
we develop a random Fourier feature-based acceleration of the signature kernel
acting on the inherently non-Euclidean domain of sequences. We show uniform
approximation guarantees for the proposed unbiased estimator of the signature
kernel, while keeping its computation linear in the sequence length and number.
In addition, combined with recent advances on tensor projections, we derive two
even more scalable time series features with favourable concentration
properties and computational complexity both in time and memory. Our empirical
results show that the reduction in computational cost comes at a negligible
price in terms of accuracy on moderate-sized datasets, and it enables one to
scale to large datasets up to a million time series.

张量代数提供了一种针对任意长度序列的相似性度量中最强大的一种方法，即具有概率分析中有吸引力的理论保证的签名核，本研究针对这严重的计算瓶颈，提出了一种在序列的非欧几里得领域上进行签名核加速的基于随机傅里叶特征的方法，并且证明了所提出无偏估计器的均匀逼近保证，同时保持其在序列长度和数量上的计算为线性，此外，结合张量投影的最新进展，我们得到了两个更可扩展的时间序列特征，具有有利的集中性质和在时间和内存上的计算复杂度，实证结果表明，计算成本的降低在中等规模数据集上几乎没有影响准确性，并且使得我们能够处理高达一百万种时间序列的大型数据集。

随机傅里叶特征

Random Fourier Signature Features

The prompt and accurate detection of faults and abnormalities in electric
transmission lines is a critical challenge in smart grid systems. Existing
methods mostly rely on model-based approaches, which may not capture all the
aspects of these complex temporal series. Recently, the availability of data
sets collected using advanced metering devices, such as Micro-Phasor
Measurement units ($\mu$ PMU), which provide measurements at microsecond
timescale, boosted the development of data-driven methodologies. In this paper,
we introduce a novel deep learning-based approach for fault detection and test
it on a real data set, namely, the Kaggle platform for a partial discharge
detection task. Our solution adopts a Long-Short Term Memory architecture with
attention mechanism to extract time series features, and uses a
1D-Convolutional Neural Network structure to exploit frequency information of
the signal for prediction. Additionally, we propose an unsupervised method to
cluster signals based on their frequency components, and apply multi task
learning on different clusters. The method we propose outperforms the winner
solutions in the Kaggle competition and other state of the art methods in many
performance metrics, and improves the interpretability of analysis.

本文介绍了一种基于深度学习的故障检测方法，利用高精度的数据采集设备收集数据来训练模型，并使用长短时记忆网络和一维卷积神经网络来提取时序特征和频率信息进行故障预测，在 Kaggle 平台上的结果表明该方法具有更好的性能和解释性。