In this paper, we employ a 1D deep convolutional generative adversarial
network (DCGAN) for sequential anomaly detection in energy time series data.
Anomaly detection involves gradient descent to reconstruct energy
sub-sequences, identifying the noise vector that closely generates them through
the generator network. Soft-DTW is used as a differentiable alternative for the
reconstruction loss and is found to be superior to Euclidean distance.
Combining reconstruction loss and the latent space's prior probability
distribution serves as the anomaly score. Our novel method accelerates
detection by parallel computation of reconstruction of multiple points and
shows promise in identifying anomalous energy consumption in buildings, as
evidenced by performing experiments on hourly energy time series from 15
buildings.

本文中，我们使用了一种 1D 深度卷积生成对抗网络（DCGAN）来进行能源时间序列数据中的顺序异常检测。通过梯度下降来重构能量子序列，通过生成器网络识别生成它们的噪声向量。我们使用可微的 Soft-DTW 作为重构损失的替代方法，发现其优于欧几里德距离。将重构损失和潜在空间的先验概率分布相结合可作为异常得分。实验证明，我们的新方法通过并行计算多个点的重构加速检测，并在 15 栋建筑的小时能源时间序列上显示出识别异常能耗的潜力。

具有软动态时间对齐和并行重构的生成对抗网络在能源时间序列异常检测中的应用

Generative Adversarial Network with Soft-Dynamic Time Warping and  Parallel Reconstruction for Energy Time Series Anomaly Detection

Computing the discrepancy between time series of variable sizes is
notoriously challenging. While dynamic time warping (DTW) is popularly used for
this purpose, it is not differentiable everywhere and is known to lead to bad
local optima when used as a "loss". Soft-DTW addresses these issues, but it is
not a positive definite divergence: due to the bias introduced by entropic
regularization, it can be negative and it is not minimized when the time series
are equal. We propose in this paper a new divergence, dubbed soft-DTW
divergence, which aims to correct these issues. We study its properties; in
particular, under conditions on the ground cost, we show that it is a valid
divergence: it is non-negative and minimized if and only if the two time series
are equal. We also propose a new "sharp" variant by further removing entropic
bias. We showcase our divergences on time series averaging and demonstrate
significant accuracy improvements compared to both DTW and soft-DTW on 84 time
series classification datasets.

本文提出了一种新的距离函数 ——soft-DTW 距离，并通过实验表明该函数在时间序列分类上的效果优于其他距离函数，如动态时间扭曲和 soft-DTW。

时间序列之间的可微分差异

Differentiable Divergences Between Time Series

We propose in this paper a differentiable learning loss between time series,
building upon the celebrated dynamic time warping (DTW) discrepancy. Unlike the
Euclidean distance, DTW can compare time series of variable size and is robust
to shifts or dilatations across the time dimension. To compute DTW, one
typically solves a minimal-cost alignment problem between two time series using
dynamic programming. Our work takes advantage of a smoothed formulation of DTW,
called soft-DTW, that computes the soft-minimum of all alignment costs. We show
in this paper that soft-DTW is a differentiable loss function, and that both
its value and gradient can be computed with quadratic time/space complexity
(DTW has quadratic time but linear space complexity). We show that this
regularization is particularly well suited to average and cluster time series
under the DTW geometry, a task for which our proposal significantly outperforms
existing baselines. Next, we propose to tune the parameters of a machine that
outputs time series by minimizing its fit with ground-truth labels in a
soft-DTW sense.

在这篇论文中，我们提出了一种基于动态时间规整（DTW）距离度量的可微学习损失函数，并利用软 DTW 来计算 DTW，该方法可用于平均时间序列和聚类时间序列，且在此任务中比现有基线表现更好。接着，我们通过最小化机器输出时间序列与基准标签的软 DTW 距离来调节其参数。