We propose a feature extraction for periodic signals. Virtually every mechanized transportation vehicle, power generation, industrial machine, and robotic system contains rotating shafts. It is possible to collect data about periodicity by measuring a shaft's rotation. However, it is difficult to perfectly control the collection timing of the measurements. Imprecise timing creates phase shifts in the resulting data. Although a phase shift does not materially affect the measurement of any given data point collected, it does alter the order in which all of the points are collected. It is difficult for classical methods, like multi-layer perceptron, to identify or quantify these alterations because they depend on the order of the input vectors' components. This paper proposes a robust method for extracting features from phase shift data by adding a graph structure to each data point and constructing a suitable machine learning architecture for graph data with cyclic permutation. Simulation and experimental results illustrate its effectiveness.
This paper proposes a machine learning framework for periodic data. The authors note that representing input data in vector form does not encode input coordinates relationship to one. Capturing this structure can be especially important for periodic signals. The authors address this by adding graph structure to each data point to encode relative structure about each coordinate. They then apply a graph neural network to the resulting structured data. They evaluate the method on an anomaly detection in a low data setting.  
This paper would be greatly improved by an addition of a related work section. It is unclear where the novelty comes in precisely in this work because it is not very well situated within previous work on (i) anomaly detection w/ periodic signals, (ii) temporal and periodic signal processing and (iii) graph neural network approaches. Contextualized this work within these related areas would improve the clarity and readability of the work and also help frame the results. 
The method is evaluated on synthetic and real datasets, comparing a couple variants of the model (one that can deal with phase shifts). Results support the main claims of the paper.
It is hard for me to assess the significance of this work since this is a very specific application of known techniques. I think the application is an important one, and also one that requires some domain knowledge, so there does appear to be a useful contribution in terms of adapting graph-based methodologies here. However, the methodology and application is outside my area of expertise.
 
Detailed suggestions / questions / comments:
- the ws-dimensional  vector v_i is defined as v_i = (x_{(i−1)∗ss+1}, x_{i+1}, . . . , x_{(i−1)∗ss+ws}). Is there a typo here? It's not obvious to me how the second index relates to the sequence or how this sequence is specified? Perhaps it should say  v_i = (x_{(i−1)∗ss}, x_{(i-1)*ss+1}, . . . , x_{(i−1)∗ss+ws})?
 - The authors mention alternative methods of capturing structured temporal information in the input features. For example, they suggest concatenating the original signal with the cross correlated signal. They also suggest time-frequency analysis methods (such as a Fourier transform and the wavelet transform) and applying a CNN to the time-frequency signal. They authors mention that these methods would require much more data than their graph convolution approach. I agree this is probably the case, but this would still be a useful empirical result to show the degree of data required for these alternative. 
- What are previous approaches to detecting the properties explored in this work? In addition to discussing previous approaches in a related work section, some empirical analysis comparison would help contextualize this work as well.  
Overall, I think this paper is a useful application of graph-based methods. The claims are verified empirically on real and synthetic data. I think it could be significantly improved with a discussion of related work and better situating of the methods / more comparisons in the results. As a result of these significant weaknesses I'm really on the fence with my recommendation -- the work is sensible but the paper has a lot of room for improvement and I'm not quite sure its ready for publication. However, it is possible underestimated the significance/impact of this work because I am not very familiar with the topic.