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- Abstract: 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 mea- suring 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 col- lected. 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.