Non-stationary time series (TS) analysis has gained an explosive interest over the recent decades in different applied sciences. In fact, several decomposition methods were developed in order to extract various components (e.g., seasonal, trend and abrupt components) from the non-stationary TS, which allows for an improved interpretation of the temporal variability. The wavelet transform (WT) has been successfully applied over an extraordinary range of fields in order to decompose the non-stationary TS into time-frequency domain. For this reason, the WT method is briefly introduced and reviewed in this paper. In addition, this latter includes different research and applications of the WT to non-stationary TS in seven different applied sciences fields, namely the geo-sciences and geophysics, remote sensing in vegetation analysis, engineering, hydrology, finance, medicine, and other fields, such as ecology, renewable energy, chemistry and history. Finally, five challenges and future works, such as the selection of the type of wavelet, selection of the adequate mother wavelet, selection of the scale, the combination between wavelet transform and machine learning algorithm and the interpretation of the obtained components, are also discussed.

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This paper addresses the problem of human action recognition from sequences of 3D skeleton data. For this purpose, we combine a deep learning network with geometric features extracted from data lie on a non-Euclidean space, which have been recently shown to be very effective to capture the geometric structure of the human pose. In particular, our approach claims to incorporate the intrinsic nature of the data characterized by Lie Group into deep neural networks and to learn more adequate geometric features for 3D action recognition problem. First, geometric features are extracted from 3D joints of skeleton sequences using the Lie group representation. Then, the network model is built from stacked units of 1-dimensional CNN across the temporal domain. Finally, CNN-features are then used to train an LSTM layer to model dependencies in the temporal domain, and to perform the action recognition. The experimental evaluation is performed on three public datasets containing various challenges: UT-Kinect, Florence 3D-Action and MSR-Action 3D. Results reveal that our approach achieves most of the state-of-the-art performance.

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