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Convolution neural networks (CNNs) represent one of the workhorses of artificial intelligence applications. As a typical artificial intelligence application, a high-resolution range profile (HRRP) target recognition method based on CNNs has aroused a lot of research interest. Most CNNs use a relatively small and single-scale convolution kernel size to control the number of parameters and computational complexity, but recent studies indicate that CNNs with a small kernel size cannot extract enough spatial information, which hurts the recognition performance. Aiming at this problem, this paper proposes a multi-scale group-fusion one-dimensional convolution neural network (MSGF-1D-CNN) for HRRP target recognition. MSGF-1D-CNN utilises multi-scale group one-dimensional convolution (MSG 1D-Conv) and point-wise convolution (PW-Conv) to replace the standard convolution. Multi-scale group one-dimensional convolution can significantly reduce complexity and capture the information of targets within HRRP in different levels of detail to enhance feature extraction, while PW-Conv can realise the fusion of multi-scale features to help boosting recognition performance. Experiments on five mid-course ballistic targets in the HRRP dataset show that MSGF-1D-CNN has superior recognition performance, and the parameter number of the model is reduced by more than 2.4 times than standard 1D-CNN. Furthermore, MSGF-1D-CNN shows better performance on fine-grained HRRP target recognition and antinoise robustness in most cases. K E Y W O R D Sconvolution neural networks, feature fusion, high-resolution range profile, multi-scale group convolution, midcourse ballistic targets, point-wise convolutionThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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As a special deep learning algorithm, the multilayer extreme learning machine (ML-ELM) has been extensively studied to solve practical problems in recent years. The ML-ELM is constructed from the extreme learning machine autoencoder (ELM-AE), and its generalization performance is affected by the representation learning of the ELM-AE. However, given label information, the unsupervised learning of the ELM-AE is difficult to build the discriminative feature space for classification tasks. To address this problem, a novel Fisher extreme learning machine autoencoder (FELM-AE) is proposed and is used as the component for the multilayer Fisher extreme leaning machine (ML-FELM). The FELM-AE introduces the Fisher criterion into the ELM-AE by adding the Fisher regularization term to the objective function, aiming to maximize the between-class distance and minimize the within-class distance of abstract feature. Different from the ELM-AE, the FELM-AE requires class labels to calculate the Fisher regularization loss, so that the learned abstract feature contains sufficient category information to complete classification tasks. The ML-FELM stacks the FELM-AE to extract feature and adopts the extreme leaning machine (ELM) to classify samples. Experiments on benchmark datasets show that the abstract feature extracted by the FELM-AE is more discriminative than the ELM-AE, and the classification results of the ML-FELM are more competitive and robust in comparison with the ELM, one-dimensional convolutional neural network (1D-CNN), ML-ELM, denoising multilayer extreme learning machine (D-ML-ELM), multilayer generalized extreme learning machine (ML-GELM), and hierarchical extreme learning machine with L21‑norm loss and regularization (H-LR21-ELM).

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