A survey of quaternion neural networks


Quaternion neural networks have recently received an increasing interest due to noticeable improvements over real-valued neural networks on real world tasks such as image, speech and signal processing. The extension of quaternion numbers to neural architectures reached state-of-the-art performances with a reduction of the number of neural parameters. This survey provides a review of past and recent research on quaternion neural networks and their applications in different domains. The paper details methods, algorithms and applications for each quaternion-valued neural networks proposed.

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Machine learning


Artificial intelligence

(R, G, B):

Red, green, blue




Complex-valued neural network


Neural network


Multilayer perceptron


Deep neural network


Recurrent neural network


Convolutional neural network


Denoising autoencoder


Convolutional autoencoder


Hopfield neural network


Support vector machine


Principal component analysis


Latent Dirichlet allocation


Rectified linear unit


Hyperbolic tangent


Exponential linear unit




Mean squared error


Gaussian angular noise


Peak signal to noise ratio


Average brightness


Histograms oriented gradient


Polarimetric synthetic aperture radar


Customer care service


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Parcollet, T., Morchid, M. & Linarès, G. A survey of quaternion neural networks. Artif Intell Rev 53, 2957–2982 (2020). https://doi.org/10.1007/s10462-019-09752-1

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  • Hypercomplex numbers
  • Quaternion neural networks
  • Deep Learning