A survey of quaternion neural networks

Parcollet, Titouan; Morchid, Mohamed; Linarès, Georges

doi:10.1007/s10462-019-09752-1

Cited by 139 publications

(94 citation statements)

References 65 publications

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“…The quaternion convolution is one of the main operations of deep neural networks in the quaternion domain [11,13]. Considering a generic quaternion input vector, q, defined similarly to (1), and a generic quaternion filter matrix defined as W = W a + W bî + W c + W dκ , the quaternion convolution can be expressed as the following Hamilton product:…”

Section: Network Architecturementioning

confidence: 99%

“…The Hamilton product of (11) allows quaternion neural networks to capture internal latent relations within the features of a quaternion. Each quaternion convolutional layer is followed by a split quaternion Leaky-ReLU activation function [13]. Quaternion batch normalization is not taken into account as it may be considered as a source of randomness that could cause instability [5,6].…”

Section: Network Architecturementioning

confidence: 99%

“…This work has been supported by "Progetti di Ricerca Grandi" of Sapienza University of Rome under grant number RG11916B88E1942F. number of parameters with respect to real-valued neural networks [11][12][13]. These advantages are due to the properties of quaternion algebras, including the Hamilton product that is used in quaternion convolutions.…”

Section: Introductionmentioning

confidence: 99%

“…These advantages are due to the properties of quaternion algebras, including the Hamilton product that is used in quaternion convolutions. This has recently paved the way to the development of novel deep quaternion neural networks [11,13,14], often tailored to specific applications, including theme identification in telephone conversation [15], 3D sound event localization and detection [16,17], heterogeneous image processing [18] and speech recognition [19]. Other properties of quaternion algebra that may be exploited in learning processes are related to the second-order statistics.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Quaternion-Valued Variational Autoencoder

Grassucci

Comminiello

Uncini

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Deep probabilistic generative models have achieved incredible success in many fields of application. Among such models, variational autoencoders (VAEs) have proved their ability in modeling a generative process by learning a latent representation of the input. In this paper, we propose a novel VAE defined in the quaternion domain, which exploits the properties of quaternion algebra to improve performance while significantly reducing the number of parameters required by the network. The success of the proposed quaternion VAE with respect to traditional VAEs relies on the ability to leverage the internal relations between quaternion-valued input features and on the properties of second-order statistics which allow to define the latent variables in the augmented quaternion domain. In order to show the advantages due to such properties, we define a plain convolutional VAE in the quaternion domain and we evaluate its performance with respect to its real-valued counterpart on the CelebA face dataset.

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Section: Network Architecturementioning

confidence: 99%

Section: Network Architecturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Quaternion-Valued Variational Autoencoder

Grassucci

Comminiello

Uncini

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…This paper uses the best fit algorithm which has been tested many times by the author to get the results. The whole process of building algorithms in supervised models is discussed, but the author puts much emphasis on feature selection [6]. Many algorithms may over-fit the original data or neglect the period of natural causes.…”

Section: Introductionmentioning

confidence: 99%

Credit Card Transaction Fraud Using Machine Learning Algorithms

Huang¹

2020

Proceedings of the 2019 International Conference on Education Science and Economic Development (ICESED 2019)

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Credit cards offered significant advantages over all forms of money: they're pocket size, easily portable, relatively secure and have no intrinsic value themselves. However, payment fraud is an ideal use case for machine learning algorithms and has a long track record of successful use. Machine learning has just been invented, or just been applied to payments fraud for the first time. This paper focuses on the main function of the feature selection in supervised model. The methods used to support the topic are neural net, boosted tree, random forest etc. and the material is credit card transaction data. The conclusion of the research is that banks should deny about 3% clients for balance the profits and loss of goods. A month was spent doing this research with the author's partners and professor for getting the results as accurate as possible.

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