Quaternion Extreme Learning Machine

Lv, Hui; Zhang, Huisheng

doi:10.1007/978-3-319-57421-9_3

Cited by 5 publications

(2 citation statements)

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“…The ELMs maintain the universal approximation capabilities of a multilayer Perceptron while also drastically decreasing training's computational complexity [34][35][36]. Complex-valued and quaternion-valued ELMs have been developed respectively by Li et al [37], Minemoto et al [30], and Lv et al [38]. This paper extends the ELMs to more general hypercomplex number systems.…”

Section: Introductionmentioning

confidence: 93%

A General Framework for Hypercomplex-valued Extreme Learning Machines

Vieira,

Valle

2021

Preprint

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This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. Hypercomplex neural networks are machine learning models that feature higher-dimension numbers as parameters, inputs, and outputs. Firstly, we review broad hypercomplex algebras and show a framework to operate in these algebras through real-valued linear algebra operations in a robust manner. We proceed to explore a handful of well-known four-dimensional examples. Then, we propose the hypercomplex-valued ELMs and derive their learning using a hypercomplex-valued least-squares problem. Finally, we compare real and hypercomplex-valued ELM models' performance in an experiment on time-series prediction and another on color image autoencoding. The computational experiments highlight the excellent performance of hypercomplex-valued ELMs to treat high-dimensional data, including models based on unusual hypercomplex algebras.

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Section: Introductionmentioning

confidence: 93%

A General Framework for Hypercomplex-valued Extreme Learning Machines

Vieira,

Valle

2021

Preprint

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“…When it comes to 3-D and 4-D data sources, such as measurements from seismometers, ultrasonic anemometers, and inertial body sensors, quaternions in quaternion domain H have inherent advantages over real vectors in representing 3-D and 4-D data owing to the natural ability to encode the cross-channel correlation and the accurate modeling of rotation and orientation [14]. In order to take advantage of the quaternion representation, a number of quaternionvalued neural models have been proposed, such as quaternion LMS algorithm [15], quaternion nonlinear adaptive filter [16], quaternion Kalman filter [17], quaternion independent component analysis algorithm [18], quaternion support vector machine [19], quaternion multi-valued neural networks [20], and quaternion ELM (QELM) [21]. Analogous with the complex case, the augmented quaternion statistics reveal that the covariance matrix is not adequate to capture the full second-order statistics of a quaternion vector [22], [23], which makes the Quaternion Widely Linear (QWL) processing become the optimal linear processing for general quaternion-valued signals.…”

Section: Introductionmentioning

confidence: 99%

Augmented Quaternion Extreme Learning Machine

Zhang

2019

IEEE Access

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As an efficient training strategy for single hidden layer neural networks, extreme learning machine, and its variants have been widely used due to its fast learning speed and superior generalization performance. However, when used for quaternion signal processing, extreme learning machine cannot make full use of the cross-channel correlation and quaternion statistics and thus often provides only suboptimal solutions. To this end, in this paper, we extend the extreme learning machine to quaternion domain and then propose two augmented quaternion extreme learning machine models for quaternion signal processing. These two models incorporate the involutions of the network input and hidden nodes, respectively, and can fully capture the second-order statistics of quaternion signals. In order to overcome the possible overfitting problem, two corresponding regularized augmented algorithms are also derived with the help of the generalized HR calculus. The superiority of the proposed models is verified by the simulation results. INDEX TERMS Extreme learning machine, quaternion signal processing, augmented quaternion statistics, regularization.

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