Comparison of high-dimensional neural networks using hypercomplex numbers in a robot manipulator control

Takahashi, Kazuhiko

doi:10.1007/s10015-021-00687-x

Cited by 16 publications

(8 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because they have the same multiplication table, the hypercomplex algebra B[−1, +1] corresponds to the tessarines, also known as commutative quaternions [19], [17]. Similarly, the algebra B[−1, −1] corresponds to the bicomplex numbers [12] while B[+1, +1] is equivalent to the Klein 4-group, a commutative algebra of great interest in symmetric group theory [28]. Concluding, we have a total of eight four-dimensional hypercomplex algebras.…”

Section: B Four-dimensional Hypercomplex Algebrasmentioning

confidence: 99%

“…For example, quaternions provide an efficient tool for describing 3D rotations used in computer graphics. Furthermore, quaternion-valued neural networks have been effectively applied for signal processing and control [11], [12], image classification [13], [14], and many other pattern recognition tasks [15], [16]. However, besides the quaternions, many other hypercomplex-valued algebras exist, including the coquaternions, the tessarines, Clifford algebras, and Cayley-Dickson algebras.…”

Section: Introductionmentioning

confidence: 99%

“…A family of hypercomplex algebras, obtained from the recursive process of Cayley-Dickson, can be used to develop effective HvNNs [25], [26]. Furthermore, four-dimensional hypercomplex algebras have been used for designing neural networks for controlling a robot manipulator [12].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, we shall focus only on eight four-dimensional associative hypercomplex algebras, four of which are commutative. We consider the tessarines, the bi-complex numbers, and the Klein 4-group algebra among the commutative algebras [12], [28]. The four non-commutative hypercomplex algebras include quaternions and coquaternions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

Vieira¹,

Valle²

2022

Preprint

View full text Add to dashboard Cite

This paper features convolutional neural networks defined on hypercomplex algebras applied to classify lymphocytes in blood smear digital microscopic images. Such classification is helpful for the diagnosis of acute lymphoblast leukemia (ALL), a type of blood cancer. We perform the classification task using eight hypercomplex-valued convolutional neural networks (HvCNNs) along with real-valued convolutional networks. Our results show that HvCNNs perform better than the real-valued model, showcasing higher accuracy with a much smaller number of parameters. Moreover, we found that HvCNNs based on Clifford algebras processing HSV-encoded images attained the highest observed accuracies. Precisely, our HvCNN yielded an average accuracy rate of 96.6% using the ALL-IDB2 dataset with a 50% train-test split, a value extremely close to the stateof-the-art models but using a much simpler architecture with significantly fewer parameters.

show abstract

Section: B Four-dimensional Hypercomplex Algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

Vieira¹,

Valle²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Their usefulness lies in the fact that they operate in higher-dimensional spaces, and are thus able to explain the relationships between the dimensions. As an example, we can mention the use of hypercomplex domains in virtual reality [17,18], acoustic applications [19,20], communication [21,22], image processing [23,24], seismic phenomena [25,26], robotics [27,28], materials [29,30], avionics [31,32], etc.…”

Section: Introductionmentioning

confidence: 99%

The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions

et al. 2021

View full text Add to dashboard Cite

This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under Tk-properness conditions. Observations from each sensor can be updated, delayed, or contain only noise, and a correlation is assumed between the state and the observation noises. Recursive algorithms for the optimal local linear filter at each sensor as well as both centralized and distributed linear fusion estimators are derived using an innovation approach. The Tk-properness assumption implies a reduction in the dimension of the augmented system, which yields computational savings in the previously mentioned algorithms compared to their counterparts, which are derived from real or widely linear processing. A numerical simulation example illustrates the obtained theoretical results and allows us to visualize, among other aspects, the insignificant difference in the accuracy of both fusion filters, which means that the distributed filter, although suboptimal, is preferable in practice as it implies a lower computational cost.

show abstract

Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks

Vital

Vieira

Valle

2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Comparison of high-dimensional neural networks using hypercomplex numbers in a robot manipulator control

Cited by 16 publications

References 20 publications

Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions

Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks

Contact Info

Product

Resources

About