Root-Power Mean Aggregation-Based Neuron in Quaternionic Domain

Kumar, Sachin; Tripathi, Bipin Kumar

doi:10.1080/03772063.2018.1436473

Cited by 4 publications

(7 citation statements)

References 39 publications

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“…To improve the efficiency of NNs broad attempts have been made to develop higher order neuron structures. These attempts contributes pi-sigma [5,6], second order neurons [7], generalized neurons [8,9] and other higher order neurons [10][11][12]. Among them higher order neurons have verified to be the most efficient Moreover, the conventional NN employs BP algorithm for training of the network.…”

Section: Related Workmentioning

confidence: 99%

“…NN with conventional neurons is widely used classifier in different domains. To improve the efficiency of conventional NNs broad attempts have been made to develop various neuron structures [5][6][7][8][9][10][11][12]. Though among them higher order neurons have evidenced to be most efficient but due to combinatorial outburst of terms they experience the curse of dimensionality specifically when they are implemented in complex domain.…”

Section: Introductionmentioning

confidence: 99%

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Development of Hybrid Learning Machine in Complex Domain for Human Identification

Srivastava¹,

Tripathi²

2019

IJISA

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This paper presents a hybrid learning machine for human identification. It is a merger of eigenface with fisherface method, genetic fuzzy clustering and complex neural network. The non-linear aggregation based summation and radial basis function neural networks (NLA-SRBF NNs) are proposed as one of the functional component of the novel learning machine. The architecture of NLA-SRBF NNs incorporates hidden neurons, with summation and radial basis aggregation, and output neurons with only summation aggregation, along with complex resilient propagation (ČRPROP) learning procedure. The improved learning and speedy convergence of NLA-SRBF NN enables the hybrid machine to provide better recognition accuracy. The learning machine consists of feature extraction, unsupervised clustering and supervised classification module. The aim of our proposal is to enhance the performance of biometric based recognition system. The efficacy and potency of our hybrid learning machine demonstrated on three benchmark biometric datasetsextended Cohn-Kanade, FERET and AR face datasets to comprehend the motivation. The performance comparisons of different variations of hidden neuron and learning algorithm thoroughly presented the superiority of the proposed NN based hybrid learning machine.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of Hybrid Learning Machine in Complex Domain for Human Identification

Srivastava¹,

Tripathi²

2019

IJISA

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“…The processing of high-dimensional data is one of the most difficult and time-consuming tasks for researchers, as it necessitates the employment of specialized approaches to maintain the relationship between characteristics. According to current research, quaternion has the capacity to keep the relationship between characteristics of high-dimensional data [1][2][3]. In the recent research, the quaternion is employed for the applications containing 3D and 4D related issues, particularly in the encoding and processing of color image pixels with red, green, and blue channels [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…In the recent studies [3,24,25], it has been mentioned that neural networks with quaternions provide a smaller number of neural parameters with superior learning and better generalization capability as compared to networks with real or complex values. Apart from these, quaternion-valued neural networks (QVNN) store and learn the spatial relationships in the various transformations of 3D coordinates [2,3] and in between the color pixels [26], whereas real/complexvalued neural network fails. These qualities have motivated the researchers to apply QVNN in many fields such as automatic speech recognition [27,28], image classification [29], PolSAR land classification [30], prostate cancer Gleason grading [31], color image compression [32], facial expression recognition [33], robot manipulator [34], spoken language understanding [35], attitude control of spacecraft [36], and banknote classification [37].…”

Section: Introductionmentioning

confidence: 99%

“…The neurobiologists are studying the non-linear aggregation based on the multiplication of input signals due to three basis intentions: (1) how the input signals with their synaptic weights process through dendrites in a non-linear manner, (2) how to analyze the behavior of its output signal, and (3) how the simple but non-linear model recognizes the complicated behavior using possible biological methods. These studies have indicated that multiplicative aggregation has a major role in the artificial neural system, particularly for computing the motion perception and its learning [52][53][54].…”

Section: Introductionmentioning

confidence: 99%

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A novel non-linear neuron model based on multiplicative aggregation in quaternionic domain

Kumar¹,

Singh²,

Chaudhary

2022

Complex Intell. Syst.

Self Cite

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The learning algorithm for a three-layered neural structure with novel non-linear quaternionic-valued multiplicative (QVM) neurons is proposed in this paper. The computing capability of non-linear aggregation in the cell body of biological neurons inspired the development of a non-linear neuron model. However, unlike linear neuron models, most non-linear neuron models are built on higher order aggregation, which is more mathematically complex and difficult to train. As a result, building non-linear neuron models with a simple structure is a difficult and time-consuming endeavor in the neurocomputing field. The concept of a QVM neuron model was influenced by the non-linear neuron model, which has a simple structure and the great computational ability. The suggested neuron’s linearity is determined by the weight and bias associated with each quaternionic-valued input. Non-commutative multiplication of all linearly connected quaternionic input-weight terms accommodates the non-linearity. To train three-layered networks with QVM neurons, the standard quaternionic-gradient-based backpropagation (QBP) algorithm is utilized. The computational and generalization capabilities of the QVM neuron are assessed through training and testing in the quaternionic domain utilizing benchmark problems, such as 3D and 4D chaotic time-series predictions, 3D geometrical transformations, and 3D face recognition. The training and testing outcomes are compared to conventional and root-power mean (RPM) neurons in quaternionic domain using training–testing MSEs, network topology (parameters), variance, and AIC as statistical measures. According to these findings, networks with QVM neurons have greater computational and generalization capabilities than networks with conventional and RPM neurons in quaternionic domain.

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A Comprehensive Review on the Advancement of High-Dimensional Neural Networks in Quaternionic Domain with Relevant Applications

Kumar¹,

Rastogi²

2023

Arch Computat Methods Eng

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Root-Power Mean Aggregation-Based Neuron in Quaternionic Domain

Cited by 4 publications

References 39 publications

Development of Hybrid Learning Machine in Complex Domain for Human Identification

Development of Hybrid Learning Machine in Complex Domain for Human Identification

A novel non-linear neuron model based on multiplicative aggregation in quaternionic domain

A Comprehensive Review on the Advancement of High-Dimensional Neural Networks in Quaternionic Domain with Relevant Applications

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