High Dimensional Neural Networks and Applications

Tripathi, Bipin Kumar; Kalra, Prem

doi:10.1007/978-3-642-11676-6_10

Cited by 5 publications

(3 citation statements)

References 25 publications

(3 reference statements)

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“…Therefore real valued CNN’s are unable to encode the relationship among the three channels and hence causes the information loss which is hindrance in obtaining more accuracy. High dimensional neural networks (HDNN) [ 32 , 33 ] have been extended from real valued neural networks by applying the concepts of complex and hyper complex algebra. Complex valued Neural network [ 3 , 15 ] has emerged as a stronger substitute to conventional neural networks.…”

Section: Background and Related Workmentioning

confidence: 99%

Pneumonia classification using quaternion deep learning

Singh

Tripathi²

2021

Multimed Tools Appl

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Pneumonia is an infection in one or both the lungs because of virus or bacteria through breathing air. It inflames air sacs in lungs which fill with fluid which further leads to problems in respiration. Pneumonia is interpreted by radiologists by observing abnormality in lungs in case of fluid in Chest X-Rays. Computer Aided Detection Diagnosis (CAD) tools can assist radiologists by improving their diagnostic accuracy. Such CAD tools use neural networks which are trained on Chest X-Ray dataset to classify a Chest X-Ray into normal or infected with Pneumonia. Convolution neural networks have shown remarkable performance in object detection in an image. Quaternion Convolution neural network (QCNN) is a generalization of conventional convolution neural networks. QCNN treats all three channels (R, G, B) of color image as a single unit and it extracts better representative features and which further improves classification. In this paper, we have trained Quaternion residual network on a publicly available large Chest X-Ray dataset on Kaggle repository and obtained classification accuracy of 93.75% and F-score of .94. We have also compared our performance with other CNN architectures. We found that classification accuracy was higher with Quaternion Residual network when we compared it with a real valued Residual network.

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Section: Background and Related Workmentioning

confidence: 99%

Pneumonia classification using quaternion deep learning

Singh

Tripathi²

2021

Multimed Tools Appl

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“…For complex activation, holomorphic (a.k.a. analytic) function has been an important topic [Hitzer, 2013, Jalab and Ibrahim, 2011, Vitagliano et al, 2003, Kim and Adali, 2001, Mandic and Goh, 2009, Tripathi and Kalra, 2010 , since it makes the back-propagation simpler thus training becomes faster [Amin et al, 2011 . The importance of Complex Phase Angle of CANN has been suggested, including similarity to biological neuron [Reichert and Serre, 2013].…”

Section: Motivationmentioning

confidence: 99%

A Generalization Method of Partitioned Activation Function for Complex Number

HyeonSeok¹,

Seon²

2018

Preprint

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A method to convert real number partitioned activation function into complex number one is provided. The method has 4em variations; 1 has potential to get holomorphic activation, 2 has potential to conserve complex angle, and the last 1 guarantees interaction between real and imaginary parts. The method has been applied to LReLU and SELU as examples.The complex number activation function is an building block of complex number ANN, which has potential to properly deal with complex number problems.But the complex activation is not well established yet. Therefore, we propose a way to extend the partitioned real activation to complex number.

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“…Traditional ANN is usually in real domain, which deals with data in single dimension. There has been an increasing interest of high dimensional ANN [4], [5], which provides an easy implementation of high dimensional information. A complex number is directly related to the 2-D data.…”

Section: Introductionmentioning

confidence: 99%

Functional mapping with complex higher order compensatory neuron model

Tripathi¹,

Kalra

2010

The 2010 International Joint Conference on Neural Networks (IJCNN)

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The basic ideas to develop artificial neural net work (ANN) were originated with the investigation of brain's micro-structure. It has been a steady endeavor in the research that followed to develop it further and integrate additional discoveries about the human brain with a view to evolve the artificial neuron model closer to the actual brain functioning.The pursuit has ever been on to replicate the typical charac teristic of the neuron. The neuron response to the input signals impinged onto it, is defined how they are aggregated with in the unit. A substantial body of evidence has grown to support the presence of non-linear integration of synaptic inputs in the neuron cells. Superior functionality of ANN in complex domain has been observed in recent researches, which presented the second generation of development in ANN. In this paper, we explore the functional capabilities of a compensatory neuron model with complex-valued high order non-linear aggregation function. The strength and effectiveness of considered neuron is evaluated with an efficient learning algorithm in a complex domain. The performance analysis is carried out through a solid set of simulations. B K Tripathi is with the

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High Dimensional Neural Networks and Applications

Cited by 5 publications

References 25 publications

Pneumonia classification using quaternion deep learning

Pneumonia classification using quaternion deep learning

A Generalization Method of Partitioned Activation Function for Complex Number

Functional mapping with complex higher order compensatory neuron model

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