A Fair Performance Comparison between ComplexValued and RealValued Neural Networks for Disease Detection
Abstract
:1. Introduction
Review of the State of the Art of the Technique
2. Materials
2.1. ISIC2017
2.2. PH2
2.3. PASCAL
3. Methods
3.1. Dataset Preprocessing
3.2. Experiment Design
3.2.1. Structure Factor
3.2.2. ComplexValued Structure
3.3. Measurement and CrossValidation
3.4. Hypothesis Test
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Authors  Dataset Used  Task  Methods  Results 

Yue Qi, Qiu Hua Lin, Li Dan Kuang, Wen Da Zhao, Xiao Feng Gong, Fengyu Cong, Vince D. Calhoun [8]  Used 82 restingstate complexvalued fMRI datasets, including 42 SZs and 40 HCs  Classifying schizophrenia patients (SZs) and healthy controls (HCs)  This study proposes a novel framework combining independent component analysis (ICA) and complexvalued convolutional neural networks (CVDL). ICA is first used to obtain components of interest that have been previously implicated in schizophrenia. 

Shizhen Hu, Seko Nagae, Akira Hirose [13]  They prepared 7 different concentration samples and measured 30 times for each sample  Glucose concentration estimation  In this paper, an adaptive glucose concentration estimation system is proposed. The system estimates glucose concentration values noninvasively by making full use of transmission magnitude and phase data. The 60–80 GHz frequency band millimeter wave is chosen, and a single output neuron complexvalued neural network (CVNN) is built for adaptive concentration estimation. 

Joshua Bassey, Xiangfang Li, Lijun Qian [3]  Used 167 publications  Discuss the recent development of CVNNs  A detailed review of various CVNNs in terms of activation function, learning and optimization, input and output representations, and their applications in tasks such as signal processing and computer vision are provided, followed by a discussion on some pertinent challenges and future research directions.  Complexvalued neural networks, compared to their realvalued counterparts, are still considered an emerging field and require more attention and action from the deep learning and signal processing research community. 
Yang Ximei [6]  A total of 5 radar data preprocessing approaches were implemented to generate dataset samples, including FFT and STFT  Humanmotion classification based on monostatic radar  This thesis proposes three complexvalued convolutional neural networks (CNNs) for humanmotion classification based on monostatic radar. The rangetime, rangeDoppler, rangespectrumtime, and timefrequency spectrograms of microDoppler signatures are adopted as the input to CVNNs with different pluralhandled approaches. A series of experiments determine the optimal approach and data format that achieves the highest classification accuracy. 

Shubhankar Rawat, K.P.S. Rana, Vineet Kumar [7]  A total of 5232 CXR images from 5856 patients aged 1 to 5 years from Guangzhou Women and Children’s Medical Center, Guangzhou, Guangdong province (China). For this work, out of the 5232 images, only 500 images were considered for MID experimentations, which were randomly selected  Investigate a novel complexvalued convolutional neural networkbased model, termed CVMIDNet, for medical image denoising  The model uses residual learning, which learns noise from noisy images and then subtracts it from noisy images so as to obtain clean images. To assess the denoising performance of CVMIDNet, standard image quality metrics, namely, peak signal to noise ratio and the structural similarity index, have been used for 5 different additive white Gaussian noise levels in chest Xray images. Chest Xray denoising performance of CVMIDNet was compared with 4 recent stateoftheart models, namely, BlockMatching and 3D (BM3D) filtering, DnCNN, and Featureguided Denoising Convolutional Neural Network. (FDCNN), and deep CNN with residual learning.  CVMIDNet was found to be superior. For instance, for a Gaussian noise level of σ = 15, the peak signaltonoise ratio and structural similarity index values achieved by the CVMIDNet are 37.2010 and 0.9227, respectively, against the 36.2292 and 0.9086, 36.3203 and 0.9139, 35.0995 and 0.9005, 36.1830 and 0.8968, 34.2436 and 0.8874 achieved by BM3D filtering, DnCNN, RVMIDNet, FDCNN, and deep CNN with residual learning, respectively. 
Theresa Scarnati, Benjamin Lewis [4]  SAMPLE dataset includes 10 classes with equal numbers of measured and synthetic SARimages: 1366 measured and 1366 synthetic. Total: 2732  They present a survey of several complex neural network techniques as applied to a SAR dataset consisting of military targets  Specifically, they evaluate a multichannel approach with Deep Complex Networks and SurReal against (i) limited training data and (ii) when the training and testing data exhibit a domain mismatch. 

Bungo Konishi, Akira Hirose, Ryo Natsuaki [14]  An interferogram around Mt. Fuji observed on 25 November 2010 and 12 April 2011. An interferogram around Shinmoedake observed on 14 April 2009 and 30 May 2009  In this paper, they propose complexvalued reservoir computing (CVRC) to deal with complexvalued images in interferometric synthetic aperture radar (InSAR)  They classify InSAR image data by using CVRC successfully with a higher resolution and a lower computational cost, i.e., one hundredth learning time and onefifth classification time than convolutional neural networks.  CVRC is found applicable to quantitative tasks dealing with continuous values as well as discrete classification tasks with higher accuracy. 
Linfang Xiao, Yilong Liu, Zheyuan Yi, Yujiao Zhao, Linshan Xie, Peibei Cao, Alex T L Leong, Ed X Wu [15]  T1w GRE axial brain dataset: 57 and 10 subjects with 200 axial slices extracted from each subject were used for training and testing, respectively  To provide a complexvalued deep learning approach for partial Fourier (PF) reconstruction of complex MR images  They propose a complexvalued deep learning approach with an unrolled network architecture for PF reconstruction that iteratively reconstructs OF sampled data and enforces data consistency. They evaluate their approach for reconstructing both spinecho and gradientecho data. They compared the proposed deep learning PF (DLPF) method to the conventional POCSPF method.  The proposed method outperformed the iterative POCS PF reconstruction method. It produced better artifact suppression and recovery of both image magnitude and phase details in the presence of local phase changes. Moreover, the network trained on axial brain data could reconstruct sagittal and coronal brain and knee data. 
Duan C, Xiong Y, Cheng K, Xiao S, Lyu J, Wang C, Bian X, Zhang J, Zhang D, Chen L, Zhou X, Lou X [16]  SWI data were acquired from 117 participants who underwent clinical brain MRI examinations between 2019 and 2021, including patients with tumor, stroke, hemorrhage, traumatic brain injury, etc.  Propose a deep learning model to accelerate susceptibilityweighted imaging (SWI) acquisition times and evaluate the clinical feasibility of this approach  A complexvalued convolutional neural network (ComplexNet) was developed to reconstruct highquality SWI from highly accelerated kspace data. ComplexNet can leverage the inherently complexvalued nature of SWI data and learn richer representations by using complexvalued networks.  The average reconstruction time of ComplexNet was 19 ms per section (1.33 s per participant). ComplexNet achieved significantly improved quantitative image metrics compared to a conventional compressed sensing method and a realvalued network with acceleration rates of 5 and 8 (p < 0.001). ComplexNet showed comparable diagnostic performance to the fully sampled SWI for visualizing a wide range of pathology, including hemorrhage, cerebral microbleeds, and brain tumors. 
Haozhen Li, Boyuan Zhang, Haoran Chang, Xin Liang, Xinyu Gu [5]  CSI dataset generated by COST2100 channel model is used. The training, validation, and testing sets contain 100,000, 30,000, and 20,000 samples, respectively  They present a complexvalued lightweight neural network for channel state information (CSI) feedback named CVLNet  The CVLNet adopts the complexvalued neural network components in a multiscale feature augmentation encoder and a multiresolution Xshaped reconstruction decoder with a series of lightweight details.  The experiment results show that the proposed CVLNet maintains the samelevel parameters of the encoder with stateoftheart (SOTA) lightweight networks while outperforming them with at most a 33.4% improvement in accuracy under severe compression rates. 
Name of the Database  Normal Data  Abnormal Data  Data Type  Associated Illness 

ISIC2017  1621  374  Dermatoscopy image  Melanoma 
PH2  160  40  Dermatoscopy image  Melanoma 
PASCAL  320  141  Sounds/Scalogram  Heart murmurs 
Structure/Database  ISIC2017  PH2  PASCAL 

Complexvalued structure  Accuracy, F1 Score, Precision, Recall, Sensitivity, Specificity  ibidem  Ibidem 
Realvalued structure  ibidem  ibidem  Ibidem 
Hyperparameter  ComplexValued  RealValued 

Activation function  Complex Relu  Relu 
Learning Rate  0.001  0.001 
Optimizer  ADAM with Complex Correction  ADAM 
Layer  Amount of Parameters ComplexValued  Amount of Parameters RealValued 

Conv1  71,940  290,400 
Conv2  186,608  285,144 
Conv3  725,760  1,492,992 
Fully Connected 1  169,600  359,552 
Fully Connected 2  1200  1200 
Fully Connected 3  500  500 
Output  2  2 
Structure/Metric  Fold  F1 Score  Precision  Recall/Sensitivity  Accuracy  Specificity 

ComplexValued Convolution Neural Networks  1  0.90410  0.89411  0.914328  0.77889  0.73888 
2  0.91490  0.90734  0.922586  0.76382  0.74650  
3  0.93140  0.93938  0.923584  0.79899  0.75860  
4  0.91270  0.91895  0.906528  0.80402  0.73957  
5  0.92270  0.94316  0.903088  0.79397  0.78863  
6  0.93140  0.93279  0.930083  0.79397  0.74694  
7  0.89580  0.89813  0.893478  0.77387  0.75531  
8  0.90550  0.92049  0.890943  0.76884  0.75336  
9  0.91700  0.90336  0.931074  0.80402  0.74156  
10  0.93320  0.94119  0.925291  0.82412  0.76313  
Max Complex  0.93320  0.94316  0.931074  0.93107  0.78863  
Min Complex  0.89580  0.89411  0.890943  0.89094  0.73888  
Mean Complex  0.91690  0.91989  0.914098  0.91409  0.75325  
Normality Test/pvalue  0.55702  0.28137  0.09199  0.70872  0.21898 
Structure/Metric  Fold  F1 Score  Precision  Recall/Sensitivity  Accuracy  Specificity 

RealValued Convolution Neural Networks  1  0.86960  0.86078  0.87854  0.66834  0.66298 
2  0.88730  0.90188  0.87316  0.69347  0.66127  
3  0.87180  0.86158  0.88229  0.67337  0.64810  
4  0.86750  0.86807  0.86694  0.73869  0.67762  
5  0.88280  0.90251  0.86399  0.68342  0.63900  
6  0.87890  0.87545  0.88247  0.68342  0.63624  
7  0.87910  0.87691  0.88128  0.66332  0.67711  
8  0.86120  0.87116  0.85153  0.69849  0.67995  
9  0.87420  0.88535  0.86323  0.66834  0.67312  
10  0.88780  0.88409  0.89156  0.65829  0.67185  
Max  0.88780  0.90251  0.89156  0.73869  0.67995  
Min  0.86120  0.86078  0.85153  0.65829  0.63624  
Mean  0.87600  0.87878  0.87350  0.68291  0.66272  
Normality Test/pvalue  0.10060  0.32868  0.77467  0.07353  0.11563 
Metric  Student’s tTest Comparison of Means—pValue 

F1 Score  0.00001 
Precision  0.00004 
Recall  0.00002 
Accuracy  0.00001 
Specificity  0.00001 
Structure/Metric  Fold  F1 Score  Precision  Recall/Sensitivity  Accuracy  Specificity 

ComplexValued Convolution Neural Networks  1  0.90909  0.93750  0.88235  0.88235  0.66667 
2  0.90909  0.93750  0.88235  0.88235  0.66667  
3  0.86667  0.92857  0.81250  0.81250  0.75000  
4  0.87500  0.93333  0.82353  0.82353  0.66667  
5  0.84615  0.91667  0.78571  0.78571  0.83333  
6  0.89655  0.92857  0.86667  0.86667  0.80000  
7  0.90323  0.93333  0.87500  0.87500  0.75000  
8  0.91429  0.94118  0.88889  0.88889  0.50000  
9  0.86667  0.92857  0.81250  0.81250  0.75000  
10  0.88889  0.92308  0.85714  0.85714  0.83333  
Max Complex  0.91429  0.94118  0.88889  0.85000  0.83333  
Min Complex  0.84615  0.91667  0.78571  0.80000  0.50000  
Mean Complex  0.88756  0.93083  0.84866  0.83000  0.72167  
Normality Test/pvalue  0.71070  0.14828  0.36900  0.00017  0.14913 
Structure/Metric  Fold  F1 Score  Precision  Recall/Sensitivity  Accuracy  Specificity 

RealValued Convolution Neural Networks  1  0.81818  0.90000  0.75000  0.80000  0.87500 
2  0.82353  0.87500  0.77778  0.70000  0.00000  
3  0.81250  0.86667  0.76471  0.70000  0.33333  
4  0.81250  0.86667  0.76471  0.70000  0.33333  
5  0.76923  0.83333  0.71429  0.70000  0.66667  
6  0.81250  0.86667  0.76471  0.70000  0.33333  
7  0.81250  0.86667  0.76471  0.70000  0.33333  
8  0.80000  0.85714  0.75000  0.70000  0.50000  
9  0.78571  0.84615  0.73333  0.70000  0.60000  
10  0.81250  0.86667  0.76471  0.70000  0.33333  
Max  0.82353  0.90000  0.77778  0.80000  0.87500  
Min  0.76923  0.83333  0.71429  0.70000  0.00000  
Mean  0.80592  0.86450  0.75489  0.71000  0.43083  
Normality Test/pvalue  0.21406  0.05052  0.15922  0.00001  0.31439 
Metric  Student’s tTest Comparison of Means—pValue 

F1 Score  7.71763 × 10^{8} 
Precision  1.13570 × 10^{7} 
Recall  6.08852 × 10^{6} 
Specificity  4.11085 × 10^{3} 
Structure/Metric  Fold  F1 Score  Precision  Recall/Sensitivity  Accuracy  Specificity 

ComplexValued Convolution Neural Networks  1  0.82540  0.89655  0.76471  0.76596  0.76923 
2  0.87273  0.92308  0.82759  0.84783  0.88235  
3  0.80702  0.88462  0.74194  0.76087  0.80000  
4  0.88889  0.92308  0.85714  0.86957  0.88889  
5  0.81967  0.89286  0.75758  0.76087  0.76923  
6  0.84211  0.88889  0.80000  0.80435  0.81250  
7  0.83582  0.90323  0.77778  0.76087  0.70000  
8  0.86792  0.92000  0.82143  0.84783  0.88889  
9  0.83077  0.90000  0.77143  0.76087  0.72727  
10  0.83582  0.90323  0.77778  0.76087  0.70000  
Max Complex  0.88889  0.92308  0.85714  0.86957  0.88889  
Min Complex  0.80702  0.88462  0.74194  0.76087  0.70000  
Mean Complex  0.84261  0.90355  0.78974  0.79399  0.79384  
Normality Test/pvalue  0.22495  0.58013  0.48847  0.00280  0.18135 
Structure/Metric  Fold  F1 Score  Precision  Recall/Sensitivity  Accuracy  Specificity 

RealValued Convolution Neural Networks  1  0.74510  0.82609  0.67857  0.72340  0.78947 
2  0.76923  0.83333  0.71429  0.73913  0.77778  
3  0.76667  0.85185  0.69697  0.69565  0.69231  
4  0.78788  0.83871  0.74286  0.69565  0.54545  
5  0.75862  0.84615  0.68750  0.69565  0.71429  
6  0.75000  0.82759  0.68571  0.65217  0.54545  
7  0.80702  0.85185  0.76667  0.76087  0.75000  
8  0.76471  0.83871  0.70270  0.65217  0.44444  
9  0.77966  0.85185  0.71875  0.71739  0.71429  
10  0.80702  0.85185  0.76667  0.76087  0.75000  
Max  0.80702  0.85185  0.76667  0.76087  0.78947  
Min  0.74510  0.82609  0.67857  0.65217  0.44444  
Mean  0.77359  0.84180  0.71607  0.70930  0.67235  
Normality Test/pvalue  0.06181  0.17432  0.41637  0.36105  0.05332 
Metric  Student’s tTest Mean Comparative 

F1 Score  4.0131 × 10^{9} 
Precision  1.4683 × 10^{4} 
Recall  5.0077 × 10^{6} 
Specificity  0.01450 
Metric  Dataset  Test Executed  pValue 

Accuracy  PH2  U  0.00134 
Accuracy  Pascal  U  0.02377 
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Jojoa, M.; GarciaZapirain, B.; Percybrooks, W. A Fair Performance Comparison between ComplexValued and RealValued Neural Networks for Disease Detection. Diagnostics 2022, 12, 1893. https://doi.org/10.3390/diagnostics12081893
Jojoa M, GarciaZapirain B, Percybrooks W. A Fair Performance Comparison between ComplexValued and RealValued Neural Networks for Disease Detection. Diagnostics. 2022; 12(8):1893. https://doi.org/10.3390/diagnostics12081893
Chicago/Turabian StyleJojoa, Mario, Begonya GarciaZapirain, and Winston Percybrooks. 2022. "A Fair Performance Comparison between ComplexValued and RealValued Neural Networks for Disease Detection" Diagnostics 12, no. 8: 1893. https://doi.org/10.3390/diagnostics12081893