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<front>
<journal-meta>
<journal-id journal-id-type="pmc">FDMP</journal-id>
<journal-id journal-id-type="nlm-ta">FDMP</journal-id>
<journal-id journal-id-type="publisher-id">FDMP</journal-id>
<journal-title-group>
<journal-title>Fluid Dynamics &#x0026; Materials Processing</journal-title>
</journal-title-group>
<issn pub-type="epub">1555-2578</issn>
<issn pub-type="ppub">1555-256X</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">24836</article-id>
<article-id pub-id-type="doi">10.32604/fdmp.2023.024836</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Hemodynamic Analysis and Diagnosis Based on Multi-Deep Learning Models</article-title><alt-title alt-title-type="left-running-head">Hemodynamic Analysis and Diagnosis Based on Multi-Deep Learning Models</alt-title><alt-title alt-title-type="right-running-head">Hemodynamic Analysis and Diagnosis Based on Multi-Deep Learning Models</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Deng</surname><given-names>Xing</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-2" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Da</surname><given-names>Feipeng</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref><email>dafp@seu.edu.cn</email>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Shao</surname><given-names>Haijian</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>School of Automation, Key Laboratory of Measurement and Control for CSE, Ministry of Education, Southeast University</institution>, <addr-line>Nanjing, 210096</addr-line>, <country>China</country></aff>
<aff id="aff-2"><label>2</label><institution>School of Computer, Jiangsu University of Science and Technology</institution>, <addr-line>Zhenjiang, 212003</addr-line>, <country>China</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Electrical and Computer Engineering, University of Nevada</institution>, <addr-line>Las Vegas, 89154</addr-line>, <country>USA</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Feipeng Da. Email: <email>dafp@seu.edu.cn</email></corresp></author-notes>
<pub-date date-type="collection" publication-format="electronic"><year>2023</year></pub-date>
<pub-date date-type="pub" publication-format="electronic"><day>26</day><month>1</month><year>2023</year></pub-date>
<volume>19</volume>
<issue>6</issue>
<fpage>1369</fpage>
<lpage>1383</lpage>
<history>
<date date-type="received"><day>08</day><month>6</month><year>2022</year></date>
<date date-type="accepted"><day>25</day><month>10</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Deng et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Deng et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_FDMP_24836.pdf"></self-uri>
<abstract><p>This study employs nine distinct deep learning models to categorize 12,444 blood cell images and automatically extract from them relevant information with an accuracy that is beyond that achievable with traditional techniques. The work is intended to improve current methods for the assessment of human health through measurement of the distribution of four types of blood cells, namely, eosinophils, neutrophils, monocytes, and lymphocytes, known for their relationship with human body damage, inflammatory regions, and organ illnesses, in particular, and with the health of the immune system and other hazards, such as cardiovascular disease or infections, more in general. The results of the experiments show that the deep learning models can automatically extract features from the blood cell images and properly classify them with an accuracy of 98&#x0025;, 97&#x0025;, and 89&#x0025;, respectively, with regard to the training, verification, and testing of the corresponding datasets.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Blood cell analysis</kwd>
<kwd>deep learning models</kwd>
<kwd>classification-detection</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label><title>Introduction</title>
<p>The goal of a routine blood examination is to measure the number and concentration of blood cells in a patient&#x2019;s blood in order to determine, among other things, if the patient has anemia or an infection. Therefore, high-precision blood cell detection technology is essential for human health diagnostics [<xref ref-type="bibr" rid="ref-1">1</xref>]. There are five different types of white blood cells, neutrophils, eosinophils, basophils, lymphocytes, and monocytes. There are now two available types of cell detection and counting technologies. Traditional image processing techniques like automatic cell recognition technology based on Hough transform [<xref ref-type="bibr" rid="ref-2">2</xref>], watershed method based on distance transform [<xref ref-type="bibr" rid="ref-3">3</xref>], and method based on threshold [<xref ref-type="bibr" rid="ref-4">4</xref>] were used in the early stages, but they will not be accurate enough for real-world applications, especially in areas with a lot of cell overlap. In the earliest stages of pre-blood cell identification, which is divided into two categories, traditional image processing technology was mostly used. The most prevalent technique was hand-staining, followed by manual inspection and classification under a microscope [<xref ref-type="bibr" rid="ref-5">5</xref>]. This method requires examiners to have a comprehensive understanding of cell morphology and to have mastered the capacity to spot and recognize patterns via consistent study and practice. Due to the vast amount of microscopic image data and the diversity of blood cell morphology, traditional blood cell identification methods are becoming more unsuitable for addressing the various complex challenges confronted by blood cell analysis inspectors. Many effective deep learning-based object detection algorithms, such as R-CNN, Mask-R-CNN [<xref ref-type="bibr" rid="ref-6">6</xref>], YOLO [<xref ref-type="bibr" rid="ref-7">7</xref>], and RetinaNet [<xref ref-type="bibr" rid="ref-8">8</xref>], have been presented in recent years, and they are now frequently employed in blood cell detection applications.</p>
<p>Francois Chollet proposed CNNs that are superior to Inception by substituting depth-wise separable convolutions. An experiment with a larger dataset of 350 million images and 17,000 classes for image classification [<xref ref-type="bibr" rid="ref-9">9</xref>] shows that the Xception can improve the performance of CNNs. Christian et al. scaled networks using correctly factorized convolutions and aggressive regularization [<xref ref-type="bibr" rid="ref-10">10</xref>]. He et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] introduced a residual learning framework and evaluated residual networks with up to 152 layers using the ImageNet dataset. Han et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] proposed a three-step strategy to eliminate superfluous connections to circumvent the issues that neural networks are difficult to deploy on embedded systems and that traditional neural networks can correct the design prior to training. Start by training the network and identifying the vital links. Second, eliminate any unnecessary connections. The network must then be retrained. Szegedy et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] proposed the Inception architecture for deep convolutional neural networks. In addition, the Hebbian principle and multi-scale processing intuition were used to maximize quality in design decisions. Ma et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] created the novel ShuffeNet V2 architecture to analyze the direct metric on the target platform. Wang et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] proposed an end-to-end training method for a residual attention network employing an attention mechanism and a hybrid feed-forward network architecture. The proposed network achieves state-of-the-art object performance on three benchmark datasets, including CIFAR-10, CIFAR-100, and ImageNet. Zoph et al. [<xref ref-type="bibr" rid="ref-16">16</xref>] made a new search space called the &#x201C;NASNet search space&#x201D; and a new regularization method called Scheduled DropPath to make the NASNet models more general.</p>
<p>Hegde et al. [<xref ref-type="bibr" rid="ref-17">17</xref>] categorized white blood cells using both traditional image processing techniques and deep learning methods. The output of the classifier was evaluated using a neural network with hand-crafted features that had an average accuracy of 99.8 percent. In addition, white blood cells were classified with approximately 99&#x0025; accuracy using CNN and transfer learning. Kutlu et al. [<xref ref-type="bibr" rid="ref-18">18</xref>] utilized Regional Convolutional Neural Networks (R-CNN) and merged AlexNet, VGG16, GoogLeNet, and ResNet50 architectures to recognize WBC cells. When the sample size is small, Baydilli et al. [<xref ref-type="bibr" rid="ref-19">19</xref>] classified WBC using capsule networks. Shahin et al. [<xref ref-type="bibr" rid="ref-20">20</xref>] proposed transfer learning using deep activation characteristics and fine-tuning of existing deep networks for the identification of WBCs. In addition, &#x201C;WBCsNet,&#x201D; a novel end-to-end convolutional deep architecture, was proposed and utilized to balance the categorization of the WBCs dataset. Sharma et al. [<xref ref-type="bibr" rid="ref-21">21</xref>] created a deep learning system that uses convolutional neural networks to make the whole process of classifying white blood cells (WBC) automatic. Sahlol et al. [<xref ref-type="bibr" rid="ref-22">22</xref>] proposed a more effective hybrid technique for classifying WBCs. The hybrid strategy consisted primarily of two steps, Initially, features were extracted from WBC images using VGGNet. The collected features were then filtered using the Salp Swarm Algorithm (SESSA). Zhang et al. [<xref ref-type="bibr" rid="ref-23">23</xref>] added the deformable convolution layer to the standard U-Net structure to deform U-Net (dU-Net) and improve the accuracy of RBC classification in order to further address the low image quality resulting from noise and artifacts. Iqbal et al. [<xref ref-type="bibr" rid="ref-24">24</xref>] utilized machine learning techniques such as logistic regression, support vector machine (SVM), and CNN to differentiate between healthy and diseased cells. Kassim et al. [<xref ref-type="bibr" rid="ref-25">25</xref>] introduced the RBCNet pipeline, which consists of a U-Net first stage for cell-clusteror superpixel segmentation and a faster R-CNN second refinement stage for recognizing tiny objects within connected component clusters. Jiang et al. [<xref ref-type="bibr" rid="ref-26">26</xref>] proposed a new deep learning method called attention-YOLO, which adds a channel attention mechanism and a spatial attention mechanism to a feature extraction network in order to effectively realize the automation of blood count and solve the problems of inadequate positioning of the bounding boxes in the YOLO detection method. Compared to RBC cell classification, Aliyu et al. [<xref ref-type="bibr" rid="ref-27">27</xref>] proposed a method to classify abnormalities based on images of RBCs with deformed shapes using SVM and Deep learning. Bold&#x00FA; et al. [<xref ref-type="bibr" rid="ref-28">28</xref>] used pre-trained CNNs (VGG16, ResNet101, DenseNet121, and SENet154) to adjust their layers to datasets, after which they selected the optimal architecture and created a system with two parallel modules (ALNet). Mohamed et al. [<xref ref-type="bibr" rid="ref-29">29</xref>] classified WBC using ten distinct pre-trained models and six distinct machine learning techniques. Reference [<xref ref-type="bibr" rid="ref-30">30</xref>] proposed geometric-feature spectrum ExtremeNet (GFS-ExtremeNet), a geometry-aware deep-learning technique for cell detection. Khouani et al. [<xref ref-type="bibr" rid="ref-31">31</xref>] developed an approach based on deep learning for automatically recognizing white blood cells in images of peripheral blood and bone marrow. In particular, the application of combined predictions and corrections increased model outputs, as did the use of a new technique that improved segmentation quality by collaborating model results with geographical information. Tran et al. [<xref ref-type="bibr" rid="ref-32">32</xref>] used cutting-edge deep learning semantic segmentation techniques to separate red and white blood cells in blood smear images.</p>
<p>The rest of this work is arranged as follows, <xref ref-type="sec" rid="s2">Section 2</xref> contains the deep learning classification model and model classification assessment criteria, such as model architecture design and analysis, and <xref ref-type="sec" rid="s3">Section 3</xref> contains the model optimization approach. <xref ref-type="sec" rid="s3">Section 3</xref> presents a feature distribution study of the four blood cells as well as a comparison of nine deep learning models for classification. The <xref ref-type="sec" rid="s4">Section 4</xref> of this paper brings the paper to a conclusion.</p>
</sec>
<sec id="s2">
<label>2</label><title>Proposed Approaches for Hemodynamic Classification Analysis</title>
<p>On numerous occasions, deep neural networks outperform conventional machine learning techniques. Complex nonlinear relationships between input and output variables are modeled by DNNs. Given sufficient data, deep neural networks can provide a reliable solution for hemodynamic classification tasks. CNNS learns features implicitly from training data. Because neurons on the same feature map surface have identical weights, the networks can be trained concurrently. The structure of local weight sharing reduces network complexity and provides unique benefits for image classification tasks. Resnet&#x2019;s residual structure enables the network to be deeper, to converge more rapidly, and to be optimized with fewer parameters and less complexity than earlier models. Based on InceptionV3, Xception replaces the Inception module with depth-separable convolutions and combines Resnet skip-connection structures. This expedites the model&#x2019;s convergence and increases its precision. However, the computational process of the InceptionV3 network structure is relatively dispersed, and the performance of existing convolutional neural networks for classification tasks is inadequate. SqueezeNet is a traditional lightweight network, and on the ImageNet dataset, AlexNet can achieve comparable results with 50 times fewer parameters than SqueezeNet. GoogleNet includes an additional classifier during training, which can mitigate the effects of vanishing gradients. Once the model has been trained, the supplementary classifier is no longer required. Additionally, the fully connected layer and a global average pooling layer are utilized to reduce the number of parameters in the model, allowing it to be successfully applied to image classification tasks. SuffleNetV2&#x2019;s primary function is to alter the data flow using channel shuffling. It reduces the number of parameters and computation required for small models. Its disadvantage is that it creates a boundary effect in which only a small portion of the input channel is used to generate the output channel. Attention 56 performs better when the output sequence and input sequence are not in the same order. NASNet can be applied to arbitrary classification tasks by stacking network units. NASNet is essentially a more complicated version of Inception. We think that these traditional neural networks can do a good job of analyzing how blood moves through the body.</p>
<p>In this paper, a multi-deep learning model-based classification analysis for hemodynamics is proposed. This paper uses a total of 12,444 images, which are divided into training sets, verification sets, and test sets, totaling 7965, 1992, and 2487 images, respectively. These images are categorized as eosinophils, neutrophils, monocytes, and lymphocytes. All datasets are subjected to uniform data preprocessing, including normalization distribution testing. The CNNs, Xception, InceptionV3, ResNet50, Squeeze, GoogleNet, SuffleNetV2, Attention56, and NasNet deep learning models are used for the four categories. The performance of the proposed approaches is measured by the TP, TN, FP, FN, accuracy, and model loss.</p>
<p><xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the process flow for this paper. In the classification task&#x2019;s overall architecture, the original data set is processed before the training set, validation set, and test set are proportionally divided. The processing networks CNNs, Xception, InceptionV3, ResNet50, Squeeze, GoogleNet, SuffleNetV2, Attention56, and NasNet receive the processed data. Then, visualize the training epoch&#x2019;s curve using the loss and accuracy values obtained during model training. At the conclusion, each model&#x2019;s test results were evaluated using a confusion matrix.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption><title>The processing diagram of this paper</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-1.tif"/>
</fig>
<sec id="s2_1">
<label>2.1</label><title>The Classification Model Based on Deep Learning</title>
<p>Without the need for manual feature creation and cell position calibration, deep learning models can accept training samples, extract valid features from the samples, and perform classification recognition without the need for manual feature creation and cell position calibration. Additionally, they can extract valid features from the sample and perform classification recognition. By increasing the number of hidden layers, deep neural networks can analyze and process a substantial amount of cell data, and this increase in the number of layers improves accuracy and overcomes the limitations of shallow neural networks [<xref ref-type="bibr" rid="ref-33">33</xref>,<xref ref-type="bibr" rid="ref-34">34</xref>]. In the case of the widespread ResNet network, the following model applies,</p>
<p><disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>y</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mspace width="1em" /><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula> denotes the input vector of the residual unit. <inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>
</inline-formula> and <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:msub><mml:mi>y</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula> denote the output vectors. <inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mi>&#x03C3;</mml:mi></mml:math>
</inline-formula> represents the activation function. The function <inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> represents the residual function, which represents the learned residual. <inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> is the underlying mapping of the residual unit, when <inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula> represents the identity mapping. Therefore, the features learned from shallow layer <italic>l</italic> to deep layer <italic>L</italic> can be expressed as,</p>
<p><disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>x</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mrow><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:msub><mml:mi>x</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:math>
</inline-formula> represents the output vector of the <italic>L</italic>th residual unit. The calculation formula of convolution is as follows:</p>
<p><disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mspace width="thinmathspace" /><mml:mo>&#x2212;</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>P</mml:mi></mml:mrow><mml:mi>S</mml:mi></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mspace width="thinmathspace" /><mml:mo>&#x2212;</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>P</mml:mi></mml:mrow><mml:mi>S</mml:mi></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mstyle></mml:math>
</disp-formula></p>
<p>where <italic>W</italic> represents the image width, <italic>H</italic> represents the image height, <italic>S</italic> represents the convolution kernel step size, and <italic>P</italic> represents the increased number of boundary pixel layers at the edge of the image. If the boundary pixel filling mode is the same mode, <italic>P</italic> is the number of boundary layers added to the image; if the fill mode is the valid mode, then <inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>
</inline-formula>. The model architecture of the ResNet is shown in <xref ref-type="fig" rid="fig-2">Fig. 2</xref>. The Relu activation function formula is as follows:</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption><title>The model architecture of the ResNet</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-2.tif"/>
</fig>
<p><disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mo movablelimits="true" form="prefix">max</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>x</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>where <italic>x</italic> represents the input and <inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> is the output result. During forward propagation, the Relu function only needs to set the threshold. If <inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:mi>x</mml:mi><mml:mspace width="thinmathspace" /><mml:mo>&#x003C;</mml:mo><mml:mspace width="thinmathspace" /><mml:mn>0</mml:mn></mml:math>
</inline-formula>, then <inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>
</inline-formula>; if <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mi>x</mml:mi><mml:mspace width="thinmathspace" /><mml:mo>&#x003E;</mml:mo><mml:mspace width="thinmathspace" /><mml:mn>0</mml:mn></mml:math>
</inline-formula>, then <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>x</mml:mi></mml:math>
</inline-formula>, thus speeding up the computation of forward propagation. The cross-entropy loss function is as follows:</p>
<p><disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>M</mml:mi></mml:munderover><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
</disp-formula></p>
<p>where <italic>M</italic> expressed as the number of categories, and <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:msub><mml:mi>p</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>
</inline-formula> expressed as the probability that the sample belongs to the category <italic>c</italic>. <inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:msub><mml:mi>y</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>
</inline-formula> represented as the label of the sample, when the predicted class is the same as the sample label, <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:msub><mml:mi>y</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>
</inline-formula>; otherwise, <inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:msub><mml:mi>y</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>
</inline-formula>. <italic>L</italic> expressed as the total loss value of the sample, and the total loss value is the sum of all sample loss values in the training set. The softmax function is as follows:</p>
<p><disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mi>t</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>K</mml:mi></mml:munderover><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:msub><mml:mi>z</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math>
</inline-formula> is the output value of the <italic>jth</italic> node, and <italic>K</italic> represents the number of output nodes, that is, the number of categories of classification. Through the softmax function, the range of each element is between (0, 1), and the sum of all elements is 1. Similarly, the model architecture of the Inception and Xception are shown in <xref ref-type="fig" rid="fig-3">Figs. 3</xref> and <xref ref-type="fig" rid="fig-4">4</xref>, respectively.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption><title>The model architecture of the inception</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-3.tif"/>
</fig><fig id="fig-4">
<label>Figure 4</label>
<caption><title>The model architecture of the Xception</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-4.tif"/>
</fig>
</sec>
<sec id="s2_2">
<label>2.2</label><title>Evaluation Criteria of Model Classification</title>
<p>Accuracy, Precision, Reccall and F1 values are used as measurement indexes. The Accuracy, Precision, recall rate, and F1 are defined as follows:</p>
<p><disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:mi>F</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mspace width="thinmathspace" /><mml:mo>&#x00D7;</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mo>&#x00D7;</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p>TP stands for true positive cases (both actual and predicted positive cases), TN stands for true negative cases (actually positive cases, predicted false cases), FP stands for false positive cases (actually negative cases, predicted positive cases), and FN stands for false negative cases (both actual and predicted negative cases). The utilized Adam algorithm for deep learning architecture optimization in this paper is provided in Algorithm 1.</p>
<fig id="fig-10">
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-10.tif"/>
</fig>
<p>where <italic>t</italic> represents the number of steps updated, <inline-formula id="ieqn-38">
<mml:math id="mml-ieqn-38"><mml:mi>&#x03B1;</mml:mi></mml:math>
</inline-formula> is used to control the learning rate, <inline-formula id="ieqn-39">
<mml:math id="mml-ieqn-39"><mml:mi>&#x03B8;</mml:mi></mml:math>
</inline-formula> indicates the parameters that need to be solved for the update, <inline-formula id="ieqn-40">
<mml:math id="mml-ieqn-40"><mml:msub><mml:mi>&#x03C1;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-41">
<mml:math id="mml-ieqn-41"><mml:msub><mml:mi>&#x03C1;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
</inline-formula> represents the first and second order moment attenuation coefficients, respectively. <inline-formula id="ieqn-42">
<mml:math id="mml-ieqn-42"><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:math>
</inline-formula> represents the gradient of the objective function for differentiation, <italic>s</italic> and <italic>r</italic> are the first-order moment (the expectation of the gradient <inline-formula id="ieqn-43">
<mml:math id="mml-ieqn-43"><mml:mi>g</mml:mi></mml:math>
</inline-formula>) and the second-order moment of the gradient (i.e., the expectation of the gradient <inline-formula id="ieqn-44">
<mml:math id="mml-ieqn-44"><mml:msup><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>
</inline-formula>), respectively. Both <inline-formula id="ieqn-45">
<mml:math id="mml-ieqn-45"><mml:mrow><mml:mover><mml:mi>s</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-46">
<mml:math id="mml-ieqn-46"><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> denote the bias correction in the case of zero initial value.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label><title>Experiments</title>
<p>This section contains an evaluation of feature distribution and performance. Visulization examines the typical distribution of the four sample categories. To make sure that the final classifications are correct, the performance of the eight deep learning models is compared to that of the benchmarking methods.</p>
<sec id="s3_1">
<label>3.1</label><title>Feature Distribution Analysis of the Four Blood Cells</title>
<p>The contents of granules can be released by eosinophils, causing tissue damage and accelerating the onset of inflammation. During the day and night, the quantity of eosinophils in the blood changes. White blood cells are split into two types based on physical differences, granular and non-granular, with eosinophils being a type of non-granular white blood cell. Eosinophils are white blood cell components that, like other granulocytes, are generated from bone marrow hematopoietic stem cells. Eosinophils are white blood cells that kill bacteria and parasites. They are also crucial cells in the immunological and allergy response processes. In Wright stained blood smears, Neutrophils&#x2019; cytoplasm appears colorless or extremely pale reddish, with many diffuse small (0.2&#x2013;0.4 micron) light red or light purple particles. Tissue damage, malignant tumors, aplastic anemia, agranulocytosis, myelodysplastic syndrome, hypersplenism, and autoimmune illnesses all cause it to rise or fall. Lymphocytes, the smallest white blood cells, are also a type of white blood cell. They are made by lymphoid organs and are mostly found in the lymph fluid that circulates through lymphatic channels. They are a major cellular component of the immune response function of the body and the main executor of practically all lymphatic immune functions. Lymphocytes are a type of cell that has the ability to recognize and respond to antigens. T lymphocytes (also known as T cells), B lymphocytes (also known as B cells), and natural killer (NK) cells can be classified based on their motility, surface chemicals, and roles. Monocytes are the largest white blood cells and the largest blood cells in the body. They play a crucial role in the body&#x2019;s defense system. Monocytes are produced from hematopoietic stem cells in the bone marrow and develop in the bone marrow before entering the bloodstream as immature cells. Monocytes also play a role in immunological responses, inducing a specific immune response in lymphocytes after phagocytosing antigen carried by the antigen determinant given to them. Monocytes are also the primary cellular defense against intracellular harmful bacteria and parasites, and they may recognize and kill tumor cells. Monocytes have more non-specific lipases and have a better phagocytosis than other blood cells. The total&#x0025;age of monocytes might alter when the body is inflamed or has various disorders. As a result, measuring monocyte count has become an important supplemental diagnostic tool. <xref ref-type="fig" rid="fig-5 fig-6 fig-7">Figs. 5&#x2013;7</xref> illustrate the visulization of four blood cells and the examination of eosinophils with labeling.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption><title>Visulization of four blood cells</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-5.tif"/>
</fig><fig id="fig-6">
<label>Figure 6</label>
<caption><title>Visulization of four blood cells</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-6.tif"/>
</fig><fig id="fig-7">
<label>Figure 7</label>
<caption><title>Labeling analysis of Eosinophils</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-7.tif"/>
</fig>
</sec>
<sec id="s3_2">
<label>3.2</label><title>Classification Comparison of the Deep Learning Models</title>
<p>Traditional CNNs with four hidden layers, such as Xception [<xref ref-type="bibr" rid="ref-9">9</xref>], InceptionV3 [<xref ref-type="bibr" rid="ref-10">10</xref>], ResNet50 [<xref ref-type="bibr" rid="ref-11">11</xref>], Squeeze [<xref ref-type="bibr" rid="ref-12">12</xref>], GoogleNet [<xref ref-type="bibr" rid="ref-13">13</xref>], SuffleNetV2 [<xref ref-type="bibr" rid="ref-14">14</xref>], Attention56 [<xref ref-type="bibr" rid="ref-15">15</xref>], and NasNet [<xref ref-type="bibr" rid="ref-16">16</xref>], are utilized to evaluate the final four classification detections. On the basis of deep learning&#x2019;s excellent classification performance, the Keras and Pytorch frameworks are utilized to develop the deep learning network classification model for the classified findings. Crossectropy is used to assess model loss in the trials, and the Adam method is utilized to optimize model performance. The maximum epoch length is 20 and the learning rate is 0.0001. All tests are conducted on a Dell Precision 5820 running Linux. The graphics processing unit is an NVIDIA 2080Ti 11G. <xref ref-type="table" rid="table-1">Table 1</xref> shows how the performance of nine deep learning models was judged, and <xref ref-type="fig" rid="fig-8">Figs. 8</xref> and <xref ref-type="fig" rid="fig-9">9</xref> show how the performance of nine deep learning models was judged.</p>
<table-wrap id="table-1"><label>Table 1</label>
<caption><title>The performance evaluation of nine deep learning models</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Methods</th>
<th align="left">Training loss</th>
<th align="left">Training acc (&#x0025;)</th>
<th align="left">Validation loss</th>
<th align="left">Validation acc (&#x0025;)</th>
<th align="left">Testing loss</th>
<th align="left">Testing acc (&#x0025;)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">CNNs</td>
<td align="left">0.0548</td>
<td align="left">93</td>
<td align="left">0.5620</td>
<td align="left">88</td>
<td align="left">2.0388</td>
<td align="left">72</td>
</tr>
<tr>
<td align="left">Xception [<xref ref-type="bibr" rid="ref-9">9</xref>]</td>
<td align="left">0.0459</td>
<td align="left">97</td>
<td align="left">0.0902</td>
<td align="left">96</td>
<td align="left"><bold>0.0129</bold></td>
<td align="left"><bold>89</bold></td>
</tr>
<tr>
<td align="left">InceptionV3 [<xref ref-type="bibr" rid="ref-10">10</xref>]</td>
<td align="left">0.4387</td>
<td align="left">93</td>
<td align="left">0.0338</td>
<td align="left">93</td>
<td align="left">0.2550</td>
<td align="left">85</td>
</tr>
<tr>
<td align="left">ResNet50 [<xref ref-type="bibr" rid="ref-11">11</xref>]</td>
<td align="left"><bold>0.0080</bold></td>
<td align="left">93</td>
<td align="left">0.0126</td>
<td align="left">95</td>
<td align="left">1.6920</td>
<td align="left">87</td>
</tr>
<tr>
<td align="left">Squeeze [<xref ref-type="bibr" rid="ref-12">12</xref>]</td>
<td align="left">0.1893</td>
<td align="left">96</td>
<td align="left">0.0327</td>
<td align="left">94</td>
<td align="left">0.0478</td>
<td align="left">85</td>
</tr>
<tr>
<td align="left">GoogleNet [<xref ref-type="bibr" rid="ref-13">13</xref>]</td>
<td align="left">0.9427</td>
<td align="left">96</td>
<td align="left">0.0419</td>
<td align="left">96</td>
<td align="left">0.0375</td>
<td align="left">86</td>
</tr>
<tr>
<td align="left">SuffleNetV2 [<xref ref-type="bibr" rid="ref-14">14</xref>]</td>
<td align="left">0.2830</td>
<td align="left">94</td>
<td align="left">0.0178</td>
<td align="left">95</td>
<td align="left">0.0263</td>
<td align="left">85</td>
</tr>
<tr>
<td align="left">Attention56 [<xref ref-type="bibr" rid="ref-15">15</xref>]</td>
<td align="left">0.1553</td>
<td align="left">87</td>
<td align="left">0.1405</td>
<td align="left">89</td>
<td align="left">0.0186</td>
<td align="left">83</td>
</tr>
<tr>
<td align="left">NasNet [<xref ref-type="bibr" rid="ref-16">16</xref>]</td>
<td align="left">0.0470</td>
<td align="left"><bold>98</bold></td>
<td align="left"><bold>0.0098</bold></td>
<td align="left"><bold>97</bold></td>
<td align="left">0.0410</td>
<td align="left">87</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-8">
<label>Figure 8</label>
<caption><title>Performance evaluation of five deep learning models. (a) The training, valid and testing loss curve; (b) The training, valid and testing accuracy curve; (c) Confusion matrix of the valid dataset; (d) Confusion matrix of the testing dataset</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-8.tif"/>
</fig><fig id="fig-9">
<label>Figure 9</label>
<caption><title>Performance evaluation of four deep learning models. (a) The training, valid and testing loss curve; (b) The training, valid and testing accuracy curve; (c) Confusion matrix of the valid dataset; (d) Confusion matrix of the testing dataset</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_24836-fig-9.tif"/>
</fig>
<p>In training, validation, and testing, the ResNet50, NasNet, and Xception achieve low model loss of 0.0080, 0.0098, and 0.0129, respectively. NasNet, NasNet, and Xception, respectively, have the best categorization accuracy of 98&#x0025;, 97&#x0025;, and 89&#x0025;. In terms of individual metrics, the best results for training loss, training accuracy, validation loss, validation accuracy, test loss and test accuracy are ResNet50 (0.0080), NasNet (98&#x0025;), NasNet (0.0098), NasNet (97&#x0025;), Xception (0.0129) and Xception (89&#x0025;). For overall metrics, we believe that the NasNet model achieves the best results, with the best performance in training accuracy, validation loss and validation accuracy, and is second only to Xception in test accuracy compared to other models. Despite the fact that the granulocyte appearance, diameter, and refractive index of the aforementioned four blood cells are distinct, the classification accuracy and model loss of nine deep learning models, in particular the benchmark model, were compared. It was discovered that deep learning is capable of automatically extracting features from four types of blood cells, including eosinophils, neutrophils, monocytes, and lymphocytes, and performing accurate classification analysis. This shows that the method proposed for analyzing hemodynamic categorization makes sense and works well.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label><title>Conclusions</title>
<p>In this study, nine models of deep learning were employed to classify four types of blood cells, eosinophils, neutrophils, monocytes, and lymphocytes. CNNs, Xception, InceptionV3, ResNet50, Squeeze, GoogleNet, SuffleNetV2, Attention56, and NasNet are among these models. Also presented are the statistical data derived from the aforementioned deep learning model, as well as the experiments based on 12,444 blood cell images and the experimental parameters setup. ResNet50, NasNet, and Xception achieve minimal model loss of 0.0080, 0.0098, and 0.0129 in training, validation, and testing datasets, respectively, and NasNet, NasNet, and Xception achieve 98&#x0025;, 97&#x0025; and 89&#x0025; classification accuracy in training, validation, and testing datasets, despite blood cells with varying granulocyte appearance, diameter, and refractive index. Future research will investigate the analysis of clinical datasets utilizing improved techniques.</p>
</sec>
</body>
<back>
<glossary content-type="abbreviations" id="glossary-1">
<def-list><title>Nomenclature</title>
<def-item>
<term><inline-formula id="ieqn-47">
<mml:math id="mml-ieqn-47"><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula></term>
<def>
<p>input vector of the residual unit</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-48">
<mml:math id="mml-ieqn-48"><mml:mi>&#x03C3;</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>activation function</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-49">
<mml:math id="mml-ieqn-49"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula></term>
<def>
<p>residual function</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-50">
<mml:math id="mml-ieqn-50"><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula></term>
<def>
<p>underlying mapping of the residual unit</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-51">
<mml:math id="mml-ieqn-51"><mml:mi>W</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>the image width</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-52">
<mml:math id="mml-ieqn-52"><mml:mi>H</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>the image height</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-53">
<mml:math id="mml-ieqn-53"><mml:mi>S</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>the convolution kernel step size</p>
</def>
</def-item>
<def-item>
<term>TP</term>
<def>
<p>true positive cases</p>
</def>
</def-item>
<def-item>
<term>TN</term>
<def>
<p>true negative cases</p>
</def>
</def-item>
<def-item>
<term>FP</term>
<def>
<p>false positive cases</p>
</def>
</def-item>
<def-item>
<term>FN</term>
<def>
<p>false negative cases</p>
</def>
</def-item>
</def-list>
</glossary>
<ack>
<p>The authors would like to thank the editor and the anonymous reviewers for their insightful comments and helpful suggestions to improve the quality of this manuscript, which significantly enhanced the paper&#x2019;s presentation.</p>
</ack>
<sec><title>Funding Statement</title>
<p>This project is supported by <funding-source>National Natural Science Foundation of China (NSFC)</funding-source> (Nos. <award-id>61806087</award-id>, <award-id>61902158</award-id>).</p>
</sec>
<sec sec-type="COI-statement"><title>Conflicts of Interest</title>
<p>The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</sec>
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