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Article
Automated gall bladder cancer detection using artificial gorilla troops optimizer with transfer learning on ultrasound images
Alazwari Sana 1
Alsamri Jamal 2
Alamgeer Mohammad mabdul@kku.edu.sa

3
Alotaibi Saud S. 4
Obayya Marwa 2
Salama Ahmed S. 5
1 https://ror.org/014g1a453 grid.412895.3 0000 0004 0419 5255 Department of Information Technology, College of Computers and Information Technology, Taif University, P.O. Box 11099, 21944 Taif, Saudi Arabia
2 https://ror.org/05b0cyh02 grid.449346.8 0000 0004 0501 7602 Department of Biomedical Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
3 https://ror.org/052kwzs30 grid.412144.6 0000 0004 1790 7100 Department of Information Systems, College of Science and Art at Mahayil, King Khalid University, Abha, Saudi Arabia
4 https://ror.org/01xjqrm90 grid.412832.e 0000 0000 9137 6644 Department of Information Systems, College of Computing and Information System, Umm Al-Qura University, Mecca, Saudi Arabia
5 https://ror.org/03s8c2x09 grid.440865.b 0000 0004 0377 3762 Department of Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11845 Egypt
19 9 2024
19 9 2024
2024
14 2184521 2 2024
11 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The gallbladder (GB) is a small pouch and a deep tissue placed under the liver. GB Cancer (GBC) is a deadly illness that is complex to discover in an initial phase. Initial diagnosis can significantly enhance the existence rate. Non-ionizing energy, low cost, and convenience make the US a general non-invasive analytical modality for patients with GB diseases. Automatic recognition of GBC from US imagery is a significant issue that has gained much attention from researchers. Recently, machine learning (ML) techniques dependent on convolutional neural network (CNN) architectures have prepared transformational growth in radiology and medical analysis for illnesses like lung, pancreatic, breast, and melanoma. Deep learning (DL) is a region of artificial intelligence (AI), a functional medical tomography model that can help in the initial analysis of GBC. This manuscript presents an Automated Gall Bladder Cancer Detection using an Artificial Gorilla Troops Optimizer with Transfer Learning (GBCD-AGTOTL) technique on Ultrasound Images. The GBCD-AGTOTL technique examines the US images for the presence of gall bladder cancer using the DL model. In the initial stage, the GBCD-AGTOTL technique preprocesses the US images using a median filtering (MF) approach. The GBCD-AGTOTL technique applies the Inception module for feature extraction, which learns the complex and intrinsic patterns in the pre-processed image. Besides, the AGTO algorithm-based hyperparameter tuning procedure takes place, which optimally picks the hyperparameter values of the Inception technique. Lastly, the bidirectional gated recurrent unit (BiGRU) model helps classify gall bladder cancer. A series of simulation analyses were performed to ensure the performance of the GBCD-AGTOTL technique on the GBC dataset. The experimental outcomes inferred the enhanced abilities of the GBCD-AGTOTL in detecting gall bladder cancer.

Keywords

Gallbladder cancer
Transfer learning
Artificial gorilla troops optimizer
Ultrasound images
Feature extraction
Subject terms

Image processing
Machine learning
Medical imaging
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

GBC is often identified at the final stage of the significant patients, preventing curative resection and causing an adverse prognosis. The overall average existence rate for cases with innovative GBC will be around six months, with a 5-year existence rate of less than 5%. Earlier identification is significant in increasing the survival rates of GBC patients1. For accurate diagnoses of GB diseases, ultrasound (US) imaging is the most commonly employed imaging technique, which can be considered a robust and widespread screening and analytic tool for radiologists and medical specialists. A precise analysis is required to identify the correct disease treatment plan during later screening. Generally, diagnostic data was gathered from the patient’s historical and medical analysis2. Various signs and symptoms will be unclear, mainly those relevant to GB diseases with identical indications. Consequently, highly qualified medical experts analyze and comprehend the US images. US is the early analytic method for estimating patients with suspicious GB illnesses because of the lack of accessibility, ionizing radiation effect, portability, and lower cost3. While recognizing gallstones and irregularities like GB wall thickening at repetitive US will be a simple, precise representation of earlier indications of GBC, it becomes problematic. Whether malignancy is not supposed, no more analysis will be carried out, because of which earlier GBC would be quietly developed4. As a result, it is vital to improve and comprehend the features of GBC on US images. AI methods decrease human involvement to an excessive level. Distinct conventional image-dependent “semantic” feature analysis by human specialists, DL will mechanically acquire the feature symbols at instance images with a CNN. The exploration and development of DL and deep neural networks (DNNs) based techniques offer essential evolution in medical image analysis and perception5.

Furthermore, with the high growth at the algorithmic level and accessibility of higher-performance computational machines and massive amounts of data, DL-based approaches become more popular. Nowadays, these are viewed as significant, popularly employed and complex techniques for managing numerous CV tasks6. Additionally, DL methods can support medical analysts in the earlier recognition, treatment, and identification of diseases, followed by providing proficient techniques for medical analysis7. Indeed, DL methods will be directly processed and automatically learn higher and mid-level intellectual features obtained from vast quantities of raw gathered data wherein highest-level deep features were described by integrating them with the lowest-level features to accomplish a standard level of accuracy and, lastly, to execute automated US images analysis processes namely object detection, organ segmentation, and classification8. The inspiration behind employing DL techniques arises from their ability to automate and improve the accuracy of tasks conventionally dependent on human expertise9. These models utilize huge datasets and advanced computational skills to automatically extract and learn convolutional features from medical images, enabling earlier disease recognition, precise treatment planning, and efficient medical diagnostics. The capacity of the DL to incorporate hierarchical features assists tasks such as organ segmentation, object recognition, and classification in US image evaluation, promising crucial enhancements in the medical imaging field10.

Existing works on GBC detection

Basu et al.11 propose a novel DNN model to attain interpretable symbols for medical image study. This technique constructs comprehensive attention for the area of interest and later follows bag of words (BOWs) style deep feature embedding with local attention. The regional and global feature maps are also integrated using a present modifier design to extract GBS detection from US images12. A Radscore was proposed using the minor absolute shrinkage and selection operator (LASSO) approach reliant on the radionics feature extractor. The four prediction models are constructed depending on the training group and authorized employing external and internal validation cohorts. Veena and Gowrishankar13 propose a healthcare informatics technique to investigate and detect gallstones. This model comprises quicker region-based CNNs (Faster-R-CNN, single shot detector (SSD), and mask R-CNN (Mask R-CNN). The Mask R-CNN model is presented, and dissimilar backbone models are trained to utilize it. In14, a model for segmenting GI tract organs is introduced. This model is a U-Net approach planned and employed to separate a tiny dimension of imaging to eliminate the local feature more proficiently. Additionally, the model utilized six transfer learning (TL) techniques namely InceptionResNetV2, SeResNet50, Inception V3, DenseNet121, VGG19, and EfficientNet B0 to augment the U-Net architecture. Nonsakhoo et al.15 presents a framework of TL to classify the stages of PDF employed to detect the growth of a Liver US Image Analysis System (LUIAS). Muneeswara et al.16 constructed an understandable technique that clusters the diverse soft tissues in the MRCP images. Employing the Tree Seed Algorithm (TSA), a nature-inspired optimizer technique with a DNN, presents an accurate learning machine.

Zhang et al.17 propose a model to improve the BUS-based computer-aided analysis. A designed TL classifier for integrated data with standard labels is accepted for this supervised TL. A non-parallel hyperplane-based SVM+ (NHSVM+) technique is initially presented to improve the accomplishment of the TL model. In18, a DL-based hybrid stack ensemble approach is presented. In the primary stage of the planned bi-level stack ensemble model, anticipation is achieved utilizing 5-fold cross-validation to three novel CNN models. An ML classifier is selected in the second level. Wang et al.19 presents a multi-view contrastive self-supervised (MCS) technique. The model improves focus on nodule areas by aligning transverse and longitudinal views of nodules and utilizing an adaptive loss function. Furthermore, a two-phase pre-training strategy employs ImageNet and thyroid US images to enhance the performance. Yenurkar et al.20 introduces a CNN pre-trained technique. Also, various classification models and neural networks are then utilized. In21, a novel framework, namely SegMix for US image segmentation using deep learning with minimal manual annotations is proposed. This method utilizes a segment-paste-blend concept. Additionally, US-specific augmentation techniques based on image enhancement algorithms are incorporated. Raina et al.22 proposes USQNet, a deep CNN utilizing Multi-scale and Local-to-Global Second-order Pooling (MS-L2GSoP) model. The method also employs second-order pooling in intermediate and final layers.

The referenced studies present novel models in medical image evaluation utilizing DL but portray various restrictions. For instance, while Basu et al. and Veena and Gowrishankar present effectual techniques for particular tasks such as GBS recognition and healthcare informatics utilizing advanced CNN models, their applicability may face restriction by limited validation across several datasets and potential overfitting problems. Likewise, researches such as TSA technique integrated with DNNs and MCS approach presented by Muneeswara et al. and Wang et al. illustrate promising results but still need additional validation in several clinical scenarios to confirm robustness and generalizability. Additionally, methods namely NHSVM+ and TL models for computer-aided evaluation and liver US imaging proposed by Zhang et al. and Nonsakhoo et al. may be enhanced for scalability and real-time applicability considerations. The present study aims to face the challenges namely restricted real-time data integration, handling diverse and large-scale datasets, extensive manual annotation needs, and generalizability across patient demographics. Moreover, present models mostly struggle with computational effectualness and adapting to specific alterations of medical image datasets. The notable research gap is the lack of standardized analysis metrics and benchmarks across the various DL methods presented for US image evaluation.

Paper contributions

This manuscript presents an Automated Gall Bladder Cancer Detection using an Artificial Gorilla Troops Optimizer with Transfer Learning (GBCD-AGTOTL) technique on US Images. In the initial stage, the GBCD-AGTOTL technique preprocesses the US images using a median filtering (MF) approach. For feature extraction, the GBCD-AGTOTL technique applies the Inception module, which learns the complex and intrinsic patterns in the pre-processed image. Besides, the AGTO algorithm-based hyperparameter tuning procedure takes place, which optimally picks the hyperparameter values of the Inception method. Lastly, the bidirectional gated recurrent unit (BiGRU) model is helpful for the classification of gall bladder cancer. A series of simulation analyses were performed to ensure the performance of the GBCD-AGTOTL technique on the GBC dataset.

Materials and methods

This manuscript presents an automated GBCD-AGTOTL technique for US Images. The method examines the US images for the presence of gall bladder cancer using the DL model. Figure 1 depicts the entire procedure of the GBCD-AGTOTL technique.

Fig. 1 Overall process of GBCD-AGTOTL technique.

Data used

The performance analysis of the GBCD-AGTOTL technique is tested using the GBCU dataset2. It refers to the primary public dataset for GBC recognition from US images. GBCU comprises 1255 (432 normal, 558 benign, and 265 malignant) noted abdominal US images from 218 patients. Table 1 defines the details of the dataset. Figure 2 demonstrates the sample images.

Table 1 Details of the dataset.

Class labels	No. of images	
Normal	432	
Benign	558	
Malignant	265	
Total images	1255	

Fig. 2 Sample Grad-CAM visuals of GBCNet (a) Normal, (b) Benign, and (c) Malignant.

Preprocessing

The GBCD-AGTOTL technique preprocesses the US images using the MF approach in the initial stage. In medical image processing, MF plays a vital part in improving the excellence and reliability of diagnostic photos23. Selecting the MF technique for pre-processing presents various crucial merits. MF is highly efficient at eliminating salt-and-pepper noise from images while conserving edges and fine details, which is significant to maintain the integrity of features in the data. Unlike mean filters, MFs do not blur the image, making them specifically useful for conserving sharpness and clarity. Furthermore, MF is robust to outliers and can handle varying noise levels efficiently. Its simplicity and computational effectiveness make it a practical option for real-time applications. Overall, MF gives a balance between noise reduction and detail preservation, making it an ideal pre-processing tool for several image and signal processing tasks. Figure 3 depicts the structure of MF technique.

Fig. 3 Structure of MF model.

With its capability to efficiently overwhelm salt-and-pepper noise, which is general in medical imaging owing to numerous acquisition factors, MF safeguards the protection of vital structural facts and limits within the images. This non-linear filtering model is mainly beneficial in medical uses where exact visualization of anatomical features is essential for precise analysis of US images. By modifying noise without sacrificing vital image data, MF donates to enhanced image clarity and enables more accurate and significant analysis by healthcare experts, finally improving the diagnostic efficiency of medical imaging methods.

Feature extraction

For feature extraction, the GBCD-AGTOTL technique applies the Inception module, which learns the complex and intrinsic patterns in the pre-processed image. Selecting the Inception module for feature extraction presents various key merits. The architecture of the Inception module incorporates diverse convolutional filters of different sizes and pooling operations in parallel, enabling it for capturing a diverse range of features from the input data. This multi-scale methodology improves the capability of the technique for recognizing patterns and details at various levels of abstraction. Furthermore, the Inception module utilizes dimensionality reduction methods, namely 1 × 1 convolutions, to manage computational complexity and memory usage effectively. Its deep network design assists efficient feature learning while maintaining manageable resource needs. These characteristics make the Inception module specifically efficient to handle complex datasets and attaining high performance in feature extraction tasks.

The CNN can extract features layer-wise via the slipping process of convolution kernel on the feature maps and is extensively applied in different fields24. Expanding the depth and width of the network is an effective way to enhance the network’s performance, but it results in complex network training and overfitting. The Inception model is used to resolve these challenges, which uses convolution kernel of varying sizes feature extraction and later passed over 1 × 1 convolution to reduce channel dimensionality. Lastly, channel merging is summarized to extract data features. The parameter count remains the same while extending the width of the network. Generally, Batch standardization is applied between the activation function and the convolutional layer that standardizes the information in the channel width, which could efficiently lessen overfitting, improve the training speed, and resolve vanishing gradient problems.1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}_{B}=\frac{1}{m}{\sum\limits_{i=1}^{m}}{x}_{i}$$\end{document}

2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma}_{B}^{2}=\frac{1}{m}{\sum\limits_{i=1}^{m}}({x}_{i}-{\mu}_{B})^{2}$$\end{document}

3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{{x}_{i}}=\frac{{x}_{i}-{\mu}_{B}}{\sqrt{{\sigma}_{B}^{2}-\varepsilon}}$$\end{document}

4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${y}_{i}=\widehat{\gamma\:{x}_{i}+\beta}$$\end{document}

Now, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma}_{B}^{2}$$\end{document} shows the variance of training batches; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{i}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\widehat{x}}_{i}$$\end{document}, are the ith data on the feature map before and after standardization, correspondingly; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{y}_{i}$$\end{document} denotes the after zooming and panning; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\beta\:$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\gamma\:$$\end{document} are the factors that control spatial translation and scaling, correspondingly; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mu}_{B}$$\end{document} denotes the average of the training batches, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:m$$\end{document} refers to the quantity of data. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varepsilon\:$$\end{document} indicates the constant that is evaluated once the variance is 0.

AGTO-based hyperparameter tuning

In this research, the AGTO model-based hyperparameter tuning procedure takes place, which optimally picks the hyperparameter morals of the Inception method. AGTO model is a meta-heuristic technique dependent upon gorilla social behaviour25. The AGTO method presents various merits over other optimization approaches. Firstly, its unique model replicates the behavior of gorilla troops, utilizing both exploration and exploitation efficiently to avoid local optima and improves the ability of the global search. The flexible structure of the AGTO technique allows it to adapt to diverse problem landscapes, making it adaptable across several domains. Furthermore, its simplicity in design confirms ease of implementation and computational effectiveness. The model has illustrated a strong accomplishment in handling complex optimization issues due to its robust convergence properties and capability for balancing diverse objectives. These advantages make AGTO specifically appropriate for challenging optimization tasks where conventional models may find difficulty. Figure 4 demonstrates the architecture of AGTO approach.Fig. 4 Structure of AGTO technique.

The gorilla is the most prominent and sturdiest chimpanzee. An adult male gorilla directs every cluster and has a robust intellect of land. The few male gorillas are also named silverback gorillas. A gorilla group regularly contains an adult male and female gorilla and their children. As leaders, adult male gorillas must undertake the duties of protective land, decision-making, and directing other gorillas to hunt for food. Three dissimilar operators are utilized in the exploration stage: migration to an unknown location to enhance GTO exploration. The 2nd operator, a drive to the other gorillas, upsurges the balance between exploration and exploitation. The 3rd operator in the exploration stage, migration near a recognized place, considerably enhances the GTO’s ability to hunt for dissimilar optimizer spaces. On the other hand, dual operators have been employed in the exploitation phase, which expressively enhances the hunt solution. In GTO, a dissimilar model was used for the stage variation process of exploration and exploitation. GTO commonly tracks the following numerous instructions to hunt for a solution:

The GTO algorithm holds three kinds of solutions. X is recognized as the gorilla place vector, and the GX is the gorilla candidate location vector produced in every stage. Lastly, the Silverback is the finest solution originating in every iteration.

One Silverback in the complete populace is the number of search agents nominated for optimizer processes.

Three kinds of Silverback, X, and GX solutions precisely pretend the gorillas’ everyday lifetime in nature.

This animal can enhance its influence by discovering superior food sources or locating itself in a fair and robust cluster. In GTO, solutions are generated in every iteration, recognized as GX. If the solution originates is novel (GX), it substitutes the present solution (X). Or else, it stays in GX.

The trend to everyday life amongst gorillas prevents them from being alive separately. Thus, they search for food as a cluster and endure to live below a silverback leader, who creates decisions. In the preparation stage, assuming the worst solution in the populace is the weak member in a gorilla cluster, the gorillas try to avoid the worst solution and acquire the finest solution from Silverback, enhancing the entire gorilla’s location.

AGTO algorithm is applied to define the dual stages of exploitation and exploration entirely. The gorilla’s social behaviours simulate this algorithm and employ five operators to pretend exploitation and exploration optimizer techniques concentrated on gorilla actions.

Exploration stage

Three dissimilar processes have been implemented throughout the exploration stage. Firstly, it starts with an effort to find a strange place and then to get to know the place, and lastly, it is near other gorillas. Consider three dissimilar situations to signify these processes; a factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:x$$\end{document} is initially selected to elect the way of a gorilla to a strange place. Travelling near a weird location is supposed to happen when element \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:x$$\end{document} is less than the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:rand$$\end{document}. If the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:rand$$\end{document} is more significant than or equivalent to 0.5, it is measured that there is an effort near other gorillas in the cluster. Furthermore, if the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:rand\:$$\end{document} is lesser than 0.5, it is suggested that there is an effort near the recognized spot. Equations (5)–(7) signify the states definite beyond the three processes executed throughout the exploration stage, 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F\left(k+1\right)=\left(Uppe{r}_{b}-Lowe{r}_{b}\right)\times\:{s}_{1}+Lowe{r}_{b}$$\end{document}

The abovementioned equations signify the effort to an unknown spot, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{s}_{1}$$\end{document} denotes the value selected randomly among 0 and 1. The device of action near the known place is signified in Eq. (6),6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F\left(k+1\right)=\left({s}_{2}-D\right)\times\:{A}_{s}\left(k\right)+Y\times\:Z$$\end{document}

where Y, Z, and D in the abovementioned equation have been calculated as presented in Eqs. (7)–(9),7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D=G\times\:\left(1-\frac{cur{r}_{iter}}{to{t}_{iter}}\right)$$\end{document}

8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=\text{c}\text{o}\text{s}\left(2\times\:{s}_{4}\right)+1$$\end{document}

9 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y=D\times\:y,$$\end{document}

Meanwhile, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:y$$\end{document} signifies any value specific randomly among −l to 1. 10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z=P\times\:A\left(k\right).$$\end{document}

The effort near other gorillas in the cluster is signified as displayed in Eq. (11),11 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F\left(k+1\right)=A\left(j\right)-Y\times\:\left(Y\times\:\left(A\left(k\right)-F{A}_{s}\left(k\right)\right)\right)+{s}_{3}\times\:\left(A\left(k\right)-F{A}_{s}\left(k\right)\right).$$\end{document}

At last, the cost sustained for the entire probable exploration has been calculated, and an optimal solution is measured as a silverback.

Exploitation stage

This stage includes dual main processes; in the 1st process, all the adult associates of the gorilla group take the commands assumed by the Silverback selected in the exploration stage. In the 2nd process, a fight happens between the adult gorillas once they grow to define the female gorillas. The initial process taken by the Silverback has been signified in Eq. (12),12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F\left(k+1\right)=Y\times\:B\times\:\left(A\left(k\right)-{A}_{sb}\right)+A\left(k\right),$$\end{document}

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:A\left(k\right)$$\end{document} signifies the gorilla’s place and denotes the place of the gorilla that is preferred as the Silverback.13 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B={\left({\left|\frac{1}{H}{\sum\limits_{\dot{j}}^{H}}F{A}_{\dot{j}}\left(k\right)\right|}^{f}\right)}^{\frac{1}{f}}$$\end{document}

14 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f={2}^{Y}$$\end{document}

The 2nd process of fighting for adult females is denoted in Eq. (15),15 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F\left(k\right)={A}_{sb}-\left({A}_{sb}\times\:T-A\left(k\right)\times\:T\right)\times\:M$$\end{document}

16 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=2\times\:{s}_{5}-1$$\end{document}

17 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=\delta\:\times\:N.$$\end{document}

The charge of all results acquired from the processes in the exploitation stage is calculated. In the exploration stage, the optimum solution is nominated as the Silverback.

The fitness function (FF) is an excellent way to manipulate the performance of the AGTO model. The hyperparameter range procedure includes the solution encode method to estimate the efficiency of the candidate solution. In this work, the AGTO model considers accuracy as the primary measure to project the FF, formulated as follows.18 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Fitness\:=\:\text{m}\text{a}\text{x}\:\left(P\right)$$\end{document}

19 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P=\frac{TP}{TP+FP}$$\end{document}

From the abovementioned expression, TP signifies the true positive value, and FP indicates the false positive value.

Classification using the BiGRU model

Finally, the BiGRU model helped classify gall bladder cancer. The GRU is a kind of NN that varies from other NNs owing to its interior “gate” structure26. This allows one to decide what information to discard and what is relevant based on the relationship, which effectively controls internal information and the effective transmission of data. Consequently, the GRU somewhat discourses the problems of long-term dependencies in the NN model. The GRU has three significant elements namely the hidden state, reset gate, and update gate, which work together to attain long‐term dependency and extract temporal data. The discrete functions of these gates are discussed as follows. Figure 5 illustrates the framework of the BiGRU technique.Fig. 5 Structure of the BiGRU model.

Reset and update gates

The input for the reset and update gates can be attained by the FC layer that works on the present input \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{t}$$\end{document} and the hidden layer (HL) of the prior moment \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{h}_{t-1}$$\end{document}. The activation function has converted the reset gate input into a value within the [0, 1] range. An input value of 0 is especially rejected when one is retained. This value is used to define the input relevancy. The product of the prior hidden state and reset output is component-wise calculated. The update gate controls the degree to which the prior information state is integrated into the existing state. Simultaneously, the update and reset gates affect the candidate HL of the existing neuron. The reset gate is calculated by using Eq. (20).20 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{t}=sigmoid\left(\left[{w}_{hr}|{w}_{xr}\right]\otimes\:\left[{h}_{t-1}|{x}_{t}\right]^{T}\right)$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\:{w}_{hr}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{w}_{xr}$$\end{document} denote the last time step’s HL and the input series’ weight matrix at the existing time step. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\otimes\:$$\end{document} refers to the cross creation of the matrix, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} denotes the present time step, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t-1$$\end{document} indicates the last time step, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{t}$$\end{document} implies the input series of the existing time step, and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\:h}_{t-1}$$\end{document} means the hidden layer of the last time step. They can be evaluated by Eq. (21) based on the existing data.21 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\stackrel{\sim}{{h}_{t}}=\:{\text{tanh}}\left({w}_{\stackrel{\sim}{h}}\otimes\:\left[{h}_{t-1}\circ\:{r}_{t})|{x}_{t}\right]\right)$$\end{document}

where the Hadamard operator is denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\circ\:{h}_{t}$$\end{document} refers to the HL and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{w}_{h}$$\end{document} denotes the weight matrix of the candidate HL. Equation (22) computes the update gate output, whereas the data must be upgraded.22 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${z}_{t}=sigmoid\left([{w}_{hz}|{w}_{xz}]\otimes\:\left[{h}_{t-1}|{x}_{t}\right]^{T}\right)$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{z}_{t}$$\end{document} denotes the update gate output at the present step. The information retained at the last time step is evaluated by Eq. (23) according to the update gate.23 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${h}_{t-1}^{*}=\left(1-{z}_{t}\right)\circ\:{h}_{t-1}$$\end{document}

(2) Hidden layer

The HL is the output of GRU via the candidate HL and the data of the last time step retained by the update gate, which is computed as follows:24 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${h}_{t}=\left({z}_{t}\circ\:{h}_{t}^{{\prime\:}}\right)\oplus\:{h}_{t-1}^{*}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\oplus\:$$\end{document} indicates the matrix addition operator.(3) Bi-GRU

The information attained is affected only by the data at the last time step for GRU. In general, the transmission of the HL in GRU is from front to back. However, attention should be paid to the data at the present and before the last step and the time state from back to front to extract a feature. The hidden layer of the present moment in the BiGRU can be affected by the forward HL, the backward HL, and the present time step input series. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{t}$$\end{document} shows the input of Bi-GRU, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{t}\in\:{R}^{n\times\:d}(n$$\end{document} indicates the number of small batches of input sample, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:d$$\end{document} indicates the number of input moments). Given that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\overleftarrow{{h}_{t}}\in\:{R}^{n\times\:h}$$\end{document} is a backward hidden state and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\:\overrightarrow{{h}_{t}}\in\:{R}^{n\times\:h}$$\end{document} is a forward hidden state, which is computed as follows:25 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overrightarrow{{h}_{t}}=sigmoid\left({x}_{t}{w}_{xh}^{\left(f\right)}+{h}_{t-1}{w}_{hh}^{(\overrightarrow{f)}}+{b}_{h}^{\left(f\right)}\right)$$\end{document}

26 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overleftarrow{{h}_{t}}=sigmoid\left({x}_{t}{w}_{xh}^{\left(b\right)}+\overleftarrow{{h}_{t-1}}{w}_{hh}^{\left(b\right)}+{b}_{h}^{\left(b\right)}\right)$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{w}_{xh}^{\left(f\right)}\in\:{R}^{d\times\:h}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{w}_{hh}^{\left(f\right)}\in\:{R}^{h\times\:h}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{w}_{xh}^{\left(d\right)}\in\:{R}^{d\times\:h}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{w}_{hh}^{\left(b\right)}\in\:{R}^{h\times\:h}$$\end{document} are weight matrix. The computed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\overrightarrow{h}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\overleftarrow{h}$$\end{document} have been interconnected to attain the HL \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{h}_{t}\in\:{R}^{n\times\:2 h}$$\end{document} at the present moment, and the output layer \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{o}^{t}\in\:{R}^{n\times\:q}$$\end{document} is computed by Eq. (27).27 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${o}_{t}={h}_{t}{w}_{hq}+{b}_{q}$$\end{document}

Ethics approval

This article contains no studies with human participants performed by any authors.

Experimental validation

The proposed model is simulated using Python 3.8.5 tool. The proposed model is experimented on PC i5-8600k, GeForce 1050Ti 4GB, 16GB RAM, 250GB SSD, and 1 TB HDD. Figure 6 displays the classifier outcomes of the GBCD-AGTOTL system with the test dataset. Figure 6a and b illustrates the confusion matrices accomplished by the GBCD-AGTOTL method under 70:30 of TRAPH/TESPH. This figure signified that the GBCD-AGTOTL method is correctly recognized and categorized into three classes. Figure 6c and d represent the classification analysis of the GBCD-AGTOTL technique. The simulation values implied that the GBCD-AGTOTL technique correctly recognized the presence and absence of GBC under three classes.

Fig. 6 (a,b) Confusion matrices of 70:30 TRAPH/TESPH and (c,d) Classifier outcome of 70:30 TRAPH/TESPH.

Table 2 and Fig. 7 state the overall GBC detection of the GBCD-AGTOTL method on 70:30 of TRAPH/TESPH. These results indicate that the GBCD-AGTOTL system correctly detected the presence and absence of GBC. With 70% of TRAPH, the GBCD-AGTOTL technique gains an average \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} of 96.28%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:sen{s}_{y}$$\end{document} of 94.14%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:spe{c}_{y}$$\end{document} of 96.95%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{F}_{score}$$\end{document} of 94.47%, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:AU{C}_{score}$$\end{document} of 95.54%. Meanwhile, based on 30% of TESPH, the GBCD-AGTOTL algorithm provides an average \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} of 96.29%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:sen{s}_{y}$$\end{document} of 94.25%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:a\:spe{c}_{y}$$\end{document} of 96.89%, a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{F}_{score}$$\end{document} of 94.52%, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:AU{C}_{score}$$\end{document} of 95.57%.

Table 2 GBC detection of the GBCD-AGTOTL model under 70:30 TRAPH/TESPH.

Classes	Accu y	Sens y	Spec y	F score	AUC score	
TRAPH (70%)	
Normal	95.10	91.03	97.35	92.96	94.19	
Benign	95.67	97.38	94.35	95.14	95.87	
Malignant	98.06	94.02	99.14	95.32	96.58	
Average	96.28	94.14	96.95	94.47	95.54	
TESPH (30%)	
Normal	95.76	91.67	97.67	93.22	94.67	
Benign	94.96	96.02	94.03	94.68	95.03	
Malignant	98.14	95.06	98.99	95.65	97.02	
Average	96.29	94.25	96.89	94.52	95.57	

Fig. 7 Average of the GBCD-AGTOTL model on 70:30 TRAPH/TESPH.

The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} curves for training (TRA) and validation (VL) exhibited in Fig. 8 for the GBCD-AGTOTL algorithm provide valued insights into its effectiveness at varying epochs. Mainly, it can be a reliable upgrading under TRA and TES \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} with increased epochs, signifying the proficiencies of the model for learnable and recognizable patterns from both TRA and TES data. The rising trends in TES \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} emphasize the adaptability to the TRA dataset and the ability to produce correct predictions on unnoticed data, emphasizing the capabilities of robust generalization.

Fig. 8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:Acc{u}_{y}$$\end{document} curve of the GBCD-AGTOTL method.

Figure 9 illustrates an extensive outcome of the TRA and TES loss values for the GBCD-AGTOTL technique at diverse epochs. The TRA loss reliably decreases as a model refines the weights for diminishing classification errors under both datasets. The loss curves noticeably explain the arrangement of the model with the TRA data, emphasizing the ability to capture patterns efficiently. Significant can be the continuous improvement of parameters in the GBCD-AGTOTL system, targeted at decreasing differences between actual and predicted TRA labels.

Regarding the PR curve illustrated in Fig. 10, the findings affirm that the GBCD-AGTOTL technique constantly accomplishes higher PR values in every class. These results underscore the technique’s efficient capacity for discriminating between diverse classes and emphasize its efficiency in accurately recognizing class labels.

Similarly, in Fig. 11, ROC curves created by the GBCD-AGTOTL method are indicated, signifying its proficiency in distinguishing between classes. These curves offer valuable insights into how the trade-off between TPR and FPR modifies in several classification epochs and thresholds. The results accentuate the model’s exact classification efficiency under diverse class labels, underscoring its effectiveness in overcoming numerous classification challenges.

Fig. 9 Loss curve of the GBCD-AGTOTL model.

Fig. 10 PR curve of the GBCD-AGTOTL model.

Fig. 11 ROC curve of the GBCD-AGTOTL model.

The comprehensive comparison study in terms of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:sen{s}_{y}$$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:spe{c}_{y}$$\end{document} of the GBCD-AGTOTL technique is revealed in Table 3; Fig. 1227. These obtained findings imply that the GBCD-AGTOTL method appropriately recognized the GBC. Based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document}, the GBCD-AGTOTL technique offers increased \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} of 96.29% whereas the OD-WSCL, WS-DETR, ResNet50, Inceptionv3, RadFormer, US-UCL, and Point-Beyond class (PBC), Inception-V3, VGG16 Classifier, VGG19, ResNet, and DenseNet models have shown decreased \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:acc{u}_{y}$$\end{document} of 80.50%, 85.70%, 86.70%, 86.90%, 92.10%, 92.00%, 95.30%, 92.41%, 93.16%, 94.47%, 94.74% and 95.29%, correspondingly. According to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:sen{s}_{y}$$\end{document}, the GBCD-AGTOTL technique gains higher \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:sen{s}_{y}$$\end{document} of 94.25% but, the OD-WSCL, WS-DETR, ResNet50, Inceptionv3, RadFormer, US-UCL, PBC, Inception-V3, VGG16 Classifier, VGG19, ResNet, and DenseNet methods have depicted lessened \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:sen{s}_{y}$$\end{document} of 80.90%, 81.20%, 92.60%, 91.30%, 92.10%, 91.30%, 93.30%, 89.78%, 91.13%, 91.34%, 92.43%, and 93.55%. Moreover, based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:spe{c}_{y}$$\end{document}, the GBCD-AGTOTL technique achieves an increased \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:spe{c}_{y}$$\end{document} of 96.89%. However, the OD-WSCL, WS-DETR, ResNet50, Inceptionv3, RadFormer, US-UCL, PBC, Inception-V3, VGG16 Classifier, VGG19, ResNet, and DenseNet methods attain lessened \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:spe{c}_{y}$$\end{document} of 92.30%, 88.20%, 67.80%, 70.80%, 92.30%, 73.10%, 92.40%, 92.09%, 92.30%, 92.68%, 93.59%, and 93.93%.

Table 3 Comparative outcome of the GBCD-AGTOTL model compared with other techniques.

Methods	 Accuy	Sens y	 Specy	
OD-WSCL	80.50	80.90	92.30	
WS-DETR	85.70	81.20	88.20	
ResNet50	86.70	92.60	67.80	
RadFormer	92.10	92.10	92.30	
US-UCL	92.00	91.30	73.10	
PBC	95.30	93.30	92.40	
Inception-V3	92.41	89.78	92.09	
VGG16 model	93.16	91.13	92.30	
VGG19 model	94.47	91.34	92.68	
ResNet model	94.74	92.43	93.59	
DenseNet model	95.29	93.55	93.93	
GBCD-AGTOTL	96.29	94.25	96.89	

Fig. 12 Comparative outcome of the GBCD-AGTOTL model compared with other techniques.

Therefore, the GBCD-AGTOTL technique can effectually detect the GBC on the US images.

Conclusion

In this manuscript, an automated GBCD-AGTOTL technique on US Images is presented. The GBCD-AGTOTL technique examines the US images for the presence of gall bladder cancer using the DL model. The GBCD-AGTOTL technique preprocesses the US images using the MF approach in the initial stage. For feature extraction, the GBCD-AGTOTL technique applies the Inception module, which learns the complex and intrinsic patterns in the pre-processed image. Besides, the AGTO algorithm-based hyperparameter tuning procedure takes place, which optimally picks the hyperparameter values of the Inception technique. Finally, the BiGRU model helped classify gall bladder cancer. A series of simulation analyses were performed to ensure the performance of the GBCD-AGTOTL technique on the GBC dataset. The experimental outcomes inferred the enhanced abilities of the GBCD-AGTOTL in detecting gall bladder cancer. The computational difficulties of the AGTO-based hyperparameter tuning and potential threats in real-time deployment propose a requirement for optimization and validation across various patient cohorts for broader clinical applicability. Future studies may incorporate multi-modal data and refine computational effectualness to improve diagnostic accomplishment and practical application.

Acknowledgements

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/158/45. Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R729), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. This study is partially funded by the Future University in Egypt (FUE).

Author contributions

Conceptualization: S.A. Data curation and Formal analysis: J.A. Investigation and Methodology: M.O. Project administration and Resources: A.S.S. Validation and Visualization: S.S.A. Writing—original draft, S.A. Writing—review and editing, M.A. and A.S.S. All authors have read and agreed to the published version of the manuscript.

Data availability

The datasets used and analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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