A Novel Deep Learning Framework for Accurate Classification and Survival Rate Prediction of Brain Tumors

A brand-new DL system created specifically for the diagnosis of brain tumors is presented by Zaitoon and Syed [16]. The proposed method begins with the gathering of data, which is subsequently pre-processed to improve the data using a Convolutional Normalized Mean Filter (CNMF). This readies the data for multi-class classification using the new Deep Belief–Transfer Convolutional Neural Network (DBT-CNN) classifier method. The RU-Net2+ model, which generates segmented zones to which a Cox model is applied to extract attributes, is employed for precise tumor delineation. These collected traits are essential for predicting the patients' survival rate in the final stage using a logistic regression approach.

Babu Vimala et al. [17] categorized three types of brain tumors—meningioma, glioma, and pituitary tumors—using EfficientNet models and a transfer learning–based fine-tuning technique. The pre-trained EfficientNet system is refined using a two-step procedure. First, use the ImageNet dataset's weights to initialize the framework. Then, add additional layers like top layers and a fully connected layer to facilitate tumor classification. Utilize Grad-CAM visualization to investigate the attention maps produced by the top model that accurately identify tumor regions in brain images, in order to gain a deeper understanding of the model's decision-making process.

Othman et al. [18] created a hybrid DL framework that uses two distinct classifiers and allows for decision-making using data from several sources. Utilizing various omics data from the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) dataset is anticipated to enhance the precision of patient survival estimations in comparison to relying on a single data modality. A convolutional neural network (CNN) model extracts features. As classifiers, GRU and LSTM are utilized.

A potent new hybrid approach is put out by Celik and Inik [19] to accurately classify brain cancers in numerous ways. This approach employs a specialized CNN framework for feature extraction and utilizes machine learning methods for feature classification. Moreover, nine advanced CNN models are employed to evaluate CNN performance. The optimal hyperparameter values for machine learning algorithms are determined using the Bayesian optimization procedure. As per the outcomes of the experimental investigations, the proposed hybrid model achieved a mean classification accuracy of 97.15% and recall, precision, and F1-score values of 97%.

Three very successful machine learning classifiers with deep convolutional learned features are used by Khan et al. [20] to classify medical images. The MRI images of the three types of brain tumors, which are utilized to assess the efficacy of the automated approach, are available as an open dataset on Figshare. Brain MRI data are analyzed using the DenseNet169 framework to extract features. Three multiclass machine learning classifiers (Random Forest (RF), Support Vector Machine (SVM), and XGBoost) are fed extracted features to improve performance. The suggested model outperformed the cutting-edge approach with an overall classification accuracy of 95.10%.

To improve early detection, Srinivasan et al. [21] created a deep CNN and offered three different CNN models made for various categorization tasks. The first CNN algorithm has a remarkable 99.53% accuracy rate in identifying brain tumors. With an accuracy of 93.81%, the second CNN model successfully divides brain tumors into five categories. Furthermore, the third CNN model has a 98.56% accuracy rate in classifying brain tumors into different classifications. To ensure optimal performance, all relevant CNN model hyperparameters are automatically adjusted using a grid search optimization technique.

An improved AI-based design for better brain tumor categorization is presented by Dixon et al. [22]. Furthermore, it offers a hybrid approach that creates an ensemble classifier by combining DNN with vision transformers (ViT), resulting in a more dependable framework for brain tumor classification. After preprocessing and data normalization, three different kinds of information-rich features produced from MRIs are extracted as part of the analytical pipeline. The final classification of brain MRIs is achieved by weighting, fusing, and feeding the retrieved characteristics into a machine-learning classifier. Using a variety of measures, the suggested weighted ensemble design has been assessed on locally obtained and publicly accessible brain MRIs of four classes. ShallowMRI, a simple CNN based on the classification of types of brain tumors in MRI, was developed by Khan et al. [23]. The model has a novel attention system that enhances its capacity to attend to pertinent characteristics in proper classification. The best contours are determined by erosion and dilation to take off the unnecessary areas. Also, Local Binary Patterns (LBP) complement image preprocessing by lowering the computational expenses and maximizing the feature extraction. Using three benchmark datasets, Kaggle Multiclass, BR35H Binary, and Histogram Binary, the effectiveness of ShallowMRI is evaluated against pre-trained models and current techniques.

Hekmatet et al. [24] presented an approach, which is the Attention-Fused MobileNet-LSTM model, which is designed to enhance the quality of the classification. Through the combination of the functionality of two highly established pre-trained CNN models called MobileNetV1 and MobileNetV2, we have created a dependable model. We solve the CNN training problems, such as the need to make extensive computations, the inability to identify finer details in the picture, and reduced performance because of noise or useless data. The use of a transformer to assist in feature extraction and the use of gamma correction, subsequently, then feature fusion, helps to address long-range relationships between consecutive features. But, the suggested model, based on LSTM recurrent neural networks (RNN) to directly predict class labels, may not be easy to comprehend the intermediate characteristics of the feature fusion, and this restricts the transparency of the model.

The existing techniques' advantages and disadvantages are detailed in Table 1.

This study works on developing an automatic survival rate prediction mechanism for brain tumor patients by leveraging the efficiency of DL and meta-heuristic optimization algorithms. Unlike the conventional approaches, the proposed methodology uses multi-faceted patient data, including demographic details and disease features (type and stage of tumor) for survival rate prediction. Initially, the multifaceted patient data was collected and pre-processed to enhance its quality for further processing. Then, the U-Net algorithm was applied for image segmentation, which isolates the region of interest (ROI) from the pre-processed images. Consequently, DNN is used for extracting deep features for classifying tumor types. The DNN results and the pre-processed demographic details of the patients are fed into the proposed Co-LSTM-SBO for survival rate prediction. The proposed Co-LSTM-SBO integrates the efficiency of Co-LSTM and SBO, where the Co-LSTM component learns the hierarchical feature representations and patterns within the data and makes survival rate predictions. Co-LSTM and SBO were chosen based on the characteristics of the brain tumor survival prediction problem, which is characterized by heterogeneous data with complicated spatial and contextual relationships. The traditional CNN-based models are useful to capture spatial tumor features but fail to take into consideration inter-feature and sequential dependencies, whereas traditional LSTM models can capture dependencies at the expense of missing the spatial information. Co-LSTM combines convolutional algorithms in the framework of recurrence, which allows both maintaining spatial locality and capturing hierarchical dependencies between features, which is appropriate in prognostic analysis.

Co-LSTM performance is also very sensitive to the choice of hyperparameters, and manual tuning can result in poor convergence. SBO was thus used as an adaptive meta-heuristic optimizer to effectively search the high-dimensional space of hyperparameters and enhance training stability and generalization. The combination of Co-LSTM and SBO provides the high efficiency of spatial-temporal feature learning and the optimal work of the model in predicting the survival rate. On the other hand, the SBO fine-tunes the hyperparameters of Co-LSTM efficiently, thereby improving model training and enhancing its computational efficiency. The overall process of the developed model is shown in Figure 1.

Figure 1. Process of the developed technique

4.1 Dataset description

The research utilized the publicly accessible brain tumor classification dataset [26] found on Kaggle, consisting of 3,264 MRI images categorized into four groups: pituitary (930 images), meningioma (708 images), glioma (1,426 images), and no tumor (200 images). The data will be sorted into training and testing folders.

It used stratified splitting to split the data into 80% training, and 20% test sections to have balance and reproducibility by maintaining the proportion of classes in each section. All images were preprocessed and augmented as a standard to balance out inputs and overcome class imbalance.

Although the dataset is large enough to train deep-learning-based models, the few samples assigned to each of the classes could result in bias and narrow generalization. The sampled images taken for the training and testing process are detailed in Table 2.

Table 2. Dataset details

4.2 Preprocessing

Before segmentation of the tumors using U-Net, the brain MRI images obtained were subjected to a sequence of preprocessing procedures that enhance the quality of the images and guarantee credible extraction of the features. To normalize spatial dimensions, first, all the images were resized to a standard size. To eliminate random intensity and sensor artifact variations, a median filtering technique was used to reduce noise.

Histogram equalization was used to improve the contrast of the image to help in enhancing the visibility of tumor areas, especially in low-intensity or low-illumination images. Normalization of intensity was then done to bring pixel values to a normalized range so that there is consistency in the dataset, and this makes model training stable. Lastly, rotation, flipping, and scaling were used to augment the data to improve the diversity of the dataset and to enhance the strength of the segmentation and survival prediction models.

Such preprocessing steps guarantee that the U-Net model is fed with good-quality and standardized inputs, thus enhancing the segmentation of the tumor region-of-interest and feature extraction to perform downstream prognostic analysis.

•Noise removed using a Gaussian filter

When noise is modeled as additive white Gaussian noise (AWGN), each pixel in the image differs from its initial values according to the Gaussian curve. In other words, for every pixel in an image that has an intensity value $\vec{o}_{i, i}(1 \leq i \leq m, 1 \leq i \leq n)$ for an $m \times n$ image, the noisy image's matching pixel $\vec{Z}_{i, j}$ is provided by Eq. (1),

$x_{1,2}=\frac{-b \pm \sqrt{b^2-\vec{z}_{i, j}=\vec{o}_{i, j}+\vec{g}_{i, j} 4 a c}}{2 a}$     (1)

where, each value of noise $\vec{g}$ is taken from a Gaussian distribution with zero mean. To determine thresholds, filter window size, and other parameters for many Gaussian noise removal approaches, it is necessary to understand the standard deviation, which is a measure of the degree of corruption. The conventional standard deviation formula for estimating Gaussian noise ($\delta_{gn}$) is provided by Eq. (2)

$\delta_{g n}=\sqrt{\frac{\pi}{2}} \frac{1}{6 m \times n} \sum_{i, j=1}^{m, n}\left|(\vec{z} * m s)_{i, j}\right|$     (2)

Let, $*$ be the convolution operation, and $m s$ be the mask image.

•Contrast enhancement using CLACHE

To accomplish equalization, the function is modified using the Contrast-Limited Adaptive Histogram (CLACHE) [26]. By applying CLACHE to the values, it improves the grayscale image's contrast. It works on small data sections (tiles) instead of the full image, in contrast to histogram equalization. To make the histogram of every final region roughly resemble the given histogram (uniform distribution by default), the contrast of all tiles is increased. Limiting the contrast enhancement can help prevent the image's potential noise from being amplified. The intensity of the output $i^{\prime}(a, b)$ according to Eq. (3) for a pixel in the improved image.

$i^{\prime}(a, b)=\operatorname{intp}\left(R[l-1] \times \operatorname{cdf} f_{i, j}^{n m}(i(a, b))\right)$     (3)

Let, int p () be the Tile boundaries are blended using a bilinear interpolation technique, $c d f_{i, j}^{n m}$ be the CDF normalized for the corresponding tile , $t_{i, j}, l$ be thehighest value of intensity, and R be the round. The range's pixel intensity frequency is shown by the histogram $[l-1]$.

•Resizing and normalization

Resizing: Resizing is the process of making an image a specific size. It is essential for normalizing input data so that images that are input into DL models have the same size. Reducing an image from 1024 × 1024 to 256 × 256 is necessary to make all the inputs to a neural network of the same size, which makes the model and training process easier.

Min-max normalization: In order to improve the speed and stability of neural network training, the process of normalization is used to adjust the pixel values in an image to a common scale. Min-max normalization standardizes the pixel intensities within a fixed range, which could be [0,1] or [-1, 1]. The transformation is given by Eq. (4).

$\vec{x}_{n r m}=\frac{\vec{x}-\min (\vec{x})}{\max (\vec{x})-\min (\vec{x})}$     (4)

Let, $\vec{x}_{n r m}$ be the pixel-normalized value $\vec{x}, \vec{x}$ be the image's original pixel value, $\min (\vec{x})$ be the minimum pixel value throughout the whole image, and $\max (\vec{x})$ be the maximum value of each pixel in the whole image. The pre-processed image is shown in Figure 2.

Figure 2. Pre-processed image

4.3 Segmentation

The ROI is separated from the pre-processed data using the U-Net technique [27] for image segmentation. There are two components to the U-net network: The expanding path, which employs a standard CNN design, is the first. A max-pooling layer and a ReLU activation unit come after two consecutive 3 × 3 convolutions in each block of the contracting path. This arrangement is repeated multiple times. The expanding path, the second component of U-net, is distinctive because it employs 2 × 2 up-convolution to sample the feature map at each level. Subsequently, the feature map that has been up-sampled is minimized and then concatenated with the feature map from the matching layer located in the expanding path. ReLU activation and two consecutive 3 × 3 convolutions come next. To create the segmented image and limit the feature map to the necessary number of channels, a final 1 × 1 convolution is done. The complete U-net architecture is shown in Figure 3.

Eq. (5) provides the network's energy function.

$e_f=\sum W(s) \log \left(\bar{P} e_{(s)}(s)\right)$     (5)

Let, $\bar{P} e$ be the pixel-wise SoftMax function that is applied over the finished feature map, defined as Eq. (6).

$\bar{P} e=\operatorname{Exp}\left(x_e(s)\right) / \sum_{e^{\prime}=1}^E \operatorname{Exp}\left(x_e(s)^{\prime}\right)$      (6)

Let $x_e$ be the channel activation in E. Since pixel characteristics near the margins provide the least contextual information, they must be eliminated, necessitating cropping. This creates a U-shaped network and, more significantly, spreads contextual information throughout the network, enabling it to use information from a larger overlapping area to segment items in a given area. The segmented image is shown in Figure 4.

Figure 4. Segmented image

4.4 Feature extraction

The researchers found that the DNN [28] is the best method for extracting important features used for identifying the type of tumor when working with the image dataset. The CNN operates in that it uses photos from various datasets as input, and then its many layers extract features. Since the human brain's virtual cortex (VC) is responsible for learning, the VC has an impact on DL. The VC, a part of the human brain, handles all queries from the external environment. Since each layer pulls data gathered from the layers before it and they require each other to be blended, the final layers are combined, and the photos are categorized. Similar to this, CNN contains numerous filters that each extract data about the image, such as various shapes (round, vertical, and horizontal), edges, and measurements. The DNN network uses numerous filters and layers to gather features with data from images, as seen in Figure 3. After that, it advances to the classification stage of the network, where they are categorized according to the parameters. DNN Layers are covered in detail in the items that follow:

Input layer: Grayscale or RGB input images may be placed beneath this layer. Pixels ranging from 0 to 255 make up each image. Before being passed to the following layer of the model, the range between 0 and 1 must be transformed.

Convolution Layer: The input images must first undergo filtering to obtain or detect their features under this layer. The second is that to produce a feature map that helps with input image classification, a filter must be applied to the images several times.

Pooling Layer: The constant pooling layer is applied after the convolutional layer to downsize the feature maps while aiding in the preservation of essential details or features of the input images. Moreover, it diminishes the time needed for processing. The two predominant forms of pooling are Max Pooling and Average Pooling. Eqs. (7)-(10) specify the calculations for convolutional layers, max-pooling layers, and fully connected layers, respectively.

$z_j^L=f\left(\sum_{i \in m_j} y_i^{L-1} k_{i j}^L+B_j^L\right)$     (7)

$f(z)=\max (0, z)$     (8)

$z_j^L=F\left(\beta_j^L \cdot D W_s\left(z_j^L\right)+D_j^L\right)$     (9)

$H_{w, B(z)}=f\left(w_t+B\right)$     (10)

Generally, $L$ is the $L^{\text {th }}$ layer, $L=1$ be the first layer, $L= l$ be the last layer, and $z$ be the dimension input. Filter $y$ is the dimension $k$ and $B$ bias 1 through $j$ as the iterators. When Pooling is applied, the size of the feature map is reduced. The design of the DNN technique is shown in Figure 5.

Figure 5. Architecture of the Deep Neural Network (DNN) model

The pooling layers follow to downsample the feature maps in order to maintain important information and also alleviate computational complexity. The two usual methods are max pooling, where the algorithm takes the maximum value from each section in the feature map, and average pooling, where the algorithm takes the average of each section of the feature map.

4.5 Feature fusion

The numerical data and the features extracted by the DNN are merged by concatenation of the two into a single feature vector. This step helps in incorporating both lower-level and higher-level representations into the learning process. The fused feature set $x_{\text {fus }}$ is obtained by concatenating $x_{\text {org }}$ and $x_{d n n}$ along the feature axis, which is determined in Eq. (11).

$x_{f u s}=\left[x_{o r g} \mid x_{d n n}\right]$     (11)

The $[\mid]$ symbol refers to the process of joining two matrices side by side horizontally. This fused representation can then be utilized in the subsequent layers of the DL model employed for classification problems.

The methodology proposed has been done keeping in mind domain knowledge in medicine and tumor biology to make sure it is clinical. The choice of tumor-specific features, such as the type and stage of a tumor, is informed by the oncology criteria that have been proven to affect the progression and survival of the patient. These clinical variables are combined with imaging characteristics to represent the actual diagnostic and prognostic decision-making procedures.

Biologically, U-Net-based tumor segmentation targets isolating pathological regions, which are associated with biologically significant structures, like tumor borders and regions of infiltration, which are essential to prognosis accuracy. The obtained deep features are morphological features related to tumor aggressiveness and progression, and converge with feature learning as understood in known biological variations in brain tumors.

The proposed solution will help address the gap between technical modeling and medical and biological facts by including clinical parameters and biologically relevant imaging data into the learning process, thus increasing the significance and applicability of the results in terms of survival prediction.

4.6 Classification and survival rate prediction using Convolutional Long Short-Term Memory and Secretary Bird Optimization

The survival prediction of brain tumor patients is a multifaceted learning task where there are heterogeneous data sources, such as high-dimensional spatial data in the form of medical images and structured demographic and clinical data. These data have great spatial correlations, cross-feature relationships, and also non-linear connections that cannot be well represented using traditional feedforward or shallow recurrent architectures.

Co-LSTM networks are an extension of the standard LSTM formulation with convolutional operations in the input-to-state and state-to-state transitions. This architectural structure allows Co-LSTM to maintain the spatial locality and, at the same time, long-range dependencies on feature sequences. Within the suggested framework, the deep representations of segmented tumor areas and clinical features constitute a structured sequence representation where the spatial tumor properties and interactions of features are highly essential in the estimation of survival. Thus, Co-LSTM is theoretically best suited to learn hierarchical feature representation and time-based correlations of multi-modal survival prediction tasks.

Although Co-LSTM has the representational power, its performance is very sensitive to a good choice of the hyperparameters, especially in a high-dimensional search space like the kernel size, the number of filters, learning rates, and gating parameters. In this regard, a meta-heuristic algorithm called SBO, which is a nature-inspired algorithm, is used to tune hyperparameters. The adaptive exploration-exploitation balance, which allows SBO to search efficiently, without converging prematurely to local optima, is a characteristic of SBO. Contrary to gradient-based tuning methods and more widespread meta-heuristics, SBO actively modulates the search directions through the diversity of the population, and is therefore appropriate to optimize highly recurrent architectures that have complicated loss landscapes.

Through Co-LSTM plus SBO, the model proposed has the advantage of strong feature learning and training dynamics optimization. The Co-LSTM part is used to successfully learn spatial-temporal feature representations that are useful to tumor progression, patient survival, and SBO is able to improve the convergence behavior, generalization ability, and computational efficiency by optimizing the hyperparameter setting. Such a theoretically motivated combination will provide a robust and scalable structure for the precise prediction of the survival rate.

The DNN results and the pre-processed demographic details of the patients are fed into the proposed Co-LSTM-SBO for survival rate prediction. The proposed Co-LSTM-SBO integrates the efficiency of Co-LSTM [29] and SBO [30], where the Co-LSTM component learns the hierarchical feature representations and patterns within the data and makes survival rate predictions. Among its many uses are object detection, image categorization, and tracking.

4.6.1 Convolutional neural network

A multi-layer perceptron neural network makes up the CNN. The CNN extracts features from the images and classifies them through a fully connected layer. The structure of a CNN is made up of three layers: the convolution layer, the pooling layer, and the fully connected layer. Below is an explanation of how each layer operates:

Convolution layer: The convolution layer is essential to CNN. It produces a feature map and is used to compress the image. This layer contains a set of kernels used to create a matrix of extracted features. These kernels utilize "stride(s)" for interpolation of the whole input, resulting in decimal values for the output volume's dimensions. As a result of the striding process, the input volume dimensions of the convolutional layer diminish. The convolution operation is determined in Eq. (12).

$\begin{gathered}\vec{c}(i, j)=\left(I_{i m g} * f_t\right)(i, j) \\ =\sum \sum I_{i m g}(i+x, j+y) f_t(x, y)\end{gathered}$      (12)

Let, $I_{i m g}$ be the input image, $f_t$ be the 2D filter of size, $\vec{c}(i, j)$ be the 2D feature map output. The nonlinearity in the space of features is enhanced by the rectified linear unit (ReLU) layer. ReLU keeps the threshold input at zero to compute excitation. Eq. (13) details the calculated appearance.

$f(z)=\max (0, z)$     (13)

Pooling layer: A complicated image must be reduced while retaining its essential components because it will be very large. The majority of studies used maximum polling and the maximum pooling layer, which produces the highest possible number in an input area.

Fully connected layer: This layer is used in the categorization procedure. The FC layer receives the resulting feature map and produces the result.

4.6.2 Long Short-Term Memory

To refresh and control the system's data performance, the Long Short-Term Memory (LSTM) employs a gate structure made up of input, forget, and output gates [31]. The LSTM addresses the gradient elimination problem, using memory storage cells and gate processes to meet long-term information needs, thus overcoming RNN limitations. The numerical equation for each gate is explained below;

Considering the previously hidden structure, the forget gate $\check{f}_t$ aids the LSTM in identifying the information that must be provided and removed via the cell state using Eq. (14).

$\breve{f}_t=\breve{\sigma}\left(\breve{w}_{\breve{f}} \cdot\left[\breve{h}_{t-1}, z_t\right]+\breve{b}_{\check{f}}\right)$     (14)

Let $\breve{h}_{t-1}$ denotes the previous gate, $z_t$ be the input data, $\breve{\sigma}()$ be the sigmoid activation function, $\breve{w}_{\check{f}}$ be the weight measurements, and $\breve{b}_{\check{f}}$ be the bias vector. The information will be moved to the cell state $\breve{c}_t$ of the next candidate, which is determined by the input gate $\breve{l}_t$ using Eq. (15) and (16).

$c_t=\tanh ()\left(\widetilde{w}_{\widetilde{c}} \cdot\left[\breve{h}_{t-1}, z_t\right]+\breve{b}_c\right)$     (15)

$\breve{l}_t=\breve{\sigma}\left(\breve{w}_{i \cdot} \cdot\left[\breve{h}_{t-1}, z_t\right]+\breve{b}_i\right)$     (16)

Let $\tanh ()$ be the hyperbolic tangent function. The updated new cell state $\breve{c}_t$ is produced by connecting the previous cell state $\breve{c}_{t-1}$, and the new candidate's cell state $c_t$ is created using Eq. (17).

$\breve{c}_t=\breve{f}_t * \breve{c}_{t-1}+\breve{l}_t * c_t$    (17)

The output gate $\breve{o}_t$ is then developed to regulate the result of the LSTM cell using Eq. (18). The desired result $\breve{h}$ is indicated by the following Eq. (19), which is the combination of $\breve{o}_t$ and the cell state $\breve{c}_t$ activated by the tanh function.

$\breve{o}_t=\breve{\sigma}\left(\breve{w}_{\breve{o}} \cdot\left[\breve{h}_{t-1}, z_t\right]+\breve{b}_{\breve{o}}\right)$     (18)

$\breve{h}_t=\breve{o}_t \cdot \tanh \left(\breve{c}_t\right)$     (19)

The use of the LSTM classifier is because of its exceptional performance in handling long-term dependencies in data and its ability to rapidly extract sequential properties using time. The SBO technique is used to regain efficacy by carefully selecting the model parameters for the LSTM.

4.6.3 Parameter hyper-tuning using the Secretary Bird Optimization

In the population-based metaheuristic approach known as the SBO technique, each Secretary Bird (SB) is considered a member of the process's population. The values of the decision variables hinge on the location of each SB within the search space. The locations of SBs in the SBOA technique represent potential solutions to the existing problem. Eq. (20) is used in the SBOA's initial implementation to randomly initialize the SBs' locations throughout the search space.

$\begin{gathered}Y_{a, b}=L a_b+R_n \times\left(U a_b-L a_b\right) \\ a=1,2, \ldots, n, b=1,2, \ldots \ldots, \operatorname{dim}\end{gathered}$     (20)

Let $Y_a$ be the position of the $a^{\text {th }} \mathrm{SB} L a_b$ and $U a_b$ be the lower and upper bounds, and $R_n$ be the random value between 0 and 1 . A population of potential solutions serves as the starting point for optimization in the population-based SBO, as illustrated in Eq. (21).

These potential solutions $Y$ are produced at random while adhering to the problem's upper $U a_b$ and lower $L a_b$ bound constraints. In each iteration, the best solution found so far is roughly regarded as the ideal answer.

$Y=\left[\begin{array}{cccccc}y_{1,1} & y_{1,2} & \cdots & y_{1, b} & \cdots & y_{1, \text { dim }} \\ y_{2,1} & y_{2,2} & \cdots & y_{2, b} & \cdots & y_{2, \text { dim }} \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots \\ y_{a, 1} & y_{a, 2} & \cdots & y_{a, b} & \cdots & y_{a, \text { dim }} \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots \\ y_{n, 1} & y_{n, 2} & \cdots & y_{n, b} & \cdots & y_{n, \text { dim }}[]_{n \times \text { dim }}\end{array}\right]$     (21)

Let, $Y$ be the group of the $\mathrm{SB}, Y_a$ be the $a^{\text {th }} \mathrm{SB}, Y_{a, b}$ be the $a^{\text {th }} \mathrm{SB} b^{\text {th }}$ question the value of a variable, $n$ be the secretary group members, and $\operatorname{dim}$ be the problem of variable dimension.

Every SB represents a possible solution to optimize the problem. Consequently, the suggested values for the problem variables from every SB can be employed to assess the objective function. Subsequently, Eq. (22) is employed to assemble the resulting variables of the objective function into a vector.

$f=\left[\begin{array}{c}f(1) \\ \vdots \\ f(i) \\ \vdots \\ f(n)\end{array}\right]_{n \times 1}=\left[\begin{array}{c}f\left(Y_1\right) \\ \vdots \\ f\left(Y_i\right) \\ \vdots \\ f\left(Y_n\right)\end{array}\right]_{n \times 1}$     (22)

Let $f$ be the vector of values for the objective function, and $f(i)$ be the objective function value gained by the $a^{\text {th }} \mathrm{SB}$. Two different SB natural behaviors were used to update the SBOA employees. These two types of behavior consist of: (a) the hunting method of the SB and (b) the evasion method of the SB. Every individual of the SB colony is upgraded in two stages on every iteration.

•The secretary bird's hunting strategy (period of exploration)

When hunting snakes, SBs typically exhibit three phases in their hunting behavior: locating prey, consuming prey, and striking at prey.

Stage 1 (searching for prey): SBs typically begin their hunting by searching for potential prey, especially snakes. SBs can easily detect snakes concealed in the savannah's tall grass, thanks to their remarkable vision. They meticulously watch their surroundings and delicately sweep the ground with their long legs, looking for any indications of snakes. Consequently, Eqs. (23) and (24) are appropriate for quantitatively simulating the process of updating the SB's position during the Searching for Prey phase.

while $T<\frac{1}{3} t, y_{a, b}^{\text {new } 1}=y_{a, b}+\left(y_{r n 1}-y_{r n 2}\right) \times r_1$     (23)

$Y_a=\left\{\begin{array}{cc}y_a^{\text {newq } 1}, & \text { if }\left(f_a^{\text {new } q 1}<f_a\right) \\ Y_a, & \text { else }\end{array}\right\}$    (24)

Let, $T$ be the current iteration number, $t$ be the maximum iteration number, $y_a^{\text {newq } 1}$ be the new state of the $a^{\text {th }} \mathrm{SB}$ in the first stage, $y_{r n 1}$ and $y_{r n 2}$ are the first stage iteration's random candidate solutions, $r_1$ symbolizes a dimension array that is produced at random $1 \times \operatorname{dim}$ from the interval $[0,1], \operatorname{dim}$ be the solution space dimensionality. $y_{a, b}^{\text {newq } 1}$ be the $b^{\text {th }}$ dimension value, and $f_a^{\text {new, } q 1}$ be the objective function fitness value.

Stage 2 (consuming prey): An SB uses a unique hunting technique after finding a snake. Unlike other raptors that swiftly swoop in to fight, the SB utilizes its agile footwork to navigate around the snake. Here, we utilize Brownian motion (RB) to simulate the SB's unpredictable movements. Eq. (25) provides a mathematical framework for Brownian motion.

$r b=R_n(1, \operatorname{dim}())$     (25)

Eqs. (26) and (27) provide a mathematical framework for updating the position of the SB in the Consuming Prey phase.

$\begin{gathered}\text { while } \frac{1}{3} t<T<\frac{2}{3} t, y_{a, b}^{\text {newq } 1}=y_{\text {best }} \\ +\exp ((T / t) \wedge 4) \times(r b-0.5) \times\left(y_{\text {best }}-y_{a, b}\right)\end{gathered}$    (26)

$Y_a=\left\{\begin{array}{cc}y_a^{\text {newq } 1}, & \text { if }\left(f_a^{\text {new }, q 1}<f_a\right) \\ Y_a, & \text { else }\end{array}\right\}$     (27)

Let, $y_{\text {best}}$ be the individual historical best position, $R_n(1, \operatorname{dim}())$ symbolizes a dimension array that is produced at random $1 \times \operatorname{dim}$ from a standard normal distribution and $y_{\text {best}}$ be the current best value.

Stage 3 (attacking prey): The SB identifies the chance when the snake is fatigued and promptly strikes with its powerful leg muscles. At this point, the SB typically employs its leg-kicking approach. This involves swiftly lifting its leg to deliver a precise kick at the snake with its sharp talons, often targeting the snake's head.

As a result, Eqs. (28) and (29) can serve to statistically simulate the updating of the SB's location during the Attacking Prey phase.

$\begin{gathered}\text { while } T>\frac{2}{3} t, y_{a, b}^{\text {newq } 1}=y_{\text {best }} \\ +\left(\left(1-\frac{T}{t}\right) \wedge\left(2 \times \frac{T}{t}\right)\right) \times y_{a, b} \times r l\end{gathered}$     (28)

$Y_a=\left\{\begin{array}{cc}y_a^{\text {newq } 1}, & \text { if }\left(f_a^{\text {new }, q 1}<f_a\right) \\ Y_a, & \text { else }\end{array}\right\}$    (29)

To improve the method's optimization accuracy, we employ the weighted Levy battle, which is represented as 'rl' in Eq. (30):

$r l=0.5 \times l v(\operatorname{dim}())$     (30)

where, $\operatorname{lv}(\operatorname{dim}())$ symbolizes the distribution function of the Levy battle. This is computed using Eq. (31).

$l v\left(d() \frac{U \times \sigma}{|V|^{\frac{1}{\varepsilon}}}\right)$    (31)

Let $S$ be the fixed constant of 0.01 and $\varepsilon$ be the fixed constant of 1.5. $U$ and $V$ are random values inside the range $[0,1]$.

•Escape strategy of SB (exploitation stage)

SBs are primarily targeted by large predators like eagles, hawks, foxes, and leopards, as they can attack them or take their food. SBs usually employ various evasive tactics to safeguard one another or their food source when faced with these dangers. These tactics can be roughly divided into two main categories. The first tactic involves a battle or fast running. In the first method, upon sensing a predator, SBs first look for an appropriate place to conceal. They will either fight or run quickly if there is no adequate and secure camouflage setting in the vicinity.

Both of the evasion strategies used by SBs can be represented mathematically through Eq. (32), and Eq. (33) can be used to establish this revised condition.

$\begin{gathered}y_{a, b}^{\text {newq2 }}=\left\{\begin{array}{cc}c 1: y_{\text {best }}+(2 \times r b-1) \times\left(1-\frac{T}{t}\right) \times y_{a, b} & \text { if }\left(\text {Rand}<R_a\right) \\ c 2: y_{a, b}+r 2 \times\left(y_{r n}-k \times y_{a, b}\right) & \text { else }\end{array}\right\}\end{gathered}$     (32)

$Y_a=\left\{\begin{array}{cc}y_a^{\text {newq } 2}, & \text { if }\left(f_a^{\text {new }, q 2}<f_a\right) \\ Y_a, & \text { else }\end{array}\right\}$    (33)

Let $R=0.5, r 2$ be the random creation of a dimension array $(1 \times \operatorname{dim}())$ from the normal distribution, $y_{r n}$ be the arbitrary potential solution for the current iteration, and $k$ be the random selection of integer 1 or 2 .

4.6.4 Hybrid Convolutional Long Short-Term Memory and Secretary Bird Optimization model

The proposed Co-LSTM-SBO model, combining DL and nature-inspired optimization, performs well in classification and survival rate prediction. This approach begins with the fusion of DNN-extracted features and pre-processed demographic patient data into the Co-LSTM-SBO model. Then, the Co-LSTM component, recognized for learning hierarchical features and analyzing time-series data, is utilized to predict survival rates while being capable of detecting long dependencies and patterns within the data. The paper employs a model that utilizes feature extraction via a CNN comprising convolution, pooling, and fully connected layers. The convolutional layer uses kernels to generate feature maps through a stride operation. The pooling layer decreases the size of feature maps while retaining important features and sending them to the fully connected layer for classification.

In the Co-LSTM model, the SBO has the most important function of improving the model’s performance by adjusting its parameters. SBO, which relies on hunting and avoiding SBs, is used to adjust the hyperparameters of the LSTM network for recognizing long-term dependencies in the data. The SBO algorithm operates based on the behavior observed in SBs, including foraging, consuming, and attacking to look for and find better-search solutions. While working in the exploration phase, SBO optimizes the exploration of the parameter space and, while operating in the exploitation phase, employs a finer search for the best solutions. The optimization process slashes the compromise for Co-LSTM, where there is an appreciation of enhanced impact for higher survival rate prediction on the incoming data. By applying SBO for parameter tuning, the Co-LSTM model can escape local optima and obtain higher accuracy of survival prediction from the hierarchical feature representations learned by LSTM.

This research develops a novel automatic approach for MRI tumor image detection. In creating the hybrid method applied in this research, CNN and LSTM classifiers are utilized. The features are extracted using CNN, while LSTM is utilized for classification. The SBO technique is used to select the weight values for the LSTM classifier, which represent the optimal solution. The proposed mixed CN-LSTM-SBO tumor detection framework is illustrated in Figure 6. It is suggested that the hybrid structure be made up of twenty levels. Every convolutional unit consists of a dropout network with a 25% failure probability, along with one pooling layer and a final pooling layer. The dimensions of the kernel utilized for feature extraction are triggered by the ReLU function. Several kernels are used in the max-pooling layer, which decreases the distance between image pixels. The function map is ultimately sent to the LSTM layer in the final design phase. This layer produces the final output.

Figure 6. Design of the proposed CN-LSTM-SBO framework