Sine Cosine Based Harris Hawks Optimizer: A Hybrid Optimization Algorithm for Skin Cancer Detection Using Deep Stack Auto Encoder

The cancer is considered as foremost contributor for causing a sudden upsurge in mortality rate all over the world. There exist different kinds of cancer which are determined earlier for the prior diagnosis. However, skin cancer is a major disease that tends to be a fast-growing cancer these days. As per machine research, the patients undergoing skin cancer detection are continuously growing compared to other types of cancer [1]. For both dermatologists and oncologists, the notion of early identification of skin melanoma cancer is crucial since it increases the likelihood of achieving full oncological remission. The histology of melanoma is complicated domain as late diagnosis may increase the mortality rates. The detection of skin lesion needs high experience and competence and thus the medical diagnosis is a challenging task [2]. As compared to other kinds of skin cancer, the melanoma is not frequent but it is likely to spread and grow. Skin tumor like other tissue tumors can be benign or malignant. The status and nature of skin cancer is different and thus it can be hard, soft, moving, losing or deep with respect to size or shape [3]. Melanoma cancer is considered as an advanced phase that might overrun internal organs like lungs through blood vessels, by building the treatment even difficult. Meanwhile, Early detection is key to treating melanoma, thus dermatologists recommend routine skin checks to increase the likelihood of an accurate diagnosis. Dermatologists use digital imaging to identify and treat skin cancer [4].

The most common cancer among those with fair skin is skin cancer, and as non-melanoma and melanoma cases increase in frequency, the associated medical expenses rise. Earlier melanoma diagnosis tends to improve patient outcomes and identification of skin cancer can be enhanced by screening patients using intensive skin symptoms considering examination of overall body skin [5]. As skin cancer provides epidermis which is the uppermost skin layer as it is relatively visible. This technique illustrates that the CAD model may utilise skin cancer photos without considering other important information. Skin cancer is a leading cause of mortality. Melanoma affects the skin’s melanocytes. This cancer contains cells which may cause the skin go black color. The Melanoma may lead to metastasis and has the capability to spread. Melanoma can be determined anywhere on the human which is on the human legs.

Discovery of skin cancer in the earlier stage may lead to effectual treatment and can be attained by the automatic determination of cancer types considering deep learning methods. The results show that deep convolutional neural networks (DCNNs) may be utilized to accurately and automatically identify skin cancer [6]. In recent days, the quicker extension in deep learning made prodigious accomplishments in several tasks of computer vision. Deep learning uses many processing layers to extract features and change data. Convolutional neural networks (CNN) is the major deep learning techniques that attained prodigious empirical successes in the computer aided diagnosis [7]. The analysis is performed in particular domain to precisely identify the skin cancer. Tenderness of the skin and the categorization of skin either as benign or melanoma is performed using different models like genetic algorithms, support vector machines (SVMs), artificial neural networks (ANNs), and CNNs. All given methods tend to be cost-effective and highly effective and less painful than existing medical models. However, in several computer vision problems, it is indisputable that both deep learning and CNNs are the mostly used technique [8]. The majority of the classification techniques are applied on the computer-based melanoma recognition models which involve SVM [9], Bayes networks, ANN [10], discriminate analysis [11], k-nearest neighbourhood, decision trees [12], and logistic regression. On the other hand, some advanced models of these classifiers are modelled in the existing works which includes random forest [13], hidden naive Bayes, and logistic model tree [14].

The difference between the depth automatic encoder and stacked automatic encoder is the way the two networks are trained. Depth automatic encoders are trained in the same way as a single-layer neural network, while stacked automatic encoders are trained with a greedy, layer-wise approach so the training time required to train the depth automatic encoders is less compared to that of stacked automatic encoders.

Proposed SCHHO-based Deep stacked auto-encoder is used in current research to present a skin cancer detection approach. Research’s contribution is the use of statistical and textural data to identify skin lesions. Here, the segments from which the malignant patches are diagnosed are obtained using the sparse FCM. Mean, standard deviation, variance, kurtosis, entropy, and LDP are extracted to detect lesions. A deep stacked auto-encoder finds skin lesions using these characteristics. Deep stacked auto-encoder is trained using SCHHO to learn model parameters. The suggested algorithm, SCHHO, was created by inheriting high global convergence property from HHO procedure. Therefore, deep stacked auto-encoder based on SCHHO offers effective accuracy while enabling skin cancer detection. The SCA and HHO algorithms are combined in the suggested SCHHO algorithm. Main contribution of paper is:

Proposed SCHHO-based Deep stacked auto-encoder for detection of skin cancer: Deep stacked auto-training encoder’s approach is modified with SCHHO algorithm that is newly created by combination of SCA and HHO algorithms, for best tuning of weights and biases. This classifier is known as the SCHHO-based Deep stacked auto-encoder. In order to identify lesions in skin images, recommended SCHHO-based Deep stacking auto-encoder has been updated.

The remaining portions in this paper are: The conventional skin cancer detection methods used in the literature and the difficulties encountered are outlined in Section 2 and are used as inspiration for the suggested method’s development. In Section 3, the Deep stacked auto-encoder approach for skin cancer identification is described. In Section 4, the outcomes of the suggested approach compared to other methods are shown, and Section 5 concludes.

SCHHO-based deep stack auto-encoder is presented for automated skin cancer diagnosis, extracting statistical and textural information for classification. The input skin images are first pre-processed to prepare them for subsequent processing. Images that have been previously processed are then subjected to a segmentation module, where they are segmented using Sparse FCM [24]. After getting the segments, each segment is taken into account while performing the feature extraction. Each segment's statistical characteristics are extracted.

1.png

Figure 1. Block diagram of proposed SCHHO-based Deep Stacked auto-encoder method

Feature vectors include each segment's retrieved features. Using the feature vector, a deep stacked auto encoder [24] trained with SCHHO detects skin cancer. Standard HHO and SCA are combined to create the suggested SCHHO, which inherits the benefits of both optimizations for efficient classifier training. The proposed SCHHO-based deep stacked auto encoder is used to depict framework for identification of skin cancer in Figure 1.

Simplify the diagram in Figure 1. Draw only four blocks and label them appropriately indicating functionality of each block: preprocessing, segmentation, extraction of feature and categorization. Assume a skin cancer dataset G with f number of skin images, it is given as:

$G=\left\{I_1, I_2, \ldots, I_g, \ldots, I_f\right\}$               (1)

where, I_g is g^th input image, and f is the overall amount of images.

3.1 Pre-processing utilizing skin cancer images

To remove noise and artefacts from image, pre-processing is used. The pre-processing may also be used as an image improvement module to boost contrast of the picture for the aim of identifying skin cancer. The pre-processed pictures are concurrently entered into segmentation to determine the relevant characteristics suitable for the diagnosis of skin cancer.

3.2 Segmentation of preprocessed image

Preprocessed image is input to segmentation unit while taking into account the Sparse FCM method [24]. Sparse FCM is a variant of normal FCM, and it offers high dimensional data clustering as a benefit. The pre-processed image has many segments, each of which denotes a distinct region. The sparse FCM is used in the skin cancer detection approach for image segmentation.

Consider image pixels as V, data matrix as $D=\left(V_{k l}\right) \in {\Re} ^{p \times q}$, p and q are image size. The programme forms clusters to make skin cancer diagnosis easier. Sparse FCM outputs segments. Steps of sparse FCM is described below.

1. Initially, feature weights are initialized and are represented as $\omega=\omega_1^e=\omega_2^e=\ldots=\omega_q^e=\frac{1}{\sqrt{q}}$. Pixel location is determined by features considering q=2.

2. At first, attribute weights $\omega$ and cluster centres $S \varepsilon(\Re)$ is reduced when:

$P_{k t}=\left\{\begin{array}{l}\frac{1}{N_t} ; \text { if } B_{k t}=0 \text { and } N_t=\operatorname{card}\left\{l: B_{k t}=0\right\} \\ 0 ; \text { if } B_{k t} \neq 0 \text { but } B_{k j}=0 \text { forsome } j, j \neq t \\ \frac{1}{\sum_{j=1}^n\left(\frac{B_{k t}}{B_{j t}}\right)\left(\frac{1}{\beta-1}\right)} ; \text { Otherwise }\end{array}\right.$              (2)

where, card(A) indicates cardinality of set A. Distance adapted in sparse-FCM is modelled as:

$B_{k t}=\sum_{t=1}^n \omega_l\left(V_{k l}-V_{t l}\right)^2$               (3)

3. Assume ω and $\Re$ be fixed and ε(S) is reduced if:

$S_{t l}=\left\{\begin{array}{l}0 ; i f \omega_l=0 \\ \frac{\sum_{i=1}^n P_{k t}^\beta \cdot V_{k l}}{\sum_{k=1}^n P_{k t}^\beta} ; \text { if } \omega_l \neq 0\end{array}\right.$               (4)

where, t=1, ..., n and l=1, ..., q, β indicate weight component, and is liable to control membership degree using fuzzy clusters. Role of l^th feature in objective function is represented as, ω_l and dissimilarity measure is represented as, $\Re$.

4. Class value is found using fixed clusters $\left\{s_1, s_2, \ldots, s_i, \ldots, s_n\right\}$ and the membership $P$. Class $G_l$ is evaluated on basis of following objective, $\max _\omega \sum_{l=1}^q \omega_l . G_l$ such that $\|\omega\|_2^2 \leq 1,\|\omega\|_f^f \leq \ell$ and obtain $\omega^*$.

where, $\ell$ indicate tuning parameter and $(0 \leq f \leq 1) ;\|\omega\|_f^f=$ $\sum_{l=1}^q\left|\omega_l\right|^f$

5. Iterate till halting requirement met. Stopping criterion:

$\frac{\sum_{l=1}^q\left|\omega_l^*-\omega_l^e\right|}{\sum_{l=1}^q\left|\omega_l^e\right|}<10^{-4}$               (5)

Sparse FCM outputs image segments as:

$S=\left\{s_1, s_2, \ldots, s_i, \ldots, s_n\right\}$              (6)

where, r indicates count of segments generated from preprocessed image.

3.3 Using statistical and texture characteristics, generation of a feature vector

Following the acquisition of segments, features are retrieved from the pre-processed image taking into account each segment. Statistical aspects like mean, variance, standard deviation, kurtosis, and entropy as well as texture features like LDP are among the features retrieved from the segments and are described below.

Mean: The average is determined by counting all of the pixels in image that are expressed as:

$\mu=\frac{1}{\left|d\left(S_n\right)\right|} \times \sum_{n=1}^{\left|d\left(S_n\right)\right|} d\left(S_n\right)$            (7)

where, n is the total number of segments, values of each segment's pixels, and |d(S_n)| is total number of pixels included in the segment

Variance: Based on the mean value, which is written as, the variance feature is computed as:

$\sigma=\frac{\sum_{n=1}^{\left|d\left(S_n\right)\right|}\left|S_n-\mu\right|}{d\left(S_n\right)}$             (8)

Standard deviation: Square root of variance is used to get standard deviation, which is represented by ρ.

Kurtosis: It represents evenness that defines sharpness of peak. It defines shape of an object depending on its numerical value. Probability distribution's relative peakedness is shown by the kurtosis.

Entropy: Entropy is a common metric for quantifying uncertainty in data and is applied to increase mutual information in various procedures. Appropriateness preference for a specific operation was motivated by the abundance of entropy variations. In order to pinpoint the difference between adjacent pixels or a pixel group, entropy of an image is used. Entropy is further defined as comparable intensities levels to which individual pixels can adapt. An image's entropy can be utilised for quantitative analysis, evaluation of the image's details, and better comparison of image details. As a result, the resulting probability's entropy is calculated and is represented as:

$\varepsilon=-Q \log (Q)$               (9)

where, Q is pixel probability distribution in an image.

LDP: Local Directional Pattern (LDP) [25] is a directional component that incorporates a local pattern descriptor by altering Kirsch compass kernels. In comparison to the LBP operators now in place, the LDP is less noise sensitive.

$L=L D P_c\left(a_n, b_n\right)=\sum_{x=0}^7 v\left(b_x-b_c\right) \cdot 2^x$             (10)

where, c signifies pixel location, (a_n, b_n) denotes directed bit responses, x neighborhood pixel number, b_x denotes Kirsch masks, and b_c denote c^th directional response.

$v(a)=\left\{\begin{array}{l}1 ; \text { if } a \geq 0 \\ 0 ; \text { otherwise }\end{array}\right\}$           (11)

3.3.1 Formation of feature vector

Collection of statistical and texture features is shown in Eq. (12). Consequently, each segment’s characteristics are presented as follows:

$J=\{\mu, \sigma, \rho, \kappa, \varepsilon, L\}$             (12)

where, J denotes feature vector which is extracted utilizing each segment, $\mu, \sigma, \rho, \kappa$ and $\varepsilon$ denote mean, variance, kurtosis, standard deviation, and entropy are the statistical features, whereas texture features include LDP that is represented by L. Deep stacked auto encoder receives feature vector, which it uses to classify input images based on features and determine class label. Classifier determines class label and divides input image's malignant and non-cancerous areas into categories.

3.4 The proposed SCHHO-based deep stacked auto encoder

This section describes how to identify skin cancer using the suggested SCHHO approach and how to advance the detection using a feature vector. Deep stacked auto encoder [26] is used to present extracted features for classification, and the suggested training algorithm SCHHO—a combination of the SCA and the HHO —is utilized to train classifier. Proposed SCHHO’s objective is to use the extracted features to detect malignant areas in input image. The inclusion of SCA in HHO is the planned SCHHO. Here, the sine and cosine functions are taken into account when designing the SCA algorithm. The algorithm is adept at balancing exploitation and exploration states to identify search spaces most promising regions and assists in obtaining the global optimum. The strategy benefits from the avoidance of local optima and high exploration, therefore resolving practical issues. HHO, on the other hand, draws inspiration from Harris hawks submissive conduct and chasing manner. The approach is efficient in handling various optimization problems that can result in efficient solutions. HHO can handle misleading optima, local optimum solutions, and multi-modality. To enhance the algorithm’s overall performance, SCA and HHO are integrated. The following describes the proposed SCHHO’s algorithmic phases as well as the deep stacked auto encoder's architecture.

3.4.1 Architecture of deep stacked auto encoder

Auto Encoder in Deep Neural Networks (DNN) is crucial. The relevant input characteristics are used by the auto encoder. The single layer auto encoder does not have directed loops in its output visible units, which are also hidden units at the encoder's input. Figure 2 shows the deep stack auto encoder's structural arrangement. Encoding input vector into an advanced phase concealed version, shown as K, advances auto encoder.

2.png

Figure 2. Architecture of deep stack auto-encoder

Deep Neural Networks use Auto Encoder (DNN). Auto encoder inputs are used. Single-layer auto encoder input visible units are concealed, and output visible units don't contain directed loops. Figure 2 shows the encoder's structural arrangement. The auto encoder advances by encoding input vector as K. In encoder, deterministic mapping T_θ turns input vector into hidden vector X.

$\vartheta=\operatorname{fun}\left(\omega_1 U+R_1 U\right)$                   (13)

where, R₁ is to the bias vector, and U is reconstruction, and ω₁ indicates the weight matrix. The equation will be written as after decoding the concealed version back to reconstruction:

$\widehat{U}=\operatorname{fun}\left(\omega_2 Y+R_2 Y\right)$                 (14)

where, ω₂ represent weight matrix, R₂ denote bias vectors, and Y hidden units.

Back propagation encounters difficulties with local minima and sluggish convergence. The frequent weight changes are what cause the local minima. Additionally, the Back propagation algorithm does not require input vector normalization. System’s performance can be improved by normalizing, however this technique does not allow for the determination of the error function's global minimum. Auto Encoder is trained utilizing SCHHO instead of back propagation to reduce cost function and squared reconstruction error.

$\operatorname{Jac}(\omega, R)=\frac{1}{2 z} \sum_{x=1}^z\left\|\widehat{U}_x^z-U_x^X\right\|^2$              (15)

where, ω weight set, R bias vectors, z total layers where 1≤x≤z, $U_x^z$ displays the input x^th and $U_x^X$ output reconstructions on $x^{t h}$ layer.

To prevent overfitting, a weight regularisation term and scarcity restrictions are used to create a cost function.

$\operatorname{Jac}(\theta)=\frac{1}{z} \sum_{x=1}^z\left\|U_x^z-U_x^X\right\|^2+\alpha\left(\left\|\omega_1\right\|^2+\right.\left.\left\|\omega_2\right\|^2\right)+\beta \sum_{y=1}^Y V\left(U \| U_y\right)$                (16)

where, $U_x^z$ represents input reconstruction on x^thlayer and $U_x^X$ demonstrates output reconstruction on x^th layer, α is weight for regulation condition, and β is weight for sparse condition, and $\mid \omega_1\left\|^2+\right\| \omega_2 \|^2$ denotes parametric conditions, U is the sparse parameter, and U_y denotes average activation of hidden unit y, and V(U||Y_y) denotes Kullback Leibler divergence, and Y is number of hidden units like 1≤y≤Y. Average hidden unit is formulated as:

$\widehat{U}_y=\frac{1}{z} \sum_{x=1}^z l_{2, x}^y$                     (17)

where, $l_{2, x}^y$ denote hidden layer activation function of y^th entry, and z denote total layers where 1≤x≤z. Kullback Leibler divergence is formulated as:

$V\left(U \| U_y\right)=U \log \frac{U}{U_y}+(1-U) \log \frac{1-U}{1-U_y}$                  (18)

where, U denotes sparse parameter, and U_y denotes average activation of hidden unit y. The auto-encoder is made up of a number of layers of sparse auto encoder, the outputs of which are coupled to the inputs of succeeding layers, where Y₁, Y₂, and Y₃ depicts hidden layers. Concatenation of auto-encoders that inputs of next layers are connected to outputs of auto-encoders stacked on layer. Auto-encoders are finally layered in a hierarchical fashion. Activation output of z^th layer is given as:

$l_{q x}^X=w q\left(l_{q-1}^X \omega_{q-1}+s_{q-1}^X\right)$                 (19)

where, l_1,x=u_x. By describing $p_{\omega, O}\left(u_x^X\right)=l_{o, x}$, cost function is:

$\operatorname{jac}(\omega, O)=\frac{1}{2 z} \sum_{x=1}^z\left\|p_{\omega, O}\left(u_x^X\right)-u_x\right\|^2$                     (20)

$\begin{aligned} \operatorname{jac}(\theta)=j a c(\omega, O) & +\frac{\alpha}{2} \sum_{q=1}^{i_z-1} \sum_{n=1}^{j_z} \sum_{o=1}^{j_{z+1}}\left(\omega_q^{n, o}\right)^2 +\sum_{q=z}^{i_z-1} \sum_{y=1}^{j_z} \gamma^q V\left(U^q \| \widehat{U}_y^q\right)\end{aligned}$                          (21)

where, i_q denote total layers in the network, γ_q and U_q represents hyper parameters in q^th layer.

So, there are three processes involved in processing the deep stack auto encoder. The initialization of parameters close to a local minimum for each unique auto-encoder is first stage. Learning hidden layer activations of next auto-encoder hidden layer is second stage. Using suggested SCHHO method, the fine tuning is carried out in the third stage. Each parameter in this model is changed concurrently to improve classification outcome.

3.4.2 Training of deep stacked auto encoder using SCHHO

SCHHO method is utilized to train deep stacked auto encoder classifier for skin cancer detection. This section explains how the SCHHO algorithm was implemented. The SCHHO method is utilized to build the optimal weights, which are then used to fine-tune the deep stacked auto encoder. Skin cancer identification uses a SCHHO-based deep stacked auto encoder to recognize input photos and manage fresh images from dispersed sources. Below are the SCHHO algorithmic steps:

Step 1: Initialize solution and parameters.

$A=\left\{A_1, A_2, \ldots, A_a, \ldots A_v\right\}$             (22)

where, v is total number of solution and A_a is position of $a^{t h}$ solution.

Step 2: The solution with least Mean Square Error (MSE) is best based on fitness function, or minimization problem. Here's how to compute MSE:

 $M S E=\frac{1}{f} \sum_{g=1}^f\left[F_g-F_g^*\right]^2$           (23)

where, F_g expected output and $F_g^*$ predicted output, f represents number of data samples, where 1<g≤f.

Step 3. The SCA addresses real-world problems by avoiding local optima by investigating global optimum. SCA method is very efficient and gives higher performance while assessing solutions. It requires fewer parameters for fine tuning and has a simpler algorithmic framework. Solution update per SCA algorithm [9]:

$A^{o+1}=\left\{\begin{array}{l}A_j^o+h_1 \operatorname{Sin}\left(h_2\right) \times\left|h_3 M_j^o-A_j^o\right| ; h_4<0.5 \\ A_j^o+h_1 \operatorname{Cos}\left(h_2\right) \times h_3 M_j^o-A_j^o \mid ; h_4 \geq 0.5\end{array}\right.$                     (24)

where, r₁ indicate movement direction, r₂ determines how far movement should be towards or outwards the destination, r₃ provides random weight for destination, and r₄ helps to switch between sine and cosine components, $A_j^o$ indicate the current solution, and $M_j^o$ represent the position of destination point in j^th dimension and ||indicate absolute value.

The HHO algorithm is used to enhance algorithm performance and handle optimization problems. In accordance with HHO [10], the update equation is written as:

$A^{l+1}=A_{r a b}^l-H\left|\Delta A^t\right|$          (25)

where, $A_{r a b}^l$ represent the position of rabbit, $\Delta A^t$ indicate difference between position of rabbit and current position, and represent escaping energy of prey. The above equation is also referred as:

$A^{l+1}=A_{r a b}^l-H\left|A_{r a b}^l-A^l\right|$              (26)

Considering $A_{r a b}^l>A^l$,

$A^{l+1}=A_{r a b}^l-H\left(A_{r a b}^l-A^l\right)$          (27)

$A^{l+1}=A_{r a b}^l-H A_{r a b}^l+H A^l$          (28)

$A^{l+1}=A_{\text {rab }}^l(1-H)+H A^l$             (29)

$A_{r a b}^l=\frac{A^{l+1}-H A^l}{1-H}$               (30)

As $A_{r a b}^l$ represent the target position in HHO, and $M_j^l$ indicate destination location in SCA, both can be equated:

For h₄<0.5,

$A^{l+1}=A^l+h_1 \operatorname{Sin}\left(h_2\right) \times\left(h_3\left(\frac{A^{l+1}-H A^l}{(1-H)}\right)-A^l\right)$                    (31)

$A^{l+1}=A^l+h_1 \operatorname{Sin}\left(h_2\right) \times\left(\frac{h_3 A^{l+1}}{1-H}-\frac{h_3 H A^l}{1-H}-A^l\right)$              (32)

$A^{l+1}=A^l+h_1 \operatorname{Sin}\left(h_2\right) \frac{h_3 A^{l+1}}{1-H}-h_1 \operatorname{Sin}\left(h_2\right) \frac{h_3 H A^l}{1-H}-h_1 \operatorname{Sin}\left(h_2\right) A^l$          (33)

$A^{l+1}-h_1 \operatorname{Sin}\left(h_2\right) \frac{h_3 A^{l+1}}{1-H}=A^l(1-\left.h_1 \operatorname{Sin}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)$                (34)

$A^{l+1}\left(1-\frac{h_1 \operatorname{Sin}\left(h_2\right) h_3}{1-H}\right)=A^l\left(1-h_1 \operatorname{Sin}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)$           (35)

$A^{l+1}\left(\frac{1-H-h_1 \operatorname{Sin}\left(h_2\right) h_3}{1-H}\right)=A^l\left(1-h_1 \operatorname{Sin}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)$                  (36)

$A^{l+1}=\frac{1-H}{1-H-h_1 h_3 \operatorname{Sin}\left(h_2\right)}\left[A^l\left(1-h_1 \operatorname{Sin}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)\right]$                 (37)

Likewise for h₄≥0.5,

$A^{l+1}=\frac{1-H}{1-H-h_1 h_3 \operatorname{Cos}\left(h_2\right)}\left[A^l\left(1-h_1 \operatorname{Cos}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)\right]$               (38)

Consequently, the final update equation is written as:

$A^{l+1}=\left\{\begin{array}{l}\frac{1-H}{1-H-h_1 h_3 \operatorname{Sin}\left(h_2\right)}\left[A^l\left(1-h_1 \operatorname{Sin}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)^{\prime}\right] ; h_4<0.5 \\ \frac{1-H}{1-H-h_1 h_3 \operatorname{Cos}\left(h_2\right)}\left[A^l\left(1-h_1 \operatorname{Cos}\left(h_2\right)\left(\frac{h_3 H}{1-H}+1\right)\right)^i\right] ; h_4 \geq 0.5\end{array}\right.$              (39)

In Eq. (39), exploration and exploitation are balanced by updating cosine and sine ranges as the iteration counter grows. SCA trades off exploration and exploitation to identify the best answers.

Step 4: Recalculating error utilizing equation’s answer (23). The deep stacked auto encoder is trained to find skin cancer using method that produces the least amount of error.

Step 5: The suggested SCHHO method recomputes each solution’s error and evaluates them such that the solution with the least error is utilized to train the deep stacked auto encoder.

Step 6: Iteratively determining optimum weights till the maximum number of iterations. Table 1 shows SCHHO's pseudocode.

Table 1. Pseudo code of proposed SCHHO method