Detection and Classification of Cervical Cancer Using Adaptive Neural Architecture Search with Swarm Intelligence (ANAS-SI)

Cervical cancer is a type of cancer that occurs in the cells of the cervix which can be defined as an area at the lower part of the uterus where it connects to the vagina. It is the second most common neoplasm on the planet among women (after breast cancer) which the Food and Drug Administration contends occurs primarily in low- and middle-income countries. The main origin of cervical carcinoma [1] is the persistent infection of the cervix with high-risk types of human papillomavirus (HPV), a sexually transmitted virus. A simple computer program Artificial Intelligence (AI) using algorithms to simulate components of the brain, deep learning (DL), has recently proven to be capable in numerous applications in cervical cancer diagnosis and health care. However, DL itself does not differentiate cervical cancers, and its applications are primarily directed toward enhancing diagnostic accuracy, efficiency, and accessibility. DL models in particular, convolutional neural networks (CNNs) [2] are well established for diagnostics based on medical images. Such models can be accurately trained to detect and classify abnormal cervical images — abnormalities related to cervical cancer.

Cervical cancer is mostly of types: squamous cell carcinoma which begins in the thin flat cells that make up the outer layer lining of the cervix, and adenocarcinoma which starts in gland-like cells that line. Also, why regular pap smear is so important as early on, cervical cancer [3] does not produce any symptoms. A few of the symptoms could be unusual vaginal bleeding, pelvic pain and during intercourse which might develop if you get symptomatic.

Manual interpretation by physicians lies at the heart of traditional cervical cancer screening methods such as the Pap smear and HPV test [4]. This process is the less human intervention DL helps to reduce responsibilities from health and lessen human errors. These AI-based systems work through enormous numbers of pictures uncannily quicker than human personalities could run them and keep a steady yield, prompting early recognition and mediation — when it is most fundamental.

In principle, data augmentation methods can enhance both the quality of training data (rotation transformation, scaling transformation and flipping in image transmission network) and diversity of training data. It helps build robust models capable of generalizing to different cohort imaging properties that are driven by the clinical characteristics of a wide range of potential metabolic diseases in patients. Noises in the raw data [4] cause some minor issues, so we follow Normalized and Noise removed step [5], which helps the quality of data goes to another level and get us better results through our model’s stage.

Even in those settings that lack sufficient resources, DL models for cervical cancer detection can be executed at the minimum cost. When trained, these models could be deployed on standard computer devices in everyday clinical environments. It gives a larger portion of the populace, including those in country by and large regions, access to cutting edge indicative capacities.

Over time, the DL models get better. One can evolve studying on the maximum range of data and models far better after training because then you have all cases truly. It is why AI systems need to learn iteratively, staying in tune with evolving medical knowledge and current standards for disease diagnosis.

DL can be combined with additional AI technologies, such as Natural Language Processing (NLP) for patient record analysis and genetics-based medical history understanding, and also advanced imaging modalities like OCT and digital histopathology. These integrations allow for a comprehensive understanding of cervix cancer diagnosis and treatment, thus resulting in universal diagnostic systems [6]. In summary, this relationship between cervical cancer and DL has turned upside down the method of detecting, diagnosing and treating this disease. DL is the promise of accurate, efficient and accessible cervical cancer detection facilitated through the power of AI.

The contribution deals with medical diagnostics and Artificial Intelligence (AI), the couple has proposed work on Diagnosis and Classification of Cervical Cancer [7] which is performed using adaptive neural architecture search with swarm intelligence (ANAS-SI). As below: what and why it is important; its contributions.

ANAS-SI aims to automatically discover effective architectures for neural networks to achieve accurate classification of cervical cancer. Interface has better accuracy, which is important for early detection and intervention further leading to improved patient outcomes and life preservation. Technical terms adaptive neural architecture search (ANAS) with swarm intelligence (SI) can automatically perform model selection and hyperparameter tuning. This reduces reliance on prompt tuning and DL expertise, thereby rendering it more accessible to practitioners and researchers in a laboratory environment.

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Figure 1. Basic processing of cervical cancer

Cervical cancer Basic processing. ANAS builds a larger architecture search space than ESS by automatically adjusting the size of every architecture search layer based on certain statistics from previous search epochs (Figure 1). Which leads to finding efficient models you are on the lookout for sustainability — simply optimal Models — offering decent trade-off between being complex and performant aka Optimal cost resource utilization across other such performance metrics. The built-in classifiers are characterized by a very high adaptability in relation to the condition of high-resolution cervical images from different patient demographics. This level of flexibility is essential to create useful diagnostics that can be employed across diverse clinical environments and demographic cohorts.

By automating the detection and classification process, this can be determined with less human error (in the case) – an essential quality in medical diagnostics. It assists in getting the right and exact diagnosis with minimum variability. The ANAS-SI is an inexpensive solution to cervical cancer screening, being able to be applied on regular computing hardware. This kind of scalability makes it amenable for widespread application and especially interesting in areas that are resource-limited, where advanced diagnostics are not routinely available.

The submission work marks a significant improvement in AI [8] through demonstrating NAS powered-methods driven by SI. This approach has the potential to increase research and development in AI for a variety of applications, including medical diagnostics. The ANAS-SI framework can improve patient outcomes by enabling earlier and more accurate detection of cervical cancer. But early treatment can help to prevent its progression and mortality rate.

This enables better preventive healthcare as the framework can identify precancerous transitions. These early changes, if recognized and targeted at a pre-invasive stage, can significantly prevent the progression of cervical cancer. In summary, the method and results of this work lay the basis for future studies. We anticipate that this work expands the ANAS-SI framework to other forms of cancer and medical problems as well.

Finally, the work undertaken about finding and classifying cervical cancer using ANAS-SI can be significant in sections around human analysis, AI, and general wellbeing. If widely applied, it could improve cervical cancer screening to possibly transform patient care and outcomes on a global scale through improved accuracy, automation of model optimization, and increased access.

While the automatic classification of cervical cytology images has been greatly improved by state-of-the-art DL models, there are some major limitations. Most previous studies employ handcrafted CNN architectures, but there is a long history of work that searched across hyperparameter space to find strong CNN architectures, often on the basis of expert intuition and extensive trial-and-error hyperparameter tuning. Nonetheless, such manually optimized architectures cannot generalize well to heterogeneous cervical cell datasets with large differences in cell morphologies, staining conditions, overlapping nuclei and imaging artifacts. Furthermore, conventional NAS methods have to search in a very large space which might cause high cost and low convergence speed with plenty of GPU resources usage. These limitations restrict their practical application for medical image analysis, particularly when labeled datasets are of lower sizes.

Moving to another problem, most NAS algorithms traditionally used search methods that optimize architectures with static configurations and do not adapt the search process toward intermediate performance of learning. Consequently, many candidate architectures are optimized but in an unnecessary manner and this degrades the model search process with only a small improvement in performance. Additionally, several cervical cell classification studies mostly focus on improving only the performance of classifications without considering more efficient architecture optimization, computational efficiency promotion, and automatic model reusability.

To address these limitations, we propose an ANAS-SI framework in this paper. In contrast to traditional techniques for NAS, the proposed framework utilizes an adaptive search strategy via particle swarm optimization (PSO) in order to navigate efficiently and intelligently through the architecture search space towards promising candidate solutions. PSO guarantees a complementary mechanism that balances global exploration with local exploitation when ontology optimization process, while a validation-based optimal adaptive approach for adjusting search strategy of the adaptive part. We use a hybrid approach to dramatically reduce the expensive evaluations of architectures, accelerate convergence and find an optimized CNN architecture; devoted specifically for cervical image classification problem. Finally, the proposed framework achieves superior classification performance over NAS-based approaches at a much lower computational cost.

Examples of those works in this work, we propose an ANAS framework for automatic cervical cell image classification from Pap smear microscope images.

• It utilizes a SI one-stage optimizer based on PSO that can efficiently search the search space through our NAS architecture.

• A search adaptive component that adapts the optimization based on shorth.

• A comprehensive preprocessing pipeline including image enhancement, segmentation normalization and feature extraction in order to obtain more discrimination features before optimizing the architecture.

• Extensive experimental validations on the publicly accessible SIPaKMeD dataset show that our proposed ANAS-SI framework achieves superior classification performances compared to other prevailing DL and machine learning methods.

We propose a novel framework named ANAS-SI for cellular image analysis in cell trend detection and classification of cervical cancer. The first step is collecting and preprocessing cervical cell images, in which sample methods are applied, including histogram equalization, noise reduction, contrast enhancement, and image sharpening to improve the quality of the obtained cervical cell images. Applied segmentation algorithm is Active Contour Models (ACM) in the process of extracting site relevant features. A complete feature extraction including statistic features (Gray Level Co-occurrence Matrix (GLCM), Haralick), frequency domain properties e.g., tracing and successive scale of wavelet transform, fourier transform as well as shape and size characteristic such as moment, roundness, circularity, aspect ratio & Perimeter length and area by function only. Achieve high performance on low diversity data set with small number of samples Mostly works for clear differentiation classes outputs Descriptive Nature, Feature based method – this is also one reason that most widely used in the journal [12]. Also, the close ones by texture features like LBP, LDP, LTP and Tamura Features. In this case, colour features; (colour channels: mean, standard deviation, skewness and kurtosis); gradient.; Histogram of Oriented Gradients (HOG), scale-invariant feature transform (SIFT); contrast measure for patterns in digital images energy measure picking up efficacious vector analysis text tract from chewing bass groan agree for between location type definition type definition identify traits there are also proper location-type definitions features such as correlation measure locate help modulation steer-train displacement fractal dimension-like Zernike moments were extracted. Based on these features, the optimization is done using feature selection and dimensionality reduction techniques like Principal Component Analysis (PCA), Recursive Feature Elimination (RFE), mutual information etc.

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Figure 2. Block diagram of proposed work

Then, we employ ANAS and SI to combine ANAS-SI. Finally, the search space is made up of the components of a neural network, with performance feedback from previously evaluated architectures steering the PSO-based search process. It is trained on cervical images for pathology classification as benign or malignant, where a malignancy may be further classified into stages (mild, moderate, severe), which provides an insight for treatment planning. Performance evaluation is accomplished using distinct metrics of at-a-glance accuracy, sensitivity, specificity, precision, Positive Predictive Value (PPV), Negative Predictive Value (NPV), likelihood ratios and rates of false positive and false negative. The proposed block diagram, as shown in Figure 2.

The complete framework of the proposed ANAS-SI for cervical cancer detection and classification is shown in Figure 2, which basically consists of three main components; data acquisition ∧μ data processing, feature extraction ̸classification.

Data collection and preprocessing:

We are preprocessing cervical cell images for further visualization in the first phase. Then, we can perform histogram equalization to modify a brightness value of the image, denoising techniques to clean up any background noise from the image; contrast adjustment to amplify valuable features and minimize unwanted regions, and lastly sharpening or smoothing.

Segmentation: After pre-processing, images are segmented using ACM. Now, it filters features from the background in a better way so that we focus on only extracting the important features accurately.

Feature extraction:

Statistical features: statistical texture features extracted from GLCM and Haralick features, it describes the correlation and location of pixels in the image.

Frequency domain features: These features are computed using transformations like wavelet transforms, fourier transforms etc. which extract frequency information that is crucial to the recognition patterns in a particular image data set.

Example texture descriptors used to encode local textures for image regions: Local Binary Pattern (LBP) [13], Local Directional Pattern (LDP) [12] and Local Ternary Pattern (LTP) [11].

Classification:

- Feature selection and dimensionality reduction: Reducing part of the feature space and choosing the features that are most relevant, this can be done with techniques such as PCA, RFE or Mutual information. This leads to skillful differentiation method identifies and also reduces the computational complexity.

- PSO: A PSO is introduced for controlling the NAS. This builds a min-max combinatory run of neural networks that reach the best scores and optimizes them to become the best-run.

- Neural network components: The framework has architectures of neural network components like convolutional layers, pooling and activation functions and skip connections. Elements of a neural network model. It is essential to have these elements in order to develop a great and powerful neural network model.

Finally, train the neural network using selected features for images classification to Benign or Malignant. It also classifies malignant images (Cancer staging — mild, moderate, severe) which helps guide the appropriate treatment. The Block diagram in Figure 2 provides an organized overview of the ANAS-SI framework that demonstrates the application of different stages such as preprocess, feature extraction and classification through which our data flows. The workflow has several steps and each step is important for designing a robust system of diagnosis and classification of cervical cancer.

3.1 Data collection and preprocessing

This section discusses the data collection and preprocessing stage, which is essential for preparing the input images to extract actual features that will be used in feature extraction and classification processes in the ANAS-SI framework to improve optimal detection and classification of cervical cancer. This phase guarantees that the photos are high quality and normalised, which will enable more precise analyses in the next steps.

3.1.1 Data collection

The dataset used for this project is an online dataset, typically obtained from publicly available medical image repositories. One commonly used dataset for cervical cancer research is the https://www.kaggle.com/datasets/prahladmehandiratta/cervical-cancer-largest-dataset-sipakmed dataset.

Content and Features:

•Total Images: Approximately 4049 images.

•Origin: Images are extracted from 966 cluster cell images of Pap smear slides.

•Capture Technique: Images are acquired using a CCD camera adapted to an optical microscope.

•Categories: The dataset includes:

◦Normal cervical cells

◦Abnormal cervical cells

◦Benign conditions

•Classification: Images are categorized into five distinct classes to facilitate cervical cancer detection and classification.

3.1.2 Image preprocessing

Image preprocessing is a critical step to enhance the quality of the collected cervical cell images, ensuring they are suitable for feature extraction and analysis. The preprocessing pipeline involves several techniques to improve image clarity and highlight important features:

Histogram equalization. Histogram equalization is a technique used to improve the contrast of an image. It spreads out the most frequent intensity values, enhancing the overall contrast. The transformation function for histogram equalization is defined as:

$T(i)=\left(\frac{L-1}{N}\right) \sum_{j=0}^i h(j)$   (1)

where, $T(i)$ is the transformation function. $L$ is the number of possible intensity levels. $N$ is the total number of pixels in the image. $h(j)$ is the histogram of the image.

This process results in an image with more uniformly distributed intensity values, which helps in better visualization of features. Figure 3 shows the working of pre-processing stage.

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Figure 3. Working of pre-processing stage

Noise reduction. Reduced noise is needed to remove any background sound, such noise can only ruin the important parts of an image. Gaussian filtering, one of the common used methods that make smooth the image data by taking average of pixel values with neighbors. Secondly, we have Gaussian filter which is characterized by:

$G(x, y)=\frac{1}{2 \pi \sigma^2} \exp \left(-\frac{x^2+y^2}{2 \sigma^2}\right)$   (2)

where, $G(x, y)$ is the Gaussian function. $\sigma$ is the standard deviation of the Gaussian distribution. $x$ and $y$ are the coordinates of the pixel.

The Gaussian filter helps to reduce high-frequency noise while preserving edges, making the important features more distinguishable.

Contrast adjustment. Contrast adjustment enhances the visibility of features by adjusting the brightness and contrast of the image. One common approach is to apply a linear contrast stretch, which can be represented as:

$I_{\text {new}}=\alpha \cdot\left(I_{\text {old}}-I_{\min}\right)$   (3)

where, $I_{\text {new}}$ is the new pixel value. $I_{\text {old}}$ is the original pixel value. $I_{\text {min}}$ is the minimum pixel value in the image. $\alpha$ is a scaling factor.

This technique stretches the intensity range of the image, making the features more prominent and easier to detect.

Image sharpening. It is used to increase edges & small details of the image. A frequently used technique is the unsharp mask, which subtracts a blurred version of image from original to emphasize these edges. The unsharp mask is formally defined as:

$I_{\text {sharp}}=I_{\text {original}}+\lambda \cdot\left(I_{\text {original}}-I_{\text {blurred}}\right)$   (4)

where, $I_{\text {sharp}}$ is the sharpened image. $I_{\text {original}}$ is the original image. $I_{\text {blurred}}$ is the blurred version of the original image. $\lambda$ is the sharpening factor.

By applying all these image processing steps, we obtain pre-processed images that are appropriate for the image feature extraction and classification stages. These steps are essential to make sure the images are clear, detailed and consistent which is a very relevant property for accurate analysis in the ANAS-SI framework for cervical detection and classification.

3.1.3 Segmentation

Segmentation is an important step in the image pipeline for cervical cancer detection and classification. The segmentation task is to divide the image into informative parts, usually separating the cervical cells from its background. Among them is the ACM, or snakes, which is a method for this task. ACM is an energy minimization approach of deformable curves that are used to delineate object boundaries in images.

Active Contour Model (ACM). The ACM evolves a curve, influenced by internal forces (smoothness constraints) and external forces (image gradients), to fit the object boundary. The goal is to minimize the energy functional:

$E_{\text {snake}}=\int_0^1\left[E_{\text {internal}}(v(s))+E_{\text {external}}(v(s))\right] d s$   (5)

where, $v(s)$ is the parameterized curve. $E_{\text {internal}}$ is the internal energy. $E_{\text {external}}$ is the external energy.

Internal energy. The internal energy encourages the curve to be smooth and is defined as:

$E_{\text {internal}}(v(s))=\frac{1}{2}\left[\alpha\left|\frac{\partial v}{\partial s}\right|^2+\beta\left|\frac{\partial^2 v}{\partial s^2}\right|^2\right]$   (6)

where, $\alpha$ controls the elasticity of the curve. $\beta$ controls the rigidity of the curve. $\frac{\partial v}{\partial s}$ is the first derivative of the curve, encouraging it to be short. $\frac{\partial^2 v}{\partial s^2}$ is the second derivative of the curve, encouraging it to be smooth. Figure 4 shows the working of segmented stage in pixels.

External energy. The external energy attracts the curve towards the object boundaries based on image gradients and is defined as:

$E_{\text {external}}(v(s))=-|\nabla I(v(s))|^2$    (7)

where, $\nabla I$ is the gradient of the image. $I(v(s))$ is the image intensity at point $v(s)$.

This term is minimized when the curve is aligned with high image gradients, typically at the object boundaries.

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Figure 4. Working of segmented stage in pixels

Total energy minimization. The evolution of the curve $v(s)$ over time $t$ is governed by the Euler-Lagrange equation, derived from minimizing the total energy $E_{\text {snake}}$:

$\frac{\partial v}{\partial t}=\alpha \frac{\partial^2 v}{\partial s^2}-\beta \frac{\partial^4 v}{\partial s^4}-\nabla E_{\text {external}}$   (8)

where, the first term $\alpha \frac{\partial^2 v}{\partial s^2}$ represents the tension (first-order derivative). The second term $\beta \frac{\partial^4 v}{\partial s^4}$ represents the rigidity (second-order derivative). The third term $-\nabla E_{\text {external}}$ represents the external forces pulling the snake towards the object boundaries.

The curve is updated according to this equation iteratively until it converges to the outer boundary of the object Segmentation: Using ACM, you evolve curves in images of cervical cells until a curve-snaps to our object boundary. They are based on the idea of energy minimization, which achieves a balance between internal (smoothness constraints) and external forces (image gradients), using this to develop an accurate representation of cell boundaries. Such a segmentation step forms an indispensable part for extracting relevant features thus securing optimal classification in later stages of the ANAS-SI framework for cervical cancer detection and classification.

3.2 Feature extraction and optimization

Feature extraction is a significant process during cervical cancer detection and classification in the ANAS-SI framework. This consists of gathering features from the cropped images to classify them correctly. Statistical, frequency domain, shape and size, textural, color, gradient and other relevant features are extracted. Next, we select a subset of features and perform dimensionality reduction to enhance the classification performance.

Statistical features provide information on the intensity distribution within the image.

GLCM: This matrix measures how often pairs of pixel with specific values and spatial relationships occur in an image.

$P(i, j, d, \theta)$   (9)

where, $P(i, j, d, \theta)$ is the co-occurrence matrix for pixel values $i$ and $j$ at distance $d$ and angle $\theta$. From the GLCM, features such as contrast, correlation, energy, and homogeneity can be derived:

Contrast $=\sum_{i, j}(i-j)^2 P(i, j)$   (10)

Correlation $=\sum_{i, j} \frac{\left(i-\mu_i\right)\left(j-\mu_j\right) P(i, j)}{\sigma_i \sigma_j}$   (11)

Energy $=\sum_{i, j} P(i, j)^2$   (12)

Homogeneity $=\sum_{i, j} \frac{P(i, j)}{1+|i-j|}$   (13)

Frequency domain features capture information not visible in the spatial domain. Wavelet transform: This transform decomposes the image into various frequency components.

$W_\psi(a, b)=\frac{1}{\sqrt{a}} \int_{-\infty}^{\infty} x(t) \psi^*\left(\frac{t-b}{a}\right) d t$   (14)

where, $W_\psi(a, b)$ is the wavelet coefficient. $a$ and $b$ are scaling and translation parameters. $\psi$ is the mother wavelet. Fourier transform: This transform represents the image in terms of its sinusoidal components.

$F(u, v)=\sum_{x=0}^{M-1} \sum_{y=0}^{N-1} f(x, y) e^{-j 2 \pi\left(\frac{w x}{M}+\frac{v y}{N}\right)}$   (15)

where, $F(u, v)$ is the Fourier coefficient. $f(x, y)$ is the pixel value at $(x, y)$.

Shape and size features: These features describe the geometry and dimensions of the segmented objects. Moment: Central moments capture the shape characteristics of an object.

$\mu_{p q}=\sum_x \sum_y(x-\bar{x})^p(y-\bar{y})^q I(x, y)$   (16)

where, $\mu_{p q}$ is the central moment of order $p+q .(\bar{x}, \bar{y})$ is the centroid of the object. Roundness: Describes how closely the shape of an object approaches that of a perfect circle.

Textural features, these features describe the texture of the image regions. LBP is used to captures local texture patterns.

$\operatorname{LBP}(x, y)=\sum_{p=0}^{P-1} s\left(g_p-g_c\right) \cdot 2^p$   (17)

where, $g_c$ is the value of the central pixel. $g_p$ are the values of the surrounding pixels. $s(x)$ is a step function that outputs 1 if $x \geq 0$ and 0 otherwise

Color features, these features are derived from the color information of the image. Mean: The average color intensity.

Mean $=\frac{1}{N} \sum_{i=1}^N I_i$   (18)

where, $N$ is the number of pixels. $I_i$ is the intensity of pixel $i$. Skewness and Kurtosis: Measure the asymmetry and peakedness of the color distribution.

Skewness $=\frac{\sum_{i=1}^N\left(I_i-\mu\right)^3}{(N-1) \sigma^3}$   (19)

Kurtosis $=\frac{\sum_{i=1}^N\left(I_i-\mu\right)^4}{(N-1) \sigma^4}-3$   (20)

where, $\mu$ is the mean intensity. $\sigma$ is the standard deviation.

Gradient features: these features capture edge information. HOG: Describes the distribution of gradient orientations.

$\operatorname{HOG}(x, y)=\sum_\theta\left(\sum_{i, j}|\nabla I(i, j)| \delta(\theta-\theta(i, j))\right)$   (21)

where, $\nabla I(i, j)$ is the gradient magnitude at $(i, j) . \theta(i, j)$ is the gradient orientation

3.2.1 Feature optimization

After extracting a comprehensive set of features, the next step is to optimize them to improve classification performance and reduce computational complexity. This involves feature selection and dimensionality reduction techniques.

PCA: Reduces the dimensionality of the feature space by projecting the data onto a set of orthogonal components.

$Z=X W$    (22)

where, $Z$ is the transformed feature space, $X$ is the original feature matrix, $W$ is the matrix of principal components. RFE: Iteratively selects the most important features by training a model and removing the least important features.

$\operatorname{Rank}\left(X_i\right)=\operatorname{Model}\left(X_{-i}\right)$    (23)

where, $\operatorname{Rank}\left(X_i\right)$ is the ranking of feature $X_i, X_{-i}$ is the feature set excluding $X_i$. Mutual information: Measures the dependency between each feature and the target variable.

$I(X ; Y)=\sum_{x \in X} \sum_{y \in Y} p(x, y) \log \left(\frac{p(x, y)}{p(x) p(y)}\right)$   (24)

where, $I(X ; Y)$ is the mutual information between feature $X$ and target $Y . p(x, y)$ is the joint probability distribution. $p(x)$ and $p(y)$ are the marginal distributions.

Also, in the ANAS-SI framework for cervical cancer detection and classification, feature extraction and optimization are important step. It also extracts different types of features and tunes them with PCA, RFE, mutual information etc., to leverage the most important data into its classifications. Such global and local feature extraction through the use of regional information enables improved classification accuracy while preserving efficiency in detection and staging of cervical cancer.

3.3 Adaptive neural architecture search with swarm intelligence

ANAS-SI is a recent sophisticated model for adaptive control architecture of neural networks in tasks such as cervical cancer detection and classification. NAS and SI have been implemented through this framework to produce strong yet high performing models.

3.3.1 Neural Architecture Search

NAS is a process of automating the design of artificial neural networks. It aims to find the best performing architecture on a given task. Neural Architecture Search (NAS) is an automated design process for artificial neural networks. The objective is to discover an architecture that yields optimal performance w.r.t a task.

The NAS process can be formalized as an optimization problem:

$\mathcal{A}^*=\arg \max _{\mathcal{A} \in \mathcal{S}} \mathcal{P}(\mathcal{A})$    (25)

where, $\mathcal{A}$ represents a candidate neural network architecture. $\mathcal{S}$ is the search space of all possible architectures. $\mathcal{P}(\mathcal{A})$ is the performance of architecture $\mathcal{A}$.

The performance $\mathcal{P}(\mathcal{A})$ is often evaluated using metrics such as accuracy, loss, or computational efficiency.

3.3.2 Swarm intelligence

SI is the collective behavior of decentralized, self-organized systems which can be natural phenomena such as bird flocking or fish schooling. PSO is known to be one of the most famous SI algorithms. PSO ─ it is an optimization algorithm that keeps the population of candidate solutions, called particles and these move in the solution space to discover, which candidate solution (good particle), converges towards to optimal best so that. Each particle adjusts its position based on personal experience and on the experiences of its neighbours:

$\begin{aligned} & \mathrm{v}_i(t+1)=\omega \mathrm{v}_i(t)+c_1 r_1\left(\mathrm{p}_i-\mathrm{x}_i(t)\right)+c_2 r_2\left(\mathrm{~g}-\mathrm{x}_i(t)\right) \\ & \mathrm{x}_i(t+1)=\mathrm{x}_i(t)+\mathrm{v}_i(t+1)\end{aligned}$   (26)

where, $\mathrm{v}_i(t)$ is the velocity of particle $i$ at time $t . \mathrm{x}_i(t)$ is the position of particle $i$ at time $t . \mathrm{p}_i$ is the best position found by particle $i . \mathrm{g}$ is the global best position found by any particle. $\omega$ is the inertia weight. $c_1$ and $c_2$ are acceleration coefficients. $r_1$ and $r_2$ are random numbers between 0 and 1.

3.3.3 Adaptive neural architecture search with swarm intelligence framework

The ANAS-SI framework is a cutting-edge framework for potentizing neural network architecture to receive respective task like cervical cancer detection and classification. It uses the principles of NAS and PSO to create robust, efficient neural networks. The core of how the framework operates is through an iterative search based on performance feedback to discover optimal network designs (Figure 5).

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Figure 5. Working layers of adaptive neural architecture search with swarm intelligence (ANAS-SI) framework

The operational layers of the proposed ANAS-SI framework, shown in Figure 5, are described in the following sections:

1. Convolutional layers: Convolutional layers in ANAS-SI framework are critical since they extract the spatial information from input images. The layers perform convolution operations of different kernel sizes and numbers of filters to capture these aspects. There are different combinations of edge and back projections with convolutional layers, which is learned from the search space as the framework selects for suitable combinations.

2. Pooling layers: The pooling layers reduce the dimensionality of the feature maps, which reduces computational load and helps prevent overfitting. The framework examines a few pooling strategies like max pooling and average pooling, with different pool sizes and strides.

3. Activation functions: Activation functions add nonlinearity to the network, allowing it to learn complex patterns and relationships in the data. In the ANAS-SI search process, ReLU, Leaky ReLU, and Swish are part of activation functions used to find optimal selections for various layers.

4. Skip connections: The search space also includes skip connections which, inspired by residual networks, allow the network to skip layers and promote gradient flow across training (leading to much improved stability). Such connections are placed in a better way by the framework to increase performance.

5. Fully connected layers: Fully connected layers are used for aggregating the features extracted from previous layers and providing final predictions, they are mostly found towards the end of the network. It initializes these layers, explores their various configurations, such as how many neurons to use and dropout rates among other things.

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Figure 6. Flowchart of the proposed work

The ANAS-SI framework combines NAS and SI to enable efficient searching for quality neural network architectures. Here are the major steps involved in this process:

The steps of the proposed process are described in detail based on the workflow illustrated in Figure 6.

1. Search Space Definition: Specify the types of operations and connections that are allowed in the neural network (e.g., binary variables to select CNN operations like convolutional layers, pooling layers, activation functions and skip connections).

2. Initialization: Randomly initialize a population of particles representing candidate neural network architectures.

3. Evaluation: Using a fitness function (number of classifiers was 1 in our case; although it could be Accuracy, Loss or anything else), measure how well each candidate architecture performed.

4. Particle Update: Use PSO equations to update the position and velocity of each particle.

5. Adaptive Mechanism: Adapt the search process based on performance feedback. That include adjusting the search space, or hyperparameters while training.

6. Selection: Choose architectures that perform well and improve upon them through subsequent iterations.

7. Training and Evaluation: Train the selected neural networks on the dataset of cervical cancer and evaluate their performance.

Search Space Definition. Define a set of possible operations $\mathcal{O}$, such as convolutions, pooling, and activation functions.

Define a set of possible layer configurations $\mathcal{L}$ .

$\mathcal{S}=\{\mathcal{A} \mid\mathcal{A}$ is composed of operations from $\mathcal{O}$ and configurations from $\mathcal{L}\}$   (27)

Initialization. Initialize a population of particles, each with a random architecture.

$\mathrm{x}_i(0) \sim U(\mathcal{S})$   (28)

Evaluation. Train each architecture and measure its performance $\mathcal{P}\left(\mathrm{x}_i\right)$.

$\mathcal{P}\left(\mathrm{x}_i\right)=$ Evaluate $\left(\mathrm{x}_i\right)$   (29)

Particle Update. Update the velocity and position of each particle using the PSO equations.

$\begin{aligned} & \mathrm{v}_i(t+1)=\omega \mathrm{v}_i(t)+c_1 r_1\left(\mathrm{p}_i-\mathrm{x}_i(t)\right)+c_2 r_2\left(\mathrm{~g}-\mathrm{x}_i(t)\right) \\ & \mathrm{x}_i(t+1)=\mathrm{x}_i(t)+\mathrm{v}_i(t+1)\end{aligned}$    (30)

Adaptive Mechanism. Adapt the search process dynamically, for instance by adjusting $\omega, c_1$, and $c_2$ based on performance feedback.

$\omega(t+1)=\omega(t)-\delta$   (31)

where, $\delta$ is a decay factor.

Selection. Select the best architectures based on their performance.

$g=\arg \max _{x_i} \mathcal{P}\left(x_i\right)$     (32)

The framework contains an adaptive component that alters the search process as a result of performance feedback. This can mean tuning hyperparameters, changing the designated search area or modifying PSO parameters for a better convergence. You then choose the best-performing architectures and iterate over them. This includes reassessing the chosen architectures and fine-tuning them to achieve optimal performance. We pretrain the chosen neural networks on a complete cervical cancer dataset and assess their performance using detailed quantitative metrics. Accuracy, sensitivity, specificity and other performance metrics are evaluated for the final models.

3.4 Classification of malignant images

We will try to categorise the malignant cervical images into different stages of severity of cancer after training on the data for benign & malignant separation based on ANAS-SI framework. Such finer stratification could be crucial for treatment management and prognosis. Usually by mild moderate and severe stages. The multivariate classification is applied by the ANAS-SI framework class to classify cancer images of different stages. This part contains the process of training a neural network to learn how to discriminate between the various stages based on features from image representation. Images labelled malignant are annotated on the basis of their cancerous stage. Labels are often generated by histopathological examination and clinical data from medical experts. Once again, after performing the first stage of pre-processing and feature extraction, the complete set of features is used. Such as statistical features, frequency domain features and shape and size. In contrast to the best neural network architecture from ANAS-SI framework, proper for a multi-class classification problem (e.g., output of network is generally in softmax activation function over all classes (mild and moderate and severe) on last layer.

$\hat{y}_i=\frac{e^{z_i}}{\sum_{j=1}^c e^{z_j}}$   (33)

where, $\hat{y}_i$ is the predicted probability of class $i . z_i$ is the input to the softmax function (logits) for class $i$. $C$ is the number of classes (in this case, three: mild, moderate, severe).

Loss Function: The categorical cross-entropy loss function is used to train the network for multi-class classification. This loss function measures the difference between the predicted probabilities and the true labels.

$L=-\frac{1}{N} \sum_{i=1}^N \sum_{c=1}^C y_{i c} \log \left(\hat{y}_{i c}\right)$   (34)

where, $N$ is the number of samples. $C$ is the number of classes. $y_{i c}$ is a binary indicator (0 or 1) if class label $c$ is the correct classification for sample $i . \hat{y}_{i c}$ is the predicted probability of sample $i$ being of class $c$.

The network is trained using the labeled malignant images and the categorical cross-entropy loss function. Various optimization algorithms, such as Adam or SGD, are used to minimize the loss. The performance of the model is evaluated using metrics such as accuracy, sensitivity, specificity, precision, recall, and the F1-score for each class. Confusion matrices are also used to visualize the performance across different stages.