1. Introduction

2. Related Works

3. Proposed Method

3.2. Feature Extraction Using PCA-NGIST Method

Feature extraction is a method of converting raw data into a set of significant features that can be used for further analysis such as classification or clustering. These features reduce the dimensionality of data while making it easier to capture, process and analyse essential information. PCA-NGIST combines Gabor filters for spatial feature extraction and PCA is used for dimensionality reduction, improving image representation by focusing on key spatial patterns by reducing noise and refining computational efficiency.The PCA-NGIST method uses Principal Component Analysis (PCA) and Normalized GIST (NGIST) interpretation to extract and discard significant features from images. NGIST improves on traditional GIST by normalizing features to smooth out light and shadow variations, providing a concise representation of image directions and measurements without segmentation. PCA secure hard feature extraction and dimensionality reduction increases classification accuracy by creating a more adaptive feature set while preventing overfitting.

Let $f\left(a,b\right)$ be the 2D Gabor filter of the image in $e$ dimensions and $z$ orientations, is calculated as:

$$f\left(a,b\right)=\left(\frac{1}{2\pi {\mu }_a{\mu }_b}\right)\exp \left[-\frac{1}{2}\left(\frac{a^2}{{\mu }_a^2}+\frac{b^2}{{\mu }_b^2}\right)+2\pi n\gamma a\right]$$

(4)

Here, $\gamma$ denotes the radial frequency of the Gabor filter, $n$ is the composite number ${\sqrt{-1, \mu }}_a and {\mu }_b$ are the Gabor filter Absolute and non-orthogonal bases.

The Fourier transformation of the 2D Gabor filter function $F\left(i,j\right)$and$f\left(a,b\right)$can be expressed as:

(5)

Here ${\mu }_i$ and ${\mu }_j$ can be calculated as:

$${\mu }_i={\displaystyle \frac{1}{2}}\pi {\mu }_a\mathrm{and}{\mu }_j={\displaystyle \frac{1}{2}}\pi {\mu }_b$$

(6)

Consider $f\left(a,b\right)$ as the source function of the Gabor wavelet the transformation is obtained by setting the dictionary of the Gabor filter the orientation $\theta$ and scaling factor $\delta$ parameters are as follows:

$$f_{ez}\left(a,b\right)={\delta }^{-e}f\left(a^{\prime },b^{\prime }\right),$$

(7)

where$\delta >1, e and z$are integers Magnitude number and orientation number, $\theta =z\pi /Z$and $a^{\prime }$ ,$b^{\prime }$Calculated:

$$a^{\prime }={\delta }^{-e}\left(a\cos \theta +b\sin \theta \right)$$

(8)

$$b^{\prime }={\delta }^{-e}\left(-a\sin \theta +b\cos \theta \right)$$

(9)

Let $R$ be the number of orientations and calculate the value of $\theta$ as the$\theta =z\pi /R$. The quantity $\delta$Equations (6), (7), and (8) are designed to maximize the energy freedom.

(10)

Let $H$ be an $Z\times 512$ array of NGIST feature vectors$D_m$. A PCA unsupervised learning algorithm is used to compute the selected eigenvectors $S{J}_{512\times C}$ in a redundancy-minimized manner on these feature vectors. These eigenvectors $H_{Z\times 512}$ are then used to introduce a new small feature matrix $B_{Z\times C}$ through the following equation:

$$B_{Z\times C}=H_{Z\times 512}\cdot S{J}_{512\times C}$$

(11)

The steps of the PCA algorithm for computed $S{J}_{512\times C}$ are given: Let $Q$ be the number of hand writing/results in the training dataset $H$ of $Z$ NGIST vectors. {D₁, D₂, ⋯, D_Z, $D_m \subset \mathrm{Re}alNumber;$ each exercise belongs to the class A vector n⊂{1, 2, ⋯, R. The covariance sequence is defined as:

$$O={\displaystyle \frac{1}{Z-1}}{\displaystyle {\sum }_{m=1}^Z\left(D_m-\overline{D}\right)} \cdot {\left(D_m-\overline{D}\right)}^H$$

(12)

The vector $\overline{D}$ denoted the mean of training data vectors and is assumed as follows:

$$\overline{D}={\displaystyle \frac{1}{Z}}{\displaystyle {\sum }_{u=1}^Z{D}_m}$$

(13)

Choose from K eigenvectors$S{J}_{512\times c}$, the matrix of original eigenvectors $S{J}_{512\times 512}$ is related. The upper $C$ eigenvalues ​​result from decomposition Covariance matrix$O$, which is denoted as:

$$S{J}_{512\times c}=SJ\left(m,n\right),$$

(14)

where $m=\mathrm{1.....}, 512 and n=\mathrm{1.....}, C.$

The PCA-NGIST method for feature extraction reduces the amount of data and removes similar features. Furthermore, PCA mainly deals with linear relationships and may miss more complex connections between features. After feature extraction, the feature selection is done by using AHHO algorithm.

3.3. Features Selection Using AHHO

The Adaptive herd Horse Optimization algorithm (AHHO) helps to remove most of the redundant information by selecting the most important features. AHHO can detect and exploit non-linear relationships, improving the overall quality of features. It finds the best features for specific tasks, makes the model perform better and avoids overfitting. AHHO is inspired by the herding behavior of horses. Social behavior in horses is classified into six groups based on age: sociability among (R). As with most metaheuristic algorithms,this procedure improves the accuracy and efficiency of the subsequent classification by the IGAN_AHB classifier equation by (15)

$$Classificatio{n}^{Accuracy}={\displaystyle \raisebox{1ex}{$Nccl$}\!\left/ \!\raisebox{-1ex}{$Tns$}\right.}$$

(15)

$Nccl$ denotes the number of correct classifications and $Tns$ denotes the total number of samples in the dataset.The dimension reduction rate is determined using the equation:

$$Dimension reductio{n}_{Ratio}={\displaystyle \raisebox{1ex}{$NoSF$}\!\left/ \!\raisebox{-1ex}{$Tnf$}\right.}$$

(16)

Where $NoSF$ number of specific features and $Tnf$ indicates the total number of features in the dataset.

AHHO begins by setting and modifying control parameters such as the maximum number of repetitions and population size. At (S), hierarchy (H), sociability (S) grazing (G), defense mechanism (T), imitation (I) andboth iteration, the horses move according to equation 17.

$$C_o^{e, Age}={\overrightarrow{W}}_o^{e, Age}+C_o^{\left(e-1\right), Age},$$

(17)

A new level $o$ on the $o^{th}$ horse $e$is denoted as the $e^{th}$ iteration is signified as$C_o^{e, Age}$. The old status of$o^{th}$, there is another horse$C_o^{\left(e-1\right), Age}$. Where, velocity vector $o$referred to as the $o^{th}$horse${\overrightarrow{W}}_o^{e, Age}$.

The Herd Optimization Algorithm (HOA) operates in continuous space, while the feature selection problem operates in discrete space. To use HOA to select a feature, a continuous interval must be converted into a discrete space. A U-shaped transfer function is used in this transformation proposed method. A U-shaped transfer function is assumedd the slope) and a (the width). The function is calculated as follows: d (decline) and a (width). The function is calculated as follows:

(18)

(19)

The probability value of the U-shape is connected by the U-shape transfer function $U\left(C_{o.z}^e\right)$ . The values ​​of the elements are changed to 1 or 0 using equation (19). The movement of horses in AHHO in the adaptive-representative search space is calculated using equation (20).

$$c_i^{k+1}=\text{} c_i^k+\theta \ast \left(C_{Hors{e}_{best}}^k-C_i^k\right) i=1, 2, \mathrm{.......},N$$

(20)

Positions $i$th Horse again $k and k+1$denoted as $c_i^k$ and $c_i^{k+1}$, individually. The position of the $C_{Hors{e}_{best}}^k$ is indicated in the search space $c$, A random number $r$ is equally distributed between 0 and 1,$N$ signifies the number of horses.AHHO simulation initiates by generating a randomly generated population of horses. Every horse is in position d Denoted as$C_p=\left(C_{p1}, C_{p2}, C_{p3},\mathrm{.......},C_{pn}\right)$ where $n$represents the horse in position $p=1, 2, \mathrm{.....}, N,$$z=1, 2, \mathrm{.......}, P, U\left(0,1\right)$ generate a function on a continuously distributed random value between 0 and 1. $C_z^{\min }$$C_z^{\max }$defining the search space boundaries of the boundaries in $z$ position.

$$C_{p.z}= C_z^{\min }+\left(C_z^{\max }-C_z^{\min }\right)\ast U\left(0, 1\right)$$

(21)

Improves the overall quality of AHHO features. However, it does not classify or perform calculations based on these features alone.

3.4. Improved Generative Adversarial Networks Using Classification

Improved General Adversarial Network with Artificial Hummingbird Optimization (IGAN_AHb) classifier improves the accuracy and display of predictions by optimizing the best quality features set for better classification results.Generative Adversarial Networks (GANs) use a probability theory method to generate data. The basic architecture consists of two feed-forward neural networks: a generative model $A$ and a discriminative model$B$. In this system, the generator $A$ takes random inputs $n$ and$C\left(n\right)$ transforms them into real data $C_{Data}\left(k\right)$ usage information $A\left(n\right)$(X). A discriminator$B\left(x\right)$ checks these data points and decides whether they are true or false$A$. The generator $A$ trains the discriminator $B$ to prove that the samples it generates come from the true data distribution. Therefore, $A$ and $B$ are trained by countermeasures similar to a two-player min-max game, as shown in Equation (22).

(22)

Improved variation of GANs is proposed to solve the problem of sequence of data generated by random and unconstrained mode or basic GANs. Supplementary or conditional information $t$ is used to stabilize the generating process by being fed $t$as input to both $A$and$B$. Previous entry $n$ Attached with additional information $t$ and fed into the generator$A$, in entry $k$ is the discriminant $B$and$t$. This results in an improved version of the opposite intention.

(23)

Improved GANs face many challenges such as optimal solution problems and mode collapse problems, where the generator produces limited output types. The training may be unbalanced, leading to oscillations and failure to effectively balance the generator and discriminator. In addition, GANs are too complex for hyperparameter selections, which makes the tuning process complicated and time-consuming. Training GANs is labor intensive, demanding significant computational power and time.

In order to fine tune the proposed classifier, AHHO is used in this research. The determination of loss function is given as

$$LF={\displaystyle \frac{1}{x}}{\displaystyle \sum _{a=1}^A\left(a_x-a_x\right)}$$

(24)

where $a_x$ signify the actual value, ${a^{\prime }}_x$denote the predicted value, and $X$denotes the total number in the training set. To reduce the loss, the proposed study assumed a metaheuristic based AHHO algorithm. Figure 2 represents the GAN architecture.

3.4.1. The Artificial Hummingbird Optimizer

Artificial hummingbird optimization (AHO) enables fast and efficient convergence of GANs. This minimizes mode collapse and ensures training with consistently fine-tuned parameters. AHO simplifies hyperparameter tuning and reduces computational requirements, improving overall performance.The AHHO algorithm optimizes the parameters using the following fitness function.

$$Fitness=Maximum\left[accuracy\right]$$

(25)

The AHO, recently introduced, draws inspiration from the specialized flight and foraging behaviors of hummingbirds in nature. Just as hummingbirds select flowers based on factors such as nectar quality, content of individual flowers, nectar filling rate, and time of last visit, this biologically inspired optimization approach involves early stage selection of food sources. In the AHA optimizer, each solution vector is characterized by a food source, and the fitness value is solved by the honey replenishment rate associated with each source. Higher fitness values ​​were associated with higher honey replenishment rates. . Each “hummingbird” in the optimization is directed to a specific food source, successfully placing the hummingbird and the food source in the same location. The algorithm then remembers the positions of the food sources and their fluid replenishment rates. Hummingbirds in a population share information about their last visit to each food source and their path. A visit list table records the frequency of visits to each food source. Food sources with high visit frequencies are selected in future optimization steps.

$$q_a=Fu+rand\times \left(C_Z-Fu\right)\text{}, a=1, 2, \mathrm{.......},n$$

(26)

where, denotes $q_a$th level of the food source, $Fu$and $C_Z$ represent the minimum level, the upper hard search-space constraints, and the rand represents a random number between [0, 1]. The arrival schedule of food sources is initialized as follows:

(27)

AHO tends to have a faster convergence rate compared to traditional optimization algorithms because of its dynamic and intelligent search patterns.

The AHO model which used to fine-tune the classifier improves the classification accuracy and assists to achieve better results.

4. Result and Discussion

5. Conclusion

References

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