3.1 Facial recognition data dimensionality reduction and feature extraction based on the improved PCA

In this section, the study delves into an improved PCA-based face recognition technology aimed at improving the accuracy and robustness of recognition through advanced data reduction and feature extraction techniques. The research starts with the accurate segmentation of the input face image, which not only simplifies the recognition process but also helps to extract the key digital features in the image. Then, PCA is used to extract the features of the segmented images, which lays the foundation for the recognition process by retaining key information and reducing the data dimension. To further improve the performance of the recognition technology, beta prior is introduced and a full-probability Bayesian model is constructed, which improves the traditional PCA method. Face recognition technology is a biometric recognition method that employs computer vision to analyze face images and extract feature points, including eyes, nose, and mouth. These features are then compared with known face models to achieve accurate identity matching [17,18]. This process is the core of a face recognition system, and the detailed system flow involved is shown in Fig 1. The research and improvement method, which is based on a series of coherent technical steps, optimizes the face recognition process and enhances the stability and reliability of the system when dealing with complex environmental changes. This provides a solid technical foundation for the library FRACS.

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Fig 1. Flowchart of the face recognition system.

https://doi.org/10.1371/journal.pone.0313415.g001

As shown in Fig 1, face recognition mainly involves reading the input image, completing preprocessing according to requirements, and then segmenting the image after the preprocessing is completed. This can significantly reduce the difficulty of image recognition. There is a very close relationship between image recognition and image segmentation technology. After performing segmentation operations, the required digital features can be obtained, which can be well utilized. Segmentation is an essential aspect of image processing, and its accuracy is relevant to the effectiveness of image processing. This technology covers many types, including typical histogram correction and enhanced contour. The clarity of the image has a significant impact on the viewer’s senses. The segmentation operation is carried out combined with the relevant requirements of the research, which include the recognition and location of specific objects in the image, image editing, and synthesis. The purpose of the segmentation operation is to identify and extract the target region accurately. This requires the segmentation algorithm to have high precision and can avoid false segmentation or missing segmentation to obtain reliable results. During the segmentation process, it is necessary to first clarify the target area to ensure that the segmentation technology can be carried out in an orderly manner and meet the research needs. Next, feature extraction is carried out, usually requiring reading the features of the nose, eyes, and other parts. Then, the PCA method is used to study them and compare them with the information existing in the database. Finally, it compares the output of the results. PCA transforms the raw data into a set of orthogonal principal components through linear transformation, where each principal component is a linear combination of the raw data. These principal components are sorted according to the size of variance, thus preserving as much important information as possible from the original data. The core idea of PCA is to map high-dimensional data to a low-dimensional space while preserving the information of the original data to the greatest extent possible. Specifically, PCA determines the direction of the principal components by calculating the eigenvalues and eigenvectors of the covariance matrix, and selects the most important principal components on the ground of the size of the eigenvalues. After mapping data to low dimensional space, PCA can be used for tasks such as data visualization, classification, clustering, and noise reduction. Feature face algorithms mainly extract target features through PCA, and in general, these methods can be regarded as a type of facial image description method. Its core principle is to use transformations as the core to extract valuable facial features and obtain the required eigenvalues. Afterward, the eigenvalues are chosen to construct a lower dimensional orthogonal basis space. In addition, the face can be projected into a lower dimensional space to obtain the feature face space. After performing operations on the recognized image, it is possible to determine the distance between the feature face space and the training image. If the distance is relatively close, it indicates that the similarity between the two is relatively high, which enables efficient facial recognition. In addition, the dimensionality of the projected space is usually low, and the feature face space retains the effective information of the initial image [19]. Its assumption is that the original image is represented by p indicators, and then the initial variables are represented by X₁,X₂,…,X_P. Each variable is mainly used to represent a one-dimensional vector. At this point, p variables form a p-dimensional vector, and X = (X₁,X₂,…,X_P)′. Afterward, the mean of X can be represented by μ, mainly representing the covariance matrix corresponding to X. According to the requirements, a linear transformation is performed on X, and the comprehensive variable is generally represented by Y. Afterward, this variable is specifically shown in Eq (1).

(1)

In Eq (1), X represents the raw data matrix, where each column can represent a sample, and each row can represent a feature or variable. p represents the number of features or variables, i.e. the dimensions of the original data. μ represents the mean vector, and for each row of X, the corresponding element in μ is the mean of that row. Y represents the new variable after the linear transformation and the principal component. After linear combination, a comprehensive variable with diversity can be obtained. Therefore, to optimize the reconstruction effect, the variance of Y_i = μ_iX should be maximized, and each Y_i should have relatively high independence. The constant c is specifically shown in Eq (2).

(2)

In Eq (2), c represents a coefficient vector. u_i represents the direction of the i-th principal component, and is the transpose of u_i. X is the original data matrix, and Σ is the sum over all the features. The proportion of each variable in the total variance is constantly decreasing. In reality, components with prominent variances are usually selected to meet the requirements of dimensionality reduction. Compared to the original vector, the new vector corresponds to a relatively small number of columns and typically only selects essential data items. This can refer to the original data and effectively reduce the difficulty of data analysis, and filter out many worthless data [20]. The basic principle of PCA technology is shown in Fig 2.

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Fig 2. Two-dimensional data projection diagram.

https://doi.org/10.1371/journal.pone.0313415.g002

In Fig 2, the two axes mainly refer to two-dimensional data, while the blue dots specifically refer to two-dimensional data points, the blue line is the initial coordinates, and the red line is the coordinates after the conversion. If the data of a certain axis is projected onto the space of other axes, then it can be dimensionally reduced. Applying this method could significantly improve computational efficiency while maintaining a relatively low level of difficulty. The principle of PCA can assume that it covers N images, each with a corresponding dimension of M. Afterward, a matrix B is constructed, which is composed of N images. At this point, each row vector refers to the image. Therefore, the specification of matrix B is 5*4. The corresponding schematic diagram is shown in Eq (3).

(3)

In Eq (3), B represents the data matrix, where each row is an image sample, and each column is a feature. b_m,n is the sample in the matrix, where m is the number of samples and n is the number of features. The mean values of each column are analyzed in matrix B, and the corresponding formula is shown in Eq (4).

(4)

In Eq (4), u(m) represents the mean of the m-th column in matrix B, that is, the m-th feature. n is the number of columns of matrix B, which is the number of features. X(m,n) is the element of row m and column n in matrix B, that is, the NTH eigenvalue of the m-th sample. The expression of matrix E is shown in Eq (5).

(5)

In Eq (5), B represents the original data matrix, U represents the mean value matrix, and E represents the data matrix after centralization. The composition of U is specifically shown in Eq (6).

(6)

In Eq (6), u(M) is the mean of column M of matrix B. The covariant matrix C is shown in Eq (7).

(7)

In Eq (7), C is the covariance between random variables. The specification of the covariant matrix C is M×N. For the covariant matrix C, the following relationship is satisfied, as shown in Eq (8).

(8)

In Eq (8), λ is the eigenvalue, which is a scalar, with λ = λ₁,λ₂,…,λ_m and λ₁≥λ₂≥…≥λ_m. I is the identity matrix. A square matrix whose diagonal elements are all ones and the rest are all zeros. A square matrix represents the covariance between different random variables. The eigenvector matrix is analyzed, and the calculation process is shown in Eq (9).

(9)

In Eq (9), V is the eigenvector matrix, and V⁻¹ is the inverse of V. The expression of the feature vector D is specifically shown in Eq (10).

(10)

In Eq (10), matrix V mainly represents the eigenvector matrix, and the eigenvalues corresponding to row m are λ_m. This study selects the most applicable feature vector as the base, and in addition, the first W feature vectors can be selected, which must meet the following criteria W≤M. It projects the original N images onto the specified base, and then the first W projection values can be taken. Finally, it saves the feature parameters of each part to the database. The process of conventional PCA is shown in Fig 3.

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Fig 3. Face recognition algorithm flow based on the PCA.

https://doi.org/10.1371/journal.pone.0313415.g003

In Fig 3, the steps of conventional PCA are relatively complex, with typical examples including database establishment, facial recognition, etc. Through this diagram, the working process can also be clarified, and certain areas need to be optimized. In applying traditional algorithms, the main focus is to select important feature points from the entire face, which are not unique to the face, thus hindering the optimization of the face recognition rate. Extracting data is mainly judged based on the distance between feature vectors, rather than setting specific weights based on the importance of feature points. In this way, each feature point is usually treated equally, and in specific scenarios, the distance difference between the feature vectors is too small, which affects the recognition results. Therefore, it is necessary to improve PCA by introducing a beta before constructing a full probability Bayesian model. The expression of the improved PCA model is shown in Eq (11).

(11)

In Eq (11), z_k is the k-th diagonal element in the diagonal matrix Z, and z_k∈{0,1}, therefore it can be considered that z_k follows the Bernoulli distribution, i.e. z_k∼Bernoulli(π_k). π_k represents the probability of z_k = 1. To construct a complete Bayesian architecture, a beta prior is introduced to π_k, where π_k∼Beta(a₀,b₀). a₀,b₀ are hyper-parameters. ε is the noise component, which is usually assumed to be independent of the signal component and follows a 0 mean Gaussian distribution, i.e. ε∼N(0,γ⁻¹I). This improved PCA can automatically determine the number of principal components. The use of PCA in the study not only reduces the dimensions of the data but also helps to identify and eliminate noise and redundancy in the data, thus improving the training efficiency and classification performance of the model. The differences between different individuals can be identified more clearly through the data transformed by PCA, which provides a more accurate feature representation for subsequent classification tasks. The improved PCA makes the dimensionally reduced data more suitable for face recognition tasks.

3.2 Face recognition algorithm on the ground of ASEF and KA

In this section, an advanced face recognition algorithm that integrates the ASEF algorithm and KA is studied in detail, which is designed to significantly improve the accuracy and efficiency of face recognition. The research commences with the preprocessing of the original face image, wherein filtering technology is employed to enhance the image features and reduce the noise. This serves to establish a robust foundation for the subsequent processing. Subsequently, the ASEF algorithm is employed to precisely extract data regarding the position of the human eye, a crucial step in accurately capturing the essential characteristics of the face. To ascertain the position of the human eyes, the research further adopts the use of KA, which is an effective method of classifying images according to the pose of the face. This ensures that recognition is more accurate within the same pose category. On this basis, combined with the face shape and expression features, the Adaboost algorithm is used for the final face recognition and classification, which further improves the overall recognition performance of the system. In addition, PCA is improved to make it more suitable for data reduction and feature extraction in face recognition. The enhanced PCA technology, when integrated with image filtering techniques, not only streamlines the pre-processing of facial images but also enhances the precision of extracting human eye position data [21]. The construction process of the ASEF filter is shown in Fig 4.

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Fig 4. Construction process of ASEF filter.

https://doi.org/10.1371/journal.pone.0313415.g004

In Fig 4, the face photos are from the CelebA Face Dataset, which is an open source dataset. Dataset link: http://m6z.cn/60EW0n. The basic idea of the filtering operation is to use the value of adjacent pixels to determine the output of the current pixel and realize the image preprocessing through sliding and convolution operations. The filter with a smooth denoising function is mainly used to reduce the noise in the image and improve the image quality. The filter with edge detection function is mainly used to highlight the edge information in the image, which is helpful for the subsequent image analysis and recognition. The key steps in building an ASEF filter include processing input samples, generating composite output results, and constructing a frequency domain filter. Specifically, the input sample needs to be preprocessed first to extract the information related to the human eye position. Then, based on this information, one or more filters are constructed in the frequency domain. Finally, these filters are averaged and the average filter is obtained. This process can effectively use the feature information of the input sample to improve the accuracy and stability of human eye positioning. The idea of ASEF algorithm is for learning a filter h and then performing convolution operation with image f_i, as shown in Eq (12).

(12)

The ASEF algorithm fully utilizes the information of facial shape and expression, and can better cope with the impact of lighting changes, posture changes, and other factors on facial recognition [22]. The main steps and advantages of the ASEF algorithm are shown in Fig 5.

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Fig 5. Main steps and advantages of ASEF algorithm.

https://doi.org/10.1371/journal.pone.0313415.g005

In Fig 5, the algorithm first uses a set of labeled face images to build a Shape Model, utilizing either the Active Shape Model or the Active Appearance Model. Then, based on the face shape, the expression model is further established through the marked expression samples. In the analysis of the recognized face images, the shape and expression features are extracted. The former is determined by the position coordinates of key points, and the latter is obtained by analyzing the texture and dynamic changes of expressions. These features are then fused to form a comprehensive feature representation, which can improve the robustness of the algorithm under conditions such as illumination and attitude changes. Next, the study uses machine learning algorithms to process these comprehensive features to achieve high-precision face recognition and classification. Although the ASEF algorithm has performed well in improving recognition accuracy and adaptability, it also faces some challenges, such as its reliance on high-quality labeled data and high computational complexity. Therefore, to achieve optimal performance, it is necessary to carefully select training samples, adjust parameters, and perform appropriate preprocessing and optimization. Furthermore, the research employs the use of KA, which is capable of effectively clustering data by collecting human eye distance information and applying KA, thus further enhancing the overall performance of the face recognition system. The KA is an unsupervised learning algorithm that directly puts unlabeled datasets into the algorithm to automatically generate K clustering centers and complete clustering operations. When performing algorithm operations, the first step is to randomly select K clustering centers from the image or information, and then classify the points closest to the point into that category through clustering operations. Afterward, it repeatedly recalculates the clustering center to determine the convergence position of the function. The specific algorithm inference is shown in Eq (13).

(13)

In Eq (13), F is the minimum squared error of cluster partitioning obtained from sample clustering. The expression of u_i is shown in Eq (14).

(14)

In Eq (14), u_i is the mean vector of cluster C_i. The smaller the E, the closer the samples within the cluster are around the cluster center. The most important method used in KA is the algorithm for finding the center of the point group, which is the Euclidean distance. The n-dimensional data are taken as an example, which is shown in Eq (15).

(15)

A simple example of the KA at K = 2 is shown in Fig 6.

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Fig 6. A simple example of the KA.

https://doi.org/10.1371/journal.pone.0313415.g006

Fig 6 shows an example of a simple KA for clustering face images in a face recognition system. In this example, supposing there are multiple data points in a two-dimensional space that represent the feature vectors of different facial images. Initially, two cluster centers are randomly selected, and each cluster center attracts surrounding points based on its proximity to the data point, forming two clusters. As the algorithm iterates, the position of the cluster center is adjusted according to the average position of all points in the cluster. This process is repeated until some termination condition is met, such as a maximum number of iterations or a change in the cluster center less than a set threshold. Information entropy is employed to quantify the degree of hybridization in clustering results. A higher information entropy indicates a greater number of facial categories present within each cluster, reflecting a higher degree of hybridization. Conversely, the degree of hybridization in clustering is low. The formula is shown in Eq (16).

(16)

In Eq (16), P_mn = c_mn/c_m, and c_mn is the number of category n in the m-th cluster. c_m serves as the total of samples in the m-th cluster. The improved ASEF and KA methods first perform eye localization, and then perform KA based on the distance between the left and right eyes to achieve the effect of facial pose classification. Next, it performs identity recognition within the same pose dataset using the PCA feature extraction method, and the classifier uses the Adaboost algorithm. Adaboost algorithm iteratively combines several weak classifiers into a strong classifier to improve the accuracy and robustness of classification. The main concept is to train multiple weak classifiers on the same training set and assign varying weights based on their performance. These weak classifiers are then combined to form a strong classifier. In the process of operation, the Adaboost algorithm first assigns initial weights to the training samples and then trains the weak classifier in an iterative way. In each iteration, the algorithm trains a weak classifier based on the current sample weight and calculates its error rate. A classifier with a low error rate gets a higher weight, while a classifier with a high error rate gets a lower weight. Then, the algorithm updates the sample weights according to the error rate of the classifier, so that the misclassified samples get higher weights in subsequent iterations. PCA is responsible for extracting effective feature representations, while the Adaboost algorithm uses these features for classification and recognition. By using the features extracted by PCA and the strong classification ability of the Adaboost algorithm, the identification can be effectively carried out, and the performance and security of the system can be improved. The specific process is shown in Fig 7.

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Fig 7. Face recognition algorithm flow.

https://doi.org/10.1371/journal.pone.0313415.g007

In Fig 7, numerous facial images are first collected and artificial landmark annotations are obtained. Then, the KA is applied to classify similar facial feature patterns. By encoding facial landmark positions as feature descriptors, a feature space is created to represent different facial expressions and postures. Next, it utilizes the constructed dataset to train the facial feature localization model. By using trained models, facial landmarks can be accurately located and detected in real-time scenes. In addition, the application of KA in facial feature localization also brings some advantages. It can generate labeled training data automatically, which reduces the need for manual labor and improves the efficiency of the localization process. In addition, the proposed method can also adapt to various facial appearances and postures, making it suitable for various applications in the field of facial analysis and recognition. The access control model developed in this study aims to create a secure and user-friendly system by ensuring that only authorized users can access sensitive resources through multi-level authentication. The design of the model starts from the accurate identification of the user’s identity. On this basis, the system adopts an advanced encryption algorithm to protect the user’s data and the setting of access rights. To improve the robustness of the system, an exception detection mechanism is introduced, which can monitor the access behavior in real-time and detect and respond to potential security threats in time. In terms of user interface, the focus is on intuition and ease of use, ensuring that users can easily authenticate and access requests. At the same time, it also provides detailed user guides and help documents, so that users can quickly understand the working principle and operation method of the system. By providing clear audit logs and access records, users and administrators can track and review all access activity. Finally, the model is designed with ethical and privacy considerations in mind, ensuring that all user data processing complies with relevant data protection legislation and taking appropriate measures to protect users’ privacy rights.

4.1 Performance testing for improving PCA facial recognition

The face test set adopts the LFW dataset, with a population of 20–50 people and 2–19 images per person. The sample size increases as the number of categories increases, resulting in a total of 400 images. The LFW dataset is a widely used open source facial recognition database that contains photos of celebrities collected from the Internet. The LFW dataset is open-source. Researchers and developers are free to access and use this dataset for face detection, recognition, and other computer vision tasks. This dataset is only used in the experimental part of this study to verify the validity of the face detection technique proposed in this study. To test the performance of the improved PCA library FRACS, the accuracy, recall, and fitness of the improved PCA are compared and analyzed with those without improvement, as shown in Fig 8.

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Fig 8. Precision and recall of the improved PCA model and the PCA model.

https://doi.org/10.1371/journal.pone.0313415.g008

Fig 8A shows the accuracy and recall of the ASEF algorithm in improving PCA. It indicates that the accuracy index is relatively high, ultimately stabilizing above 0.9, and the recall index is also above 0.8. Fig 8B is the accuracy and recall rate of conventional PCA, with accuracy and recall indicators ranging from 0.7 to 0.8. This indicates that the improved PCA has a higher detection accuracy than before. To improve the accuracy of the PCA library’s FRACS, standardized testing of the system can be carried out through the ORL facial database. The study selects the first 5 images of all test individuals as the pre-stored database, and the last 5 images as the face database to be recognized. Afterward, it adjusts the dimensionality of the feature face space, allowing for standardized testing of recognition performance. This study selects 40 testers and conducts experiments with the entire group, as well as with the top 20 and top 10 testers. Afterward, the dimensionality of their feature spaces is adjusted, and the specific results obtained are shown in Table 1.

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Table 1. Spatial dimension recognition rate and recognition time of 40 subjects.

https://doi.org/10.1371/journal.pone.0313415.t001

In Table 1, the improved PCA library FARACS achieves an average recognition rate of 92.6% and an average recognition speed of 0.40 seconds. This indicates that the library’s FRACS has a high recognition rate and fast recognition speed. To provide a more intuitive and clear observation of the recognition speed and rate of the improved PCA library FRACS, a comparison is conducted between the improved PCA library FRACS and the conventional PCA library FRACS. The bar graph of recognition speed and recognition rate is shown in Fig 9.

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Fig 9. Recognition speed and recognition rate histogram.

https://doi.org/10.1371/journal.pone.0313415.g009

Fig 9A and 9B represents the recognition rate and recognition speed under different feature face spatial dimensions. The recognition rate and speed of the improved PCA is higher than before, about 10% higher and 1 second faster. This indicates that the improved PCA has higher detection accuracy and better performance. To better demonstrate the recognition effect of the improved PCA library FRACS, this study introduces a multi-recognition confusion matrix to further quantitatively analyze the recognition effect. The average confusion matrix results of the improved PCA and conventional PCA are shown in Fig 10.

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Fig 10. The average confusion matrix of PCA and the improved PCA.

https://doi.org/10.1371/journal.pone.0313415.g010

In Fig 10A is the confusion matrix of the improved PCA, and 10b is the confusion matrix of the conventional PCA. The improved PCA has identified more positive cases than the conventional PCA, with 13 actual positive cases compared to 7 in the conventional PCA. This indicates that the recognition accuracy of improved PCA is higher than that of conventional PCA. This study considers multiple poses and selects 20 samples to analyze the positioning error of the ASEF algorithm in improving PCA under different angles and lighting conditions, as shown in Table 2.

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Table 2. ASEF algorithm improving the localization error of PCA algorithm.

https://doi.org/10.1371/journal.pone.0313415.t002

As evidenced by the experimental results presented in Table 2, a reduction in angle, or a closer positioning of the face to the front, is associated with a diminished positioning error. This observation suggests that the algorithm demonstrates enhanced accuracy in processing face images that are oriented toward the front or close to it. On the contrary, when the Angle increases and the face gradually turns to the side, the difficulty of positioning increases, resulting in greater errors. Under extreme lighting conditions, the positioning error of ASEF-improved PCA is relatively high regardless of the worst or best lighting. This is because the lighting conditions have a significant impact on the contrast of the image and the clarity of the features, thus affecting the accuracy of the positioning. However, even under these extreme conditions, the positioning error remains within the acceptable range, which indicates that the algorithm has a certain degree of robustness.

4.2 Performance comparison of different face recognition algorithms and comparison of different clustering methods

To demonstrate the performance of Improved PCA more scientifically, this study compares it with Linear Discriminant Analysis (LDA) facial recognition algorithm, Subspace Facial Recognition Algorithm Combining Global and Local Features (GF-SSFR), Two-dimensional Gabor Wavelet Based Facial Recognition Algorithm (Gabor2D-FR), and Circular Symmetric Gabor Transform Facial Recognition Algorithm (CSGT-FR). The accuracy comparison is shown in Fig 11.

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Fig 11. Comparison of accuracy of different methods.

https://doi.org/10.1371/journal.pone.0313415.g011

In Fig 11, the Improved PCA has the highest accuracy, reaching a maximum of 96%. PCA is a highly accurate facial recognition algorithm, surpassing other methods. This suggests that PCA is an excellent choice for facial recognition, especially after further research and improvement. The average accuracy of the five algorithms is compared, and the results are shown in Fig 12.

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Fig 12. Evaluation accuracy between different models.

https://doi.org/10.1371/journal.pone.0313415.g012

In Fig 12, the average accuracy of LDA for facial recognition of 20 samples is 83%, GF-SSFR has an average accuracy of 90%, Gabor2D-FR possesses an average accuracy of 88%, and CSGT-FR has an average evaluation accuracy of 89%. The average evaluation accuracy of Improved PCA is 96%, which is higher than the average evaluation accuracy of all four models. The results show that the improved PCA algorithm has significant performance advantages in face recognition. This performance improvement is due to the improved PCA algorithm’s stronger ability in feature extraction and data dimensionality reduction, which more effectively captures key features of the face and reduces the interference of noise and irrelevant variables. The improved PCA face recognition algorithm has better recognition performance in the compared models, which provides an effective solution for face recognition technology. The Improved PCA and LDA algorithms are combined with the KA before and after improvement, and compared with the Densit-based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The comparison results of information entropy are shown in Fig 13.

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Fig 13. Comparison of information entropy.

https://doi.org/10.1371/journal.pone.0313415.g013

In Fig 13, as the number of samples increases, the information entropy of each algorithm also increases. Information entropy is an index to measure the confounding degree of clustering effect. The higher the information entropy, the greater the uncertainty of clustering results, that is, the more chaotic the distribution of samples in clustering results. When algorithms are combined with DBSCAN, their information entropy is lower than that when they are combined with KA. The results demonstrate that, in the context of face recognition applications, the KA is capable of generating lower information entropy than the DBSCAN algorithm. This indicates that the KA is more effective than the DBSCAN algorithm in classifying samples into their corresponding categories during the clustering process, thereby reducing the uncertainty and clutter associated with classification. In particular, the improved PCA algorithm has the highest information entropy when combined with the KA. This indicates that the method employed in conjunction has the most optimal performance among all the evaluated algorithms, exhibiting the highest classification accuracy and the lowest degree of classification confounding. This combined method can effectively classify face samples into correct categories, reduce the possibility of misclassification, and improve the reliability of the face recognition system. The method in reference [7] is quite accurate, so it is compared with the method in this study to compare its accuracy and model complexity, as shown in Fig 14.

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Fig 14. Comparison between the methods in reference [7] and the research methods.

https://doi.org/10.1371/journal.pone.0313415.g014

In Fig 14, the accuracy of the method in reference [7] is higher than that in this study, but the model complexity is correspondingly higher. In the method proposed in the reference [7], a convolutional neural network is used for pre-processing, feature extraction, and face recognition, and the Softmax operator is used as the classifier. The face recognition and classification of the input images are completed using the fully connected layer of the convolutional neural network, the classification function is learned using the fully connected layer of the network, and the output is classified using the Softmax layer. Such complex models may be able to better capture the inherent laws and patterns of the data, resulting in greater accuracy on the test data. Although the method in reference [7] shows advantages in terms of accuracy, higher model complexity may also bring some negative effects. More sophisticated models often demand greater computational resources and longer training and reasoning times, which can make deployment in real-world applications challenging or result in sub-optimal real-time performance. In addition, complex models are also more prone to over-fitting, that is, over-fitting training data and poor generalization ability. The statistical test of PCA face recognition system before and after improvement is shown in Table 3.

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Table 3. Statistical test table of PCA face recognition system before and after improvement.

https://doi.org/10.1371/journal.pone.0313415.t003

In Table 3, the standard deviation of PCA after improvement is 4.8%, which is slightly lower than 5.2% before improvement, indicating that the improved system performs more stable in different tests and the recognition rate fluctuates less. The confidence interval of the improved system is narrow, which indicates that the estimation of the improved recognition rate is more accurate and the reliability of the system performance is higher. The p-value before and after the improvement is less than 0.001, indicating that the improvement effect is statistically significant.