# Deep Learning Based Face Recognition Method using Siamese Network

Enoch Solomon  Department of Computer Science
Virginia State University
Richmond, Virginia
<EMAIL_ADDRESS>Abraham Woubie  Silo AI
Helsinki, Finland
<EMAIL_ADDRESS>Eyael Solomon Emiru  Department of Information
Engineering and Computer Science
University of Trento, Italy
<EMAIL_ADDRESS>
###### Abstract

Achieving state-of-the-art results in face verification systems typically
hinges on the availability of labeled face training data, a resource that
often proves challenging to acquire in substantial quantities. In this
research endeavor, we proposed employing Siamese networks for face
recognition, eliminating the need for labeled face images. We achieve this by
strategically leveraging negative samples alongside nearest neighbor
counterparts, thereby establishing positive and negative pairs through an
unsupervised methodology. The architectural framework adopts a VGG encoder,
trained as a double branch siamese network. Our primary aim is to circumvent
the necessity for labeled face image data, thus proposing the generation of
training pairs in an entirely unsupervised manner. Positive training data are
selected within a dataset based on their highest cosine similarity scores with
a designated anchor, while negative training data are culled in a parallel
fashion, though drawn from an alternate dataset. During training, the proposed
siamese network conducts binary classification via cross-entropy loss.
Subsequently, during the testing phase, we directly extract face verification
scores from the network’s output layer. Experimental results reveal that the
proposed unsupervised system delivers a performance on par with a similar but
fully supervised baseline.

###### Index Terms:

biometrics, deep learning, face recognition, siamese network, unsupervised
method

##  I Introduction

In today’s increasingly digital world, safeguarding personal information and
ensuring security has become a top priority [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].
One of the most cutting-edge technologies addressing this concern is face
verification, a powerful tool that leverages facial recognition to
authenticate individuals [11]. This technology offers immense potential across
various industries, from financial services to law enforcement, and even
everyday consumer applications.

Deep learning methods are successful in image application specifically in face
recognition [12, 13, 14, 15, 16]. These approaches excel in learning deep
features and bottleneck features (BNF) [17], which are used within a
conventional GMM-UBM framework [18]. However, these deep learning approaches
typically rely on labeled training data.

The authors in [19] reported that PLDA is the efficient back-end for image
recognition [20, 19]. Previous works reported PLDA provide a superior
performance than cosine scoring. But, this improvement comes with the cost of
labeled training data. However, previous works show that it is not usually
easy to have access to large amounts of labeled training data. Thus, the lack
of labeled training data results in a significant performance gap between
cosine and PLDA scoring techniques [21, 22] in face recognition. Although the
authors in [23] proposed automatic labeling techniques, they could not
appropriately estimate the true labels. Although these approaches perform
reasonably well, the results are still compared to that PLDA that uses actual
labels [24]. Whereas, the authors in [25] proposed autoencoder based
unsupervised method improve the performance of face recognition systems.
Previous studies show that these approaches mainly aim at increasing the
discriminative power of face image embeddings. Thus, they can be applied as a
back-end in face verification task.

In our proposed work, the main goal is to reduce the reliance on labeled
training data for a face verification system. We aim to obtain end-to-end face
verification scores without using face image labels. We propose a siamese
network [26] consisting of double-branch networks, each with two branches that
are CNN encoders. These encoders are inspired by the VGG architecture and
adapted for face verification [27]. Traditionally, Siamese networks are
trained using pairs of training samples, such as anchor-positive and anchor-
negative pairs. However, to avoid using face image labels, we generate these
training sample pairs in an unsupervised manner. Positive training data are
chosen within one dataset based on their highest cosine scores with the anchor
sample. In contrast, negative training data are selected in a similar manner
from another dataset, ensuring that the two datasets do not include face
images from the same identity.

In our study, we introduced the utilization of a two branch Siamese network.
The network processes positive and negative samples, individually paired with
anchor samples, and computes the binary cross-entropy loss based on their
binary labels. Following the training process, decision scores for face
verification trials are derived from the last layer of the network, resulting
in an end-to-end face verification system. Our evaluation was performed on the
Labeled Faces in the Wild (LFW) dataset [28]. Despite being unsupervised, our
results show significant promise, approaching the performance of a fully
supervised baseline.

The remainder of this paper is organized as follows: Section 2 explains the
proposed method, Section 3 provides details on the experimental setup and
data, Section 4 discusses the results, and we conclude in Section 5.

##  II Proposed Method

The training of a DNN in an end-to-end fashion typically requires access to
labeled training data, which can be challenging in real-world scenarios. To
address this, especially when labeled data is unavailable, we propose the use
of siamese networks [26], characterized by a double-branch architecture. Each
branch features a CNN encoder that is motivated by the VGG network [29], which
has recently shown promise in face verification [30]. Given our objective of
avoiding reliance on face image labels, we introduce a novel approach to
generate pairs of training data in an unsupervised manner [31, 32].
Specifically, positive training data are chosen within one dataset based on
their similarly score with the anchor. Similarly, negative training data are
selected using the same criterion, but from a separate dataset, ensuring that
the two datasets do not contain face images from the same identity. This
innovative training methodology circumvents the need for labeled data, making
the process more accessible and adaptable to real-world scenarios.

The proposed work utilizes a siamese network. It is trained by minimizing
binary cross-entropy loss. This network selects the pair of negative-anchor
and positive-anchor face images samples, and processes them to generate binary
labels of 1 (positive match) or 0 (negative match) at the output. These labels
are used to compute the loss during training. Once the network is trained, we
can obtain decision scores for face recognition evaluations directly from the
network’s output. In summary, our proposed siamese network constitutes an end-
to-end face recognition system, capable of making binary classification
decisions with respect to facial similarity.

Figure 1: The architecture of the proposed siamese network. FC denotes fully
connected layer. In evaluation phase, decision scores for face recognition are
obtained directly from the last layer of the network. This layer computes the
final representation of the features extracted from the input face images,
which is then used to make binary classification decisions regarding facial
similarity.

0: Training face images $t_{i}$, 1 ¡ i ¡ n, $x_{i}\in X$ and $y_{i}\in Y$,
$1\leq i\leq n$, and threshold

0: Positive and Negative face images $P_{ij}$ and $N_{ij}$, $1\leq i\leq m$
and $1\leq j\leq k$

for each training face image $x_{i}$ do

for each training face image $x_{p}$, 1 ¡ p ¡ m do

Compute Positive Scores
${}_{i,p}=\operatorname{cosine}\left(x_{i},x_{p}\right)$

1 end for

2From Positive Scores i,p, select $k$ highest face images.

3if Positive Scores i,p ¡ threshold

4 $P_{i,j}=x_{p}$

for each training face image $y_{m}$, 1 ¡ n ¡ m do

Compute Negative Scores
${}_{i,n}=\operatorname{cosine}\left(y_{i},y_{n}\right)$

5 end for

6From Negative Scores i,n, select $k$ highest face images.

7if Negative Scores i,n ¡ threshold

$N_{i,j}=y_{n}$

end for

Algorithm 1 The proposed algorithm to select positive and negative face images
for each face image in the training dataset.

###  II-A Training Pairs Selection

The procedure for selecting negative and positive images involves utilizing
two datasets, denoted as X and X. Let $C_{X}$ and $C_{Y}$ represent the
individuals in datasets X and Y, respectively. It’s assumed that individuals
in dataset X are distinct from those in dataset Y, i.e., $C_{X}\cap
C_{Y}=\phi$. Algorithm 1 provides an overview of how the selection of negative
and positive face image vectors is conducted in an unsupervised manner.

To begin, we extract the face embedding vectors for all face images in
datasets X and Y. Next, we compute similarity scores among all face embedding
vectors within dataset X by using cosine distance metrics. For each face
embedding vector in X, we select a fixed number $k$ of neighbor face embedding
as a potential positive face embeddings. Subsequently, we introduce a
threshold to select potential $k$ positives face images.

To select the negative face image embeddings, we score all the face embeddings
in $X$ with those in $Y$, by using cosine similarity scores. For each face
embedding in $X$, we select $k$ number of face embeddings from $Y$ that by
using their cosine distance scores. Given that the person in dataset $X$ does
not appear in dataset $Y$, the $k$ selected face embeddings are considered
potential negative face images. Subsequently, we apply a threshold to their
corresponding cosine scores to identify the most challenging negative face
images. This process ensures that each face embedding in $X$ is paired with
$k$ most positive and $k$ negative face image embeddings.

Assuming there are $n$ face images in each dataset $X$ and $Y$, then we will
have a total of n plus n times k face image training data. For example, if we
have 100 training data in each datasets with k=10, then we will have
(100+100)*10 = 1000 training data. This way, we were able to increase
intrinsically the number training dataset. In our experiments, training pairs
consist of two samples, namely anchor-positive and anchor-negative.

To select the negative face embedding vectors, we compute cosine similarity
scores between all face embedding vectors in set $X$ and those in set $Y$. For
each face embedding vector in $X$, we choose $K$ face embedding vectors from
$Y$ that have the closest scores. Given that individuals in $X$ do not appear
in $Y$, these $K$ selected face embeddings represent potential negative face
images. Subsequently, we apply a threshold to the corresponding cosine scores
to identify the most challenging negatives face images among them. As a
result, each face embedding vector in $X$ is assigned $K$ positive and $K$
negative face embedding vectors.

###  II-B Proposed Siamese Network

The training of a DNN in an end-to-end manner usually requires labeled face
images for the training data, which can be challenging to obtain in practical
scenarios. When such labels are unavailable, we propose the use of siamese
networks. These networks operate in a fully unsupervised manner,
distinguishing them from a typical DNN classifiers. Traditionally, a siamese
network is trained using pairs of samples, consisting of an anchor, a
positive, and negative. To bypass the need for face image labels, we propose
generating these training pairs in an unsupervised manner, which are then fed
into the network. Specifically, we advocate for a siamese network utilizing
binary cross-entropy loss. Following the training process, we extract decision
scores from the output of the proposed network for the evaluation. This
approach allows us to perform face verification in an unsupervised manner.

###  II-C End-to-End Face Verification System

Figure 1 depicts the architecture of the proposed siamese network. This
network comprises two identical branches, both acting as CNN encoders. During
training, a pair consisting of an anchor face image along with either a
positive or negative face image is inputted into each branch of the network
respectively. These two branches share the same parameters. Following the CNN
encoder, the encoded vectors output from the two branches are concatenated.
Then, the concatenated vector is fed into the FC layers. The last layer is a
binary class layer. It will be one for the case of anchor and positive face
images, whereas it will be zero for the case of anchor and negative face
images. Throughout the training process, the network minimizes binary cross-
entropy loss.

After training with selected positive and negative samples in an unsupervised
manner, evaluations are conducted in an end-to-end way. During evaluation,
airs of test face images are inputted into the network, and decision scores
are directly obtained from the last layer. This approach establishes an
unsupervised end-to-end face verification system using the proposed Siamese
network.

###  II-D DNN Encoder

The DNN encoder block draws inspiration from the VGG architecture [33], which
has been recently tailored for face verification in [27]. This encoder is
structured with three primary blocks, with each block comprising two
convolutional layers and one max-pooling layer. Following these blocks, there
are two Fully Connected (FC) layers, having 1024 and 300 neurons,
respectively. The function of the DNN encoder is to encode the input face
image, reducing it to a 300-dimensional vector.

##  III Experimental Setup and Dataset

###  III-A Experimental Setup

The training phase utilized the CelebA dataset [34], while the evaluation was
conducted on the Labeled Faces in the Wild (LFW) dataset [28]. The performance
metrics assessed were EER and accuracy.

During the selection of positives and negatives, we divided the validation
partition of the CelebA dataset into two equal parts, creating datasets
denoted as A and B, as explained previously. The CNN encoder was identical for
both networks. The threshold values for the selection of positive and negative
samples were 0.3 and 0.1, respectively. The activation function used for both
the DNN and fully connected layers was ReLU, while the final layer of the
network employed sigmoid activation function. The network is trained for 300
epochs or until the error is no longer decreasing using a batch size of 64
images. It uses stochastic gradient descent, momentum of 0.91, weight decay of
0.00001 and a logarithmically decaying learning rate from $10^{-2}$ to
$10^{-8}$.

The baseline system underwent training utilizing the entire validation
partition of the CelebA dataset. Its architecture entails a DNN encoder
followed by a classification layer. To ensure an equitable comparison, the
architecture of the CNN encoder was precisely replicated from that of the
siamese networks. The training process involved minimizing cross-entropy loss,
employing the Adam optimizer with identical parameters as those in the siamese
networks. During evaluation, face image embeddings were extracted from the CNN
encoder of this network.

###  III-B Datasets

The CelebA dataset [34], initially introduced by Liu et al., comprises a vast
collection of over 200,000 face images showcasing 10,177 celebrities. This
dataset incorporates various elements like pose variations and background
clutter, offering a comprehensive representation of real-world scenarios. To
facilitate model training and evaluation, the dataset is divided into distinct
sets for training, validation, and testing purposes. In this work, we utilized
the training, validation, and test segments of the CelebA dataset as our
unlabeled dataset for training the autoencoder.

The Labeled Faces in the Wild dataset (LFW) [28] is a compilation of 13,233
images, featuring 5,749 distinct individuals. For testing, the dataset is
randomly and uniformly divided into ten subsets. Each subset consists of 300
matched pairs (depicting the same person) and 300 mismatched pairs (depicting
different individuals), which results in a total of 3,000 matched pairs and
3,000 mismatched pairs used for testing [28].

TABLE I: It presents a comparison of the proposed method with different values of k and the baseline methods. The evaluation metrics used is Equal Error Rate (EER). The results demonstrate the performance of the proposed method across various k values, showcasing its effectiveness compared to the baseline methods. Model |  k |  EER
---|---|---
Baseline | - | 7.93
Proposed | 2 | 7.91
Proposed | 5 | 7.83
Proposed | 10 | 6.90
Proposed | 12 | 7.01
Proposed | 15 | 8.02

##  IV Results

###  IV-A Results on LFW

In Table I, we present a comprehensive comparison between our proposed systems
and the baseline, evaluating them based on the Equal Error Rate (EER)
expressed as a percentage. The table encompasses results for different values
of $k$. Throughout the experimental trials, face recognition scores are
extracted from the output of the proposed network. The findings reveal that
increasing the value of $k$ leads to enhanced system performance. The optimal
EER of was achieved when $k$ was set to 10. While higher values of $k$ were
explored, no significant improvement has been observed, suggesting a balance
between performance and computational cost. This underscores the promising
potential of the proposed approach, particularly in unsupervised scenarios,
demonstrating its effectiveness in face verification tasks without the
reliance on labeled training data.

Table II provides a comprehensive comparison between our proposed method and
state-of-the-art approaches. It’s important to note that our method is
compared with both supervised and unsupervised training techniques. Notably,
our proposed training method demonstrates competitive performance without the
need for an extensive labeled dataset. While some methods like ArcFace,
GroupFace, Marginal Loss, and CosFace exhibit slightly higher accuracy, it’s
worth highlighting that our approach is trained on a significantly smaller
dataset (approximately 200K images), whereas most state-of-the-art methods
rely on millions of training images. This showcases the efficiency and
effectiveness of our proposed method, especially in scenarios where labeled
data is limited.

TABLE II: Comparison of the proposed method result with some of state-of-the-art methods on LFW testing dataset. Model |  Training size |  Labeled/ Unlabeled |  Testing size |  Accuracy(%)
---|---|---|---|---
UniformFace | 6.1M | Labeled | 6K | 99.80 [35]
ArcFace | 5.8M | Labeled | 6K | 99.82 [36]
GroupFace | 5.8M | labeled | 6K | 99.85 [37]
CosFace | 5M | Labeled | 6K | 99.73 [22]
Marginal Loss | 4M | Labeled | 6K | 99.48 [38]
CurricularFace | 3.8M | Labeled | 6K | 99.80 [39]
RegularFace | 3.1M | Labeled | 6K | 99.61 [40]
MDCNN | 1M | Labeled | 6K | 99.38 [41]
PSO AlexNet TL | 14M | Labeled | 6K | 99.57 [42]
Ben Face | 0.5M | Labeled | 6K | 99.20 [43]
F2C | 5.8M | Labeled | 6K | 99.83 [44]
PCCycleGAN | 0.5M | Unlabeled | 6K | 99.52 [45]
CAPG GAN | 1M | Unlabeled | 6K | 99.37 [46]
UFace | 200K | Unlabeled | 6K | 99.40 [31]
Proposed | 200K | Unlabeled | 6K | 99.67

##  V Conclusion

In this work, we introduced a siamese network for face verification that
operates without the reliance on labeled data. This network features two
branches, each functioning as a CNN encoder, and was trained as a binary
classifier. Given our objective of avoiding the need for face image labels,
the training sample pairs were generated using an unsupervised approach.
Positive training images were selected within a single dataset based on the
highest cosine scores with a designated anchor, while negative training images
followed the same selection criteria but were drawn from a different dataset.

Following the training process, decision scores were obtained using the
proposed network, and the evaluation was conducted using the LFW dataset.
Notably, our experimental results demonstrated that our proposed system,
despite being unsupervised, achieved results that closely paralleled those of
fully supervised baselines. This highlights the effectiveness of our approach
in face verification, even in the absence of labeled data.

## References

  * [1] Kumar, J. & Patel, D. A survey on internet of things: Security and privacy issues. International Journal Of Computer Applications. 90 (2014)
  * [2] Solomon, E. & Cios, K. FASS: Face Anti-Spoofing System Using Image Quality Features and Deep Learning. Electronics. 12, 2199 (2023)
  * [3] Solomon, E. & Cios, K. HDLHC: Hybrid Face Anti-Spoofing Method Concatenating Deep Learning and Hand-Crafted Features. 2023 IEEE 6th International Conference On Electronic Information And Communication Technology (ICEICT). pp. 470-474 (2023)
  * [4] Chekole, E., Chattopadhyay, S., Ochoa, M., Guo, H. & Cheramangalath, U. CIMA: Compiler-Enforced Resilience Against Memory Safety Attacks in Cyber-Physical Systems. Computers & Security. 94 pp. 101832 (2020), https://www.sciencedirect.com/science/article/pii/S0167404820301061
  * [5] Chekole, E., Ochoa, M. & Chattopadhyay, S. SCOPE: Secure Compiling of PLCs in Cyber-Physical Systems. International Journal Of Critical Infrastructure Protection. 33 pp. 100431 (2021), https://www.sciencedirect.com/science/article/pii/S1874548221000238
  * [6] Chekole, E. & Huaqun, G. ICS-SEA: Formally Modeling the Conflicting Design Constraints in ICS. Proceedings Of The Fifth Annual Industrial Control System Security (ICSS) Workshop. pp. 60-69 (2019), https://doi.org/10.1145/3372318.3372325
  * [7] Chekole, E., Castellanos, J., Ochoa, M. & Yau, D. Enforcing Memory Safety in Cyber-Physical Systems. Computer Security. pp. 127-144 (2018)
  * [8] Chekole, E., Chattopadhyay, S., Ochoa, M. & Huaqun, G. Enforcing Full-Stack Memory-Safety in Cyber-Physical Systems. Engineering Secure Software And Systems. pp. 9-26 (2018)
  * [9] Chekole, E., Thulasiraman, R. & Zhou, J. EARIC: Exploiting ADC Registers in IoT and Control Systems. Applied Cryptography And Network Security Workshops. pp. 245-265 (2023)
  * [10] Wong, A., Chekole, E., Ochoa, M. & Zhou, J. On the Security of Containers: Threat Modeling, Attack Analysis, and Mitigation Strategies. Computers & Security. 128 pp. 103140 (2023), https://www.sciencedirect.com/science/article/pii/S0167404823000500
  * [11] Kumar, N., Berg, A., Belhumeur, P. & Nayar, S. Attribute and simile classifiers for face verification. 2009 IEEE 12th International Conference On Computer Vision. pp. 365-372 (2009)
  * [12] Serengil, S. & Ozpinar, A. Lightface: A hybrid deep face recognition framework. 2020 Innovations In Intelligent Systems And Applications Conference (ASYU). pp. 1-5 (2020)
  * [13] Abraham Woubie and Tom Bäckström: Federated learning for privacy-preserving speaker recognition, In IEEE Access, 2021; pp. 149477–149485.
  * [14] Abraham Woubie and Tom Bäckström: Voice-quality Features for Deep Neural Network Based Speaker Verification Systems, In 29th European Signal Processing Conference (EUSIPCO), 2021; pp. 176–180.
  * [15] Abraham Woubie and Tom Bäckström: Federated Learning for Privacy Preserving On-Device Speaker Recognition, In ISCA Symposium on Security and Privacy in Speech Communication, 2021; pp. 1–5.
  * [16] Abraham Woubie, Pablo Zarazaga and Tom Bäckström: The Use of Audio Fingerprints for Authentication of Speakers on Speech Operated Interfaces, In ISCA Symposium on Security and Privacy in Speech Communication, 2021; pp. 6–9.
  * [17] Prasad, P., Pathak, R., Gunjan, V. & Ramana Rao, H. Deep learning based representation for face recognition. ICCCE 2019: Proceedings Of The 2nd International Conference On Communications And Cyber Physical Engineering. pp. 419-424 (2020)
  * [18] Mallouh, A., Qawaqneh, Z. & Barkana, B. New transformed features generated by deep bottleneck extractor and a GMM–UBM classifier for speaker age and gender classification. Neural Computing And Applications. 30 pp. 2581-2593 (2018)
  * [19] Ioffe, S. Probabilistic linear discriminant analysis. Computer Vision–ECCV 2006: 9th European Conference On Computer Vision, Graz, Austria, May 7-13, 2006, Proceedings, Part IV 9. pp. 531-542 (2006)
  * [20] El Shafey, L., McCool, C., Wallace, R. & Marcel, S. A scalable formulation of probabilistic linear discriminant analysis: Applied to face recognition. IEEE Transactions On Pattern Analysis And Machine Intelligence. 35, 1788-1794 (2013)
  * [21] Hafed, Z. & Levine, M. Face recognition using the discrete cosine transform. International Journal Of Computer Vision. 43 pp. 167-188 (2001)
  * [22] Wang, H., Wang, Y., Zhou, Z., Ji, X., Gong, D., Zhou, J., Li, Z. & Liu, W. Cosface: Large margin cosine loss for deep face recognition. Proceedings Of The IEEE Conference On Computer Vision And Pattern Recognition. pp. 5265-5274 (2018)
  * [23] Gao, Y., Ma, J. & Yuille, A. Semi-supervised sparse representation based classification for face recognition with insufficient labeled samples. IEEE Transactions On Image Processing. 26, 2545-2560 (2017)
  * [24] Muslihah, I. & Muqorobin, M. Texture characteristic of local binary pattern on face recognition with probabilistic linear discriminant analysis. International Journal Of Computer And Information System (IJCIS). 1, 22-26 (2020)
  * [25] Hammouche, R., Attia, A., Akhrouf, S. & Akhtar, Z. Gabor filter bank with deep autoencoder based face recognition system. Expert Systems With Applications. 197 pp. 116743 (2022)
  * [26] Chen, X. & He, K. Exploring simple siamese representation learning. Proceedings Of The IEEE/CVF Conference On Computer Vision And Pattern Recognition. pp. 15750-15758 (2021)
  * [27] Cheng, S. & Zhou, G. Facial expression recognition method based on improved VGG convolutional neural network. International Journal Of Pattern Recognition And Artificial Intelligence. 34, 2056003 (2020)
  * [28] Huang, G., Mattar, M., Berg, T. & Learned-Miller, E. Labeled faces in the wild: A database forstudying face recognition in unconstrained environments. Workshop On Faces In’Real-Life’Images: Detection, Alignment, And Recognition. (2008)
  * [29] Sengupta, A., Ye, Y., Wang, R., Liu, C. & Roy, K. Going deeper in spiking neural networks: VGG and residual architectures. Frontiers In Neuroscience. 13 pp. 95 (2019)
  * [30] Gwyn, T., Roy, K. & Atay, M. Face recognition using popular deep net architectures: A brief comparative study. Future Internet. 13, 164 (2021)
  * [31] Solomon, E., Woubie, A. & Cios, K. UFace: An Unsupervised Deep Learning Face Verification System. Electronics. 11, 3909 (2022)
  * [32] Solomon, E. Face Anti-Spoofing and Deep Learning Based Unsupervised Image Recognition Systems. (2023)
  * [33] Chang, X., Wu, J., Yang, T. & Feng, G. Deepfake face image detection based on improved VGG convolutional neural network. 2020 39th Chinese Control Conference (CCC). pp. 7252-7256 (2020)
  * [34] Liu, Z., Luo, P., Wang, X. & Tang, X. Large-scale celebfaces attributes (celeba) dataset. Retrieved August. 15, 11 (2018)
  * [35] Duan, Y.; Lu, J.; Zhou, J. Uniformface: Learning deep equidistributed representation for face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA, 15-20 June 2019; pp. 3415–3424.
  * [36] Deng, J.; Guo, J.; Xue, N.; Zafeiriou, S. Arcface: Additive angular margin loss for deep face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA, 15-20 June 2019; pp. 4690–4699.
  * [37] Kim, Y.; Park, W.; Roh, M.; Shin, J. Groupface: Learning latent groups and constructing group-based representations for face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 13-19 June 2020; pp. 5621–5630.
  * [38] Deng, J.; Zhou, Y.; Zafeiriou, S. Marginal loss for deep face recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, Honolulu, HI, USA, 21-26 July 2017; pp. 60–68.
  * [39] Huang, Y.; Wang, Y.; Tai, Y.; Liu, X.; Shen, P.; Li, S.; Li, J.; Huang, F. Curricularface: Adaptive curriculum learning loss for deep face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 13-19 June 2020; pp. 5901–5910.
  * [40] Zhao, K.; Xu, J.; Cheng, M. Regularface: Deep face recognition via exclusive regularization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA, 15-20 June 2019; pp. 1136–1144.
  * [41] Huang, X.; Zeng, X.; Wu, Q.; Lu, Y.; Huang, X.; Zheng, H. Face Verification Based on Deep Learning for Person Tracking in Hazardous Goods Factories. Processes 2022, 10, 380.
  * [42] Elaggoune, H.; Belahcene, M.; Bourennane, S. Hybrid descriptor and optimized CNN with transfer learning for face recognition. Multimed. Tools Appl. 2022, 81, 9403–9427.
  * [43] Ben Fredj, H.; Bouguezzi, S.; Souani, C. Face recognition in unconstrained environment with CNN. Vis. Comput. 2021, 37, 217–226.
  * [44] Wang, K.; Wang, S.; Zhang, P.; Zhou, Z.; Zhu, Z.; Wang, X.; Peng, X.; Sun, B.; Li, H.; You, Y. An efficient training approach for very large scale face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, Louisiana, USA, 21-24 June 2022; pp. 4083–4092.
  * [45] Liu, Y.; Chen, J. Unsupervised face frontalization for pose-invariant face recognition. Image Vis. Comput. 2021, _106_ , 104093.
  * [46] Hu, Y.; Wu, X.; Yu, B.; He, R.; Sun, Z. Pose-guided photorealistic face rotation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA, 18-23 June 2018; pp. 8398–8406.