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International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
DOI: 10.21307/ijanmc-2020-024                            23 
A Comparative Study of Face Recognition Classification 
Algorithms  
 
Wang Changyuan 
School of computer science and engineering 
Xi’an Technological University 
Xi’an, China 
E-mail: cyw901@163.com 
 
Li Guang 
Northwest Institutes of Advanced Technology 
Xi’an Technological University 
Xi’an, China 
E-mail: 865413666@qq.com 
 
Xue Pengxiang 
School of computer science and engineering 
Xi’an Technological University 
Xi’an, China 
E-mail: xuepx@xatu.edu.cn 
 
Wu Qiyou 
School of computer science and engineering 
Xi’an Technological University 
Xi’an, China 
E-mail: 314650592@qq.com 
 
 
Abstract— Due to the different classification effects and 
accuracy of different classification algorithms in 
machine learning, it is inconvenient for scientific 
researchers to choose which classification algorithm to 
use. This paper uses the face data published by 
Cambridge University as an experiment. The 
experiment first reduces the dimensionality of the data 
through the principal component analysis (PCA) 
algorithm, extracts the main features of the data, and 
then respectively through linear logic classification, 
linear discrimination LDA, nearest neighbor algorithm 
KNN, support vector machine SVM and the integrated 
algorithm Adaboost are used for classification. By 
comparing the advantages and disadvantages of the 
classification performance and complexity of different 
algorithms, the final review reviews accuracy, recall, 
f1-score, and AUC as evaluation indicators. 
Keywords-Classification Algorithm; Machine Learning; 
Face Recognition; Model Evaluation 
I. INTRODUCTION 
With the rise of artificial intelligence and machine 
learning, face recognition technology is widely used in 
life, such as station security, time and attendance 
punching, and secure payment [1-3], but different face 
recognition devices use different algorithms. Therefore, 
this paper analyzes and compares the commonly used 
classification algorithms in face recognition. The data 
set in this paper uses the ORL face data set published 
by Cambridge University in the United Kingdom. The 
methods used involve linear logistic regression, linear 
discriminant analysis (LDA), K-Nearest Neighbor 
(KNN), support vector machine (SVM), Naïve Bayes 
(NB) and other methods. The definition and advantages 
and disadvantages of the act are briefly explained. 
Finally, the five methods are compared and analyzed 
according to the evaluation indicators such as the 
accuracy rate, recall rate, F1-score, and AUC area 
commonly used in machine learning. 
International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
24 
II. RELATED WORK 
A.  Principal component analysis PCA data 
dimensionality reduction 
The data set contains a total of 400 photos. We use 
the machine learning library Scikit-learn provided by 
python to process the data, and display part of the data 
set pictures as shown in Figure1. 
 
Figure 1. ORL partial face image 
The experimental data has 4096 features per picture. 
Since the number of features is much greater than the 
number of samples, it is easy to regenerate overfitting 
during training. Therefore, a principal component 
analysis algorithm is required to reduce the dimensions 
of the features and select K main features as the input 
of the data set. . The main idea of PCA [4] uses the 
covariance matrix to calculate the degree of dispersion 
of samples in different directions, and selects the 
direction with the largest variance as the main direction 
of the sample set. Processing process: 
a) Data preprocessing normalizes and scales the 
data first. Normalization makes the mean value of data 
features 0, and scaling is to solve the case where 
feature values are different by an order of magnitude. 
b) Calculate the covariance matrix and 
eigenvectors of the processed data. The eigenvectors 
can be obtained by singular value decomposition. 
c) Retain the feature vector and feature value 
corresponding to the largest first K feature values to 
form an orthogonal basis. 
d) Project the sample into a low-dimensional 
space, and the acquired dimensionality-reduced data 
can represent the original sample approximately, but 
with a certain degree of distortion. 
This paper use formula (1) to calculate the 
distortion of PCA. 
 

  

m i
m
i
i
approx
i
X
m
XX
mX
1
2
)(
1
2
)()(
1
1
 (1) 
Through scikit-learn processing, the reduction rate 
after dimensionality reduction is obtained from the 
PCA model diagram is shown in Figure 2. It can be 
seen from the figure that the larger the value of k, the 
smaller the distortion rate. As k continues to increase, 
the data reduction rate will approach 1 Using this rule, 
choose between 10 and 300, and perform sampling 
calculation every 15th. Under the k features of all 
samples, the reduction rate is obtained after processing 
by the PCA algorithm. We select the reduction ratios at 
98%, 90%, 80%, and 70%, and the corresponding k 
values are 195, 75, 32, and 20. The corresponding 
pictures after PCA processing are displayed. The first 
line of the image is the original image, and then each 
column corresponds to the It is a picture at different 
reduction rates. The lower the reduction rate, the more 
blurred the image is shown in Figure 3. 
 
Figure 2. Relationship between reduction rate and K characteristics 
International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
25 
 
Figure 3. Relationship between reduction rate and K characteristics 
B.  Research on classification method 
1) Logistic Regression 
Supervised learning is the most widely used branch 
of machine learning in industry. Classification and 
regression are the main methods in supervised learning. 
Linear classifier is the most basic and commonly used 
machine learning model. This paper uses linear logistic 
regression to classify and recognize faces.  
The prediction function of linear regression is: 
   X
X
X
X
x T
n
n
 





















.
.
.
......,)(h
1
0
10  (2) 
Where is the prediction function, x is the feature 
vector, To handle the classification problem, this paper 
hope that the value of the function is [0,1], This paper 
introduce the Sigmoid function: 
 
ze
z


1
1
)(g  (3) 
Combined with linear regression prediction 
function: 
 
X
T
T
e
Xz




1
1
)(g)(g(x)h  (4) 
If there is a simple binary classification of class A 
or class B, then this paper can use Sigmoid as the 
probability density function of the sample, and the 
result of the input classification can be expressed by 
probability: 
 1),|0(),|1(   xyPxyP  (5) 
The cost function is a function that describes the 
difference between the predicted value and the true 
value of the model. If there are multiple data samples, 
the average value of the replacement price function is 
obtained. It is expressed by J(θ). Close to, based on the 
maximum likelihood estimate available cost function J 
(θ). 
   
m
i
iiii xhyxhy
m
J
1
)()()()( ))(1log()1()(log((
1
)(    (6) 
 
2) Linear Discriminant Analysis (LDA) 
Linear Discriminant Analysis (LDA)
 [5 ， 6]
, also 
known as Fisher Linear Discriminant (FLD), was 
introduced into the field of machine learning by 
Belhumeur. LDA is a dimensionality reduction 
technique in supervised learning, which can not only 
reduce dimensionality but also classify, and mainly 
project data features from high latitude to low latitude 
space. The core idea is that after projection, the 
projection points of the same category of data should 
be as close as possible, and the distance between the 
category centers of different categories of data should 
be increased as much as possible [5]. If the data set has 
two data sets, for the center of the two classes 
Then within-class scatter matrix (within-class 
scatter matrix): 
International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
26 
 T
xx
T
xx
uxuxuxux
S
)()()()(
21
2211
w
21





 (7) 
Between-class scatter matrix: 
 
T
b uuS )2u)(2u( 11   (8) 
3) KNN 
Among N training samples, find the k nearest 
neighbors of the test sample x. Suppose there are m 
training samples in the data set, and there are c 
categories, namely  
c
 ,...
1
, and the test sample is x. 
Then the KNN algorithm can be described as: Find k 
neighbors of x in m training samples, among which the 
number of samples belonging to category wi in k 
neighbors of x are kckk ,...,
21
, then the discriminant 
function is 
 cikxg ii ,...2,1,)(   (9) 
The core idea of K-nearest neighbor algorithm 
[7]
 is 
to calculate the distance between unlabeled data 
samples and each sample in the data set, take the K 
nearest samples, and then K neighbors vote to decide 
the type of unlabeled samples. 
KNN classification steps: 
a) Prepare the training sample set X, which 
contains n training samples, and select an appropriate 
distance measurement method according to specific 
requirements. This paper use dis(xa,xb) to represent 
the distance between ax and bx in the sample set. 
b) For the test sample x, use the distance 
measurement formula to calculate the distance 
between the test sample x and n samples to obtain the 
distance set Dis, where 
 ),(),...,,(),,(is
21 n
xxdisxxdisxxdisD 
. 
c) Sort the distance set, select the smallest k 
elements from it, and get k samples corresponding to k 
elements. 
d) Count the categories of these k samples, and 
obtain the final classification results by voting. 
Assuming that x_test is an unlabeled sample and 
x_train is a labeled sample, the algorithm is as follows: 
 
Figure 4. K nearest neighbor algorithm 
For distance measurement, Euclidean distance, 
Manhattan distance, Chebyshev distance, etc. are 
usually used. Generally, Euclidean distance is mostly 
used, such as the distance between two points and two 
points in N-dimensional Euclidean space. 
 
)(d
1 21ab   
N
i ii
xx
 (10) 
4) SVM 
Support Vector Machine (SVM)[7] for short is a 
very important and extensive machine learning 
algorithm. Its starting point is to find the optimal 
decision boundary as far as possible, which is the 
farthest from the two types of data points. Furthermore, 
is the farthest from the boundary of the two types of 
data points, so the data point closest to the boundary is 
defined as a support vector. Finally, our goal becomes 
to find such a straight line (multi-dimensional called 
hyperplane), which has the largest distance from the 
support vector. Make the generalization ability of the 
model as good as possible, so SVM prediction of future 
data is also more accurate, as shown in Figure 5 below. 
Find the best Dahua margin. 
International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
27 
 
Figure 5. Classification model diagram 
Let this plane be represented by g(x)=0, its normal 
vector is represented by w, the actual distance between 
a point and the plane is r point, and the distance from 
the plane can be measured by the absolute value of g(x) 
(called the function interval) . 
 
li
bXWy
WW
i
T
i
T
bw
....1
,1)(
2
1
min
,


 
(11)
 
The penalty function is also called the penalty 
function, which is a kind of restriction function. For 
constrained nonlinear programming, its constraint 
function is called a penalty function, and the coefficient 
is called a penalty factor. The objective function of 
SVM (soft interval support vector machine) with 
penalty factor C is: 
 
Figure 6. Introduction of C classification model diagram 
 



l
T
bw
CWW
1i
, 2
1
min 
，
 
(12)
 
Advantages of SVM: 
a) Non-linear mapping is the theoretical basis of 
SVM method, SVM uses inner product kernel function 
to replace the nonlinear mapping to high-dimensional 
space; 
b) The optimal hyperplane to divide the feature 
space is the goal of SVM, and the idea of maximizing 
the classification margin is the core of the SVM 
method; 
c) Support vector is the training result of SVM. It 
is the support vector that plays a decisive role in SVM 
classification decision. 
d) SVM is a novel small sample learning method 
with a solid theoretical foundation. It basically does 
not involve probability measurement and the law of 
large numbers, so it is different from the existing 
statistical methods. In essence, it avoids the traditional 
process from induction to deduction, realizes efficient 
"transduction inference" from training samples to 
forecast samples, and greatly simplifies the usual 
classification and regression problems. 
5) Naive Bayes 
Naive Bayes [8, 9] is a conditional independence 
assumption, and there is no correlation between leave 
and leave. Suppose there is a labeled data set, where 
the data set has a total of categories, and for new 
samples, this paper predict the value. This paper use 
statistical methods to deal with this problem, so this 
paper can understand it as the probability of the 
category to which the sample belongs. The conditional 
probability formula is: 
 )|( XCP
k
 (13) 
Therefor Ck ∈ [C1, C2 … , Cm] , this paper only 
require the probabilities of m categories, the category 
International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
28 
belongs to the largest value, and use Bayes' theorem to 
solve: 
 
)(
)|()(
)|(
XP
CXPCP
XCP kkk 
 (14) 
And because x has n feature vectors, it is in the 
determined data set ， Ck , P(x)  are fixed values, 
according to the joint probability formula: 
 P(Ck)P(x|Ck) = P(Ck, x) (15) 
III. EXPERIMENTAL RESULTS 
The data set in this paper uses the ORL face data set 
of Cambridge University, a total of 400 photos. After 
experimental analysis, this paper chose PCA to reduce 
the information rate after dimensionality reduction to 
98%, and select 195 as the main features of each 
picture as data input. In order to make the experimental 
results more generalized, 80% of the data set is used as 
the training set and 20% is used as the test set. The 
10-fold cross-validation method is used during model 
training. In order to ensure that the experimental results 
run the same data every time, a fixed random seed is 
set Is 7. For the test standard, this paper selected the 
accuracy rate (P), recall rate (R), F value, and AUC 
area. Compared with our prediction results, the 
accuracy rate indicates how many true positive samples 
are in the positive prediction samples. There are two 
possibilities for the prediction results, that is, the 
positive prediction is positive (TP), and the negative 
prediction is positive (FP), the formula is: 
 
FPTP
TP
P


 (16) 
The recall rate refers to our original sample, 
indicating how many positive examples in the sample 
were predicted correctly. There are also two 
possibilities, that is, the original positive class is 
predicted as a positive class (TP), and the other is to 
predict the original positive class as a negative class 
(FN). 
 
FNTP
TP
R


 (17) 
F1 combines the results of precision rate and recall 
rate. When F1 is higher, it means that the verification 
method is more effective. 
 
RP
PR
F


2
1
 (18) 
TABLE I.  THE COMPARISON OF EXPERIMENTAL RESULTS OF FIVE 
CLASSIFICATION ALGORITHMS 
 PCA+LR PCA+LDA PCA+SVM PCA+KNN PCA+NB 
Precision (%) 99 98 94 59 91 
Recall (%) 99 96 91 45 85 
Fl-score (%) 99 96 91 44 85 
 
IV. CONCLUSION 
Face recognition technology [10] has become one 
of the most popular research directions in computer 
vision and has made great achievements. With the 
development of computer technology, more and more 
classification methods will appear. This thesis is only 
through several common mainstream classification 
methods for experimental analysis and comparison. 
Through experiments, it is found that the PCA + linear 
logic classification method has obvious advantages in 
accuracy rate and recall rate. However, specific 
analysis should be combined with specific issues. Then 
I am ready to do experiments on different data sets, 
understand more classification algorithms, and 
constantly improve my results. 
 
International Journal of Advanced Network, Monitoring and Controls      Volume 05, No.03, 2020 
29 
REFERENCES 
[1] Wu Xiaotian. Research on Face Recognition Algorithm in Subway 
Security Inspection [D]. Dalian Jiaotong University, 2017. 
[2] Chen Fuqiang. Research on invalid face filtering method in video 
attendance [D]. Southwest Jiaotong University, 2018. 
[3] Ma Yukun. Research on key technologies of face-based secure 
identity authentication [D]. Beijing University of Technology, 2018. 
[4] Pattern Analysis; New Pattern Analysis Findings from King Saud 
University Discussed (Pcapool: Unsupervised Feature Learning for 
Face Recognition Using Pca, Lbp, and Pyramid Pooling) [J]. Journal 
of Robotics &amp; Machine Learning, 2020. 
[5] Zhang Yuting, Chen Junhua, Yang Xinkai, Zhang Liyan. An 
improved PCA+LDA face recognition algorithm [J]. Computer 
Knowledge and Technology, 2020, 16(03): 221-222. 
[6] Guan‐Hua Huang, Chih‐Hsuan Lin, Yu‐Ren Cai, Tai‐Been 
Chen, Shih‐Yen Hsu, Nan‐Han Lu, Huei‐Yung Chen, Yi‐Chen 
Wu. Multiclass machine learning classification of functional brain 
images for Parkinson's disease stage prediction [J]. Statistical 
Analysis and Data Mining: The ASA Data Science Journal, 2020, 
13(5). 
[7] Ou Lisong. Design and improvement of face recognition system 
based on SVM [J]. Network Security Technology and Application, 
2019(12): 58-60. [8]Liu Jie, Song Bo. Naive Bayesian Classifier 
Based on Genetic Simulated Annealing Algorithm [J]. Procedia 
Engineering, 2011, 23. 
[8] Tie Fuzhen. Application of face recognition system in hotel industry 
[J]. Computer Products and Circulation, 2020(07): 81+97. 
[9] Jiang Ajuan, Zhang Wenjuan. A summary of face recognition [J]. 
Computer Knowledge and Technology, 2019, 15(02): 173-174+190. 
[10] Youqiang Zhang, Guo Cao, Bisheng Wang, Xuesong Li. A novel 
ensemble method for k -nearest neighbor [J]. Pattern Recognition, 
2019, 85. 
 


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Intracerebroventricular streptozotocin induces behavioral impairments and increases short-term C3 gene expression in the hippocampus of Wistar rats

Research and Implementation of Future Network IPV9

A position paper on breastfeeding by women with epilepsy – working group report

Victimization in traditional and cyberbullying as risk factors for substance use, self-harm and suicide attempts in high school students

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A Comparative Study of Face Recognition Classification Algorithms

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