FACE RECOGNITION USING ENSEMBLE
OF NEURAL NETWORKS
M. Alekseichevs and A. Glazs
Institute of Computer Control, Automation and Computer Engineering, Riga Tehnical University
Meza 1/3-310, Riga, Latvia
Keywords: Face recognition, Neural networks, Neural network ensemble, Plurality voting, Ensemble averaging,
Weighted voting, Committee decision.
Abstract: Authors describe a novel approach for human faces recognition using ensembles (or committee) of artificial
neural networks. In the task of human faces recognition there are several problems that should be
considered: 1) overlapping of different sets (classes), for example, when distinguishing faces of twins; 2) the
training time of neural networks can be limited. In this case it is not possible to reach correct recognition of
training set during neural networks training. Therefore, the two-level hierarchical structure is used to
recognize objects of examination (testing) set. As a result of neural networks training at the lower level a
decisions set is formed. On the basis of the decisions set the final committee solution is constructed at the
upper level. A special algorithm of weighted voting is proposed to form the committee decision. The
experimental results show that the proposed algorithm is more effective in comparison with other known
committee methods, when number of training iterations is limited.
1 INTRODUCTION
The problem of face recognition on a photo and
video images is actual in different areas - from
commercial sphere to security, etc. During the last
two decades researchers have proposed many
approaches to human faces recognition.
The techniques of face recognition could be
classified by different criteria (Zhao, 2003). In this
work the usage of neural networks and ensemble (or
committee) decisions is considered. There are
known different committee decisions construction
algorithms for neural networks as well as its
comparative analysis (Sharkey, 1997; Jimenez,
1998; Haykin, 1999; Opitz, 1999; Sharkey, 1999;
Whitman, 2006; Mu, 2007; Garcia-Pedrajas, 2007).
In the given work the following algoritms are
considered: algorithm of plurality voting (Opitz,
1996; Glaz, 1991); algorithm of ensemble averaging
(Perrone, 1993); algorithm of weighted voting
(Jimenez, 1998). The architecture of such neural
network ensemble is shown on Fig. 1.
The set of the neural networks which included in
ensemble is generated in the following way: for each
i neural network, i
∈ [1:T], matrixes of initial
weights W
i
0
, V
i
0
(starting points) are generated
randomly from a given interval. Then training (back-
propagation algorithm) is conducted on each
network. Weights W
i
, V
i
are obtained during training
and are used by each neural network for
classification R
i
(X) of objects X, which do not
belong to the training set.
Achieved decisions R
i
(X) , i ∈ [1:T] are used for
obtaining an ensemble decision that in case of
dichotomy is described by following expression:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
<
≥
=
∑
∑
=
=
;)(,0
;)(,1
)(*
1
1
θ
θ
T
i
ii
T
i
ii
XRzif
XRzif
XR
(1)
where z
i
- weight of decision R
i
(X),
θ
- given
threshold.
2 ALGORITMS OF ENSEMBLE
DECISION
Different algorithms of ensemble decisions can be
obtained from (1) depending on z
i
, R
i
(X) ,
θ
values.
144
Alekseichevs M. and Glazs A. (2009).
FACE RECOGNITION USING ENSEMBLE OF NEURAL NETWORKS .
In Proceedings of the International Conference on Agents and Artificial Intelligence, pages 144-149
DOI: 10.5220/0001535701440149
Copyright
c
 SciTePress

Figure 1: The architecture of neural network ensemble.
2.1 Algorithm of Plurality Voting
In this case weights z
i
= 1 and the threshold
2
T
=
θ
(Т should be odd), outputs of neural networks R
i
(X)
can assume only two values: 0 or 1 (it means that
threshold function is realized). According to this, the
expression (1) is defined as follows:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
<
≥
=
∑
∑
=
=
;
2
)(,0
;
2
)(,1
)(*
1
1
T
XRif
T
XRif
XR
T
i
i
T
i
i
(2)
2.2 Algorithm of Weighted Voting
For algorithm of weighted voting outputs of neural
networks R
i
(X) also assume one of the values: 0 or 1,
the threshold is
θ
=
2
1
, and the weights z
i
are
defined in the following way:
,
1
∑
=
=
T
i
i
i
i
q
q
z
(3)
where q
i
– probability of correct classification by i
neural network that is estimated by using training
set. Also, all weights z
i
should satisfy the following
condition:
]:1[,0,1
1
Tizz
i
T
i
i
∈>=
∑
=
(4)
According to this, the expression (1) assumes the
following form:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
<
≥
=
∑
∑
=
=
;
2
1
)(,0
;
2
1
)(,1
)(*
1
1
T
i
ii
T
i
ii
XRzif
XRzif
XR
(5)
2.3 Algorithm of Ensemble Averaging
In this case R
i
(X) ∈ [0:1], it means that the outputs
belong to the values of logistic function, the
threshold is
θ
=
2
1
and weights z
i
=
T
1
. According
to this, expression (1) assumes the following form:
1
1
11
1, ( ) ;
2
*( )
11
0, ( ) ;
2
T
i
i
T
i
i
if R X
T
RX
if R X
T
=
=
⎧
⎪
≥
⎪
⎪
=
⎨
⎪
<
⎪
⎪
⎩
∑
∑
(6)
FACE RECOGNITION USING ENSEMBLE OF NEURAL NETWORKS
145

Figure 2: Examples of two classes of faces.
3 PROPOSED ALGORITM
In the result of training, the reliability of training set
recognition q
i
by i neural network is in the interval
0.5 ≤ q
i
≤ 1. That is why in the proposed algorithm
of the weighted voting weight z
i
is defined as
follows:
z
i
= (q
i
– 0.5)*2, i ∈ [1:T]
(7)
Thus, weights values are in the interval
0 ≤ z
i
≤ 1 and the threshold
θ
is defined according
to expression
∑
=
=
T
i 1
i
z
2
1
θ
(8)
In this case outputs of neural networks R
i
(X) are
values of logistic function. It means that R
i
(X) ∈
[0:1] and the proposed algorithm of the weighed
voting can be written down in the following form:
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
<
≥
=
∑
∑
∑
∑
=
=
=
=
;
2
)(,0
;
2
)(,1
)(*
1
1
1
1
T
i
i
T
i
ii
T
i
i
T
i
ii
z
XRzif
z
XRzif
XR
(9)
4 EXPERIMENTAL RESULTS
Ensemble methods that are described in this paper
have been applied to solve a task of recognition of
two classes of faces, which conform to twins.
The initial array included 64 color images (32 in
each class). In fig. 2 the fragment of initial array is
shown. The initial array of images has been divided
into 2 parts: training set (10+10) and examination set
(22+22). Each image was coded by a matrix
200x133. Input vector X of each neural network in
ensemble included 26600 elements, the number Т of
ICAART 2009 - International Conference on Agents and Artificial Intelligence
146

Figure 3: The results of training for 10 neural networks of one training set.
Figure 4: The results of examination for 10 neural networks of one training set.
FACE RECOGNITION USING ENSEMBLE OF NEURAL NETWORKS
147

Figure 5: The results of application of ensemble methods for examination.
neural networks (members of ensemble) was 45.
Elements of weights matrixes W
i
, V
i
were randomly
distributed in intervals 0 ÷ 0.01 and i
∈ [1:45]. Each
element x
j
of input vector X , j ∈ [1:26600],
described intensity of the corresponding pixel, which
was normalized according to
,
256
*256*256
3
2
jjj
j
BGR
X
++
=
(10)
where R
j
, G
j
, B
j
- values of colors in RGB system
for j pixel. The algorithm of training (back-
propagation) was used for training each neural
network. As each image was coded by 26600
elements, it was necessary to limit the time of
training (iterations number).
As shown on fig. 3 and 4 the results of training
and examination for each neural network can differ.
This explains by the random choice of initial values
of the weights matrixes W
i
and V
i
, i ∈ [1:10] .
As seen from the Fig. 5, the proposed algorithm
of the weighed voting is more effective in
comparison with known methods. Its advantage is
especially noticeable, when the number of training
iterations is limited. If the number of iterations is not
limited, all the algorithms give comparable results.
However in this case the training time becomes very
long.
The similar situation was obtained in the cases of
other training sets.
5 CONCLUSIONS
1. To solve the problem of similar human faces
recognition (for example, faces of twins)
ensemble methods that are realized in neural
networks can be used.
2. The amount of time taken for training such neural
networks can be significant, that is why it is
necessary to limit the number of training
iterations during network training. In these cases
the effective method of ensemble decisions is the
proposed algorithm of weighed voting.
3. The results of experiments show, that the
proposed algorithm of weighed voting is more
effective in comparison with known methods:
algorithm of plurality voting, algorithm of
ensemble averaging and algorithm of weighed
voting. Its advantage is especially noticeable,
when the number of training iterations is limited.
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148

ACKNOWLEDGEMENTS
This work has been partly supported by the
European Social Fund within the National
Programme “Support for the carrying out doctoral
study programm’s and post-doctoral research”
project “Support for the development of doctoral
studies at Riga Technical University”.
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