analysis of unsupervised learning techniques for face recognition
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Analysis of Unsupervised Learning Techniques for FaceRecognition
Dinesh Kumar,1 C. S. Rai,2 Shakti Kumar3
1 Department of Computer Science and Engineering, Guru Jambheshwar University of Science &Technology, Hisar, Haryana, India
2 University School of Information Technology, GGS Indraprastha University, Kashmere Gate, Delhi, India
3 Computational Intelligence Lab, Institute of Science & Technology, Klawad,District Yamuna Nagar, Haryana, India
Received 16 January 2008; accepted 15 May 2010
ABSTRACT: Face recognition has always been a potential researcharea because of its demand for reliable identification of a human
being especially in government and commercial sectors, such as se-
curity systems, criminal identification, border control, etc. where a
large number of people interact with each other and/or with the sys-tem. The last two decades have witnessed many supervised and
unsupervised learning techniques proposed by different researchers
for the face recognition system. Principal component analysis (PCA),self-organizing map (SOM), and independent component analysis
(ICA) are the most widely used unsupervised learning techniques
reported by research community. This article presents an analysis
and comparison of these techniques. The article also includes twoSOM processing methods global SOM (GSOM) and local SOM
(LSOM) for performance evaluation along with PCA and ICA. We have
used two different databases for our analysis. The simulation result
establishes the supremacy of GSOM in general among all the unsu-pervised techniques. VVC 2010 Wiley Periodicals, Inc. Int J Imaging
Syst Technol, 20, 261–267, 2010; View this article online at wileyonlinelibrary.
com. DOI 10.1002/ima.20248
Key words: face recognition; principal component analysis; self-
organizing maps; independent component analysis
I. INTRODUCTION
Face recognition has gained a lot of popularity in the past 15 to 20
years due to recent advancements and a large number of real world
applications such as surveillance, secured access, information secu-
rity, voter ID, etc. Face recognition approaches were broadly
grouped into three categories (Chellapa et al., 1995; Zhao et al.,
2003): feature based (Kelly, 1970; Manjunath et al., 1992; Samaria
and Fallside, 1993), holistic or appearance based (Kirby and Siro-
vich, 1990; Turk and Pentland, 1991; Etemed and Chellappa, 1997;
Teixeira and Beveridge, 2003), and hybrid techniques (Pentland
et al., 1994; Penev and Atick, 1996; Weyrauch et al., 2004).
Although all the three approaches are important, it has been
observed that the appearance-based approach has attracted the
attention of majority of researchers. This approach extracts the
holistic representation of whole face image and a comparison is
done with several such images to find a match. Turk and Pentland
(1991) made significant contribution toward machine recognition of
the faces and their discovery led to the design of reliable real-time
automated face recognition systems.
Principal Component Analysis (PCA) technique, pioneered by
Kirby and Sirovich (1990), was used to reduce the dimensions of
the data by removing less useful information and decomposing the
face into uncorrelated components known as Eigenfaces (Turk and
Pentland, 1991). This approach was purely based on second-order
statistics. Linear Discriminant Analysis (LDA) also known as Fish-
erfaces was proposed in (Swets and Weng, 1996; Belhumeur et al.,
1997). This technique was proposed with the aim as to maximize
between class variance and minimize the within class variance.
LDA was insensitive to large variations in lighting and facial
expressions. Although it was claimed that LDA is better than PCA,
yet it was proved that PCA outperformed LDA especially when the
training data set was small (Martinez and Kak, 2001). Besides,
PCA was found to be less sensitive to different training data set.
Another technique known as Laplacianfaces was proposed (He
et al., 2005) to preserve the local structure of the data. Locality Pre-
serving Projections (LPP) was used for mapping the face images
into face subspace. The technique was found more suitable for fron-
tal face images. Several other methods such as Probabilistic Sub-
spaces (Moghaddam and Pentland, 1995, 1998; Moghaddam, et al.,
1998; Moghaddam, 1999), Feature Line Method (Li and Lu, 1999),
Evolutionary Pursuit (Liu and Wechsler, 2000), Support Vector
Machines (SVM) (Phillips, 1999), etc., have also been proposed by
various researchers with their relative advantages and
disadvantages.Correspondence to: Dinesh Kumar; e-mail: dinesh_chutani@yahoo.com
' 2010 Wiley Periodicals, Inc.
A large number of face recognition algorithms use PCA that
deals with second-order statistics of the images and does not take
the higher order dependencies into consideration. Independent
Component Analysis (ICA) (Comon, 1994; Hyvarinen, 1999) is one
such technique that decorrelates the higher order moments of the
input besides second-order ones. There exit a large number of statis-
tical techniques based on information theoretic concepts and alge-
braic approaches for performing ICA. Neural algorithms derived
from these approaches are used for extracting the independent com-
ponents. Bartlett and Sejnowski (Bartlett and Sejnowski, 1997;
Bartlett et al., 1998, 2002) developed method based on ICA for rep-
resenting the images for face recognition using two different archi-
tectures. Self-organizing map (SOM) (Kohonen, 1988, 1997) is
another algorithm used for self-organization or unsupervised learn-
ing that discovers the significant features in the input data. These
have also been successfully used as a way of dimensionality reduc-
tion and feature selection for face space representations (Lawrence
et al., 1996; Neagoe and Ropot, 2002; Tan et al., 2005).
We have used two different popularly used standard face data-
bases (ORL and Yale) for our experimental work. ORL face data-
base (http://www.cam-orl.co.uk/facedatabase.html) is composed of
400 images containing as many as 40 different subjects (persons),
each having his/her 10 different images. These images vary in terms
of facial expressions (open/close eyes, smiling/no-smiling) and fa-
cial details (glasses/no-glasses). These images with slightly varying
illumination are in up-right front position with slight left–right rota-
tion. Yale face database (http://www1.cs.columbia.edu/belhumeur/
pub/images/yalefaces/) contains images of 28 human subjects under
nine poses and 64 illumination conditions. For performing the
experiments, two different sets, each having 10 subjects, were pre-
pared. Yale Pose set had 10 subjects each having nine different
poses, whereas the other set, Yale Illumination had 10 subjects each
having 10 face images with different illumination. Another database
was prepared that had face images from ORL, Yale Pose, and Yale
Illumination face databases. This database had a total of 40 subjects
(20 from ORL, 10 each from Yale Pose and Yale Illumination).
This article investigates the performance of two approaches
global SOM (GSOM) and local SOM (LSOM) for face recognition
for the above said databases. These two approaches have been com-
pared in terms of recognition rate of the face recognition system. A
comparison of PCA, SOM, and ICA has also been carried out. This
article has been divided into five sections. Section II introduces
SOM, PCA, and ICA followed by description of GSOM and LSOM
in Section III. Section IV is devoted to performance evaluation of
the system in terms of recognition rate. Based on the results and dis-
cussions presented in the previous section, conclusions have been
drawn in Section V.
II. SOM, PCA, AND ICA
A. Self-Organizing Maps. SOM is a feed forward neural net-
work approach that belongs to unsupervised class. It uses unsuper-
vised training algorithm. It follows a process of self-organization
and configures the output units in such a way that the topological
representation of the original data is preserved. SOM transforms the
high-dimensional data onto 1D or 2D layer of neurons. There is a
competition among the neurons to be activated and fired. Only that
neuron is activated that is the winner of the competition. The neigh-
borhood function is centered around this winning neuron. The
neighborhood function initially covers the entire lattice and it is
allowed to shrink gradually until it has the winning neuron. The
algorithm goes through two phases: ordering phase, during which
the topological ordering of the weight vectors takes place, whereas
convergence phase covers the fine tuning of the computational map.
B. Principal Component Analysis. PCA is a popular statisti-
cal unsupervised technique because of its wide use in many applica-
tions such as signal processing and pattern recognition. It is used to
reduce the dimensionality of the data by compressing the data into
lower dimensions. It linearly transforms the original set of variables
into a smaller set of variables. These variables are uncorrelated and
contain most of the information as contained by the original set of
data. A smaller set of data is much easier to handle with, requires
less storage space, and reduces the computational complexity while
retaining the maximum information. PCA has successfully been
used for face recognition applications where the dimensionality of
data is very high. For face recognition applications, consider a set
of N sample images G 5 {G1,G2,. . .,GN} taking values in an n-dimensional image space. Assume each face image has m 3 n 5 Mpixels and is represented as M 3 1 column vector. A training set Gwith N number of face images of known individuals forms a M 3 Nmatrix. Covariance matrix
C ¼XN
k¼1
Ck �Wð Þ Ck �Wð ÞT ;
is computed where C is the mean image of all the samples and
eigenvectors and eigenvalues of the C are determined such that CF5 kF where k 5 diag(k1,k2,. . .,kN) is a diagonal matrix defined by
the eigenvalues of the matrix C; F 5 [V1,V2,. . .,VN] are the associ-
ated eigenvectors. The dimensionality can be reduced by selecting
first L < N eigenvectors to find the data in the new directions and
discarding the rest.
C. Independent Component Analysis. ICA is a generaliza-
tion of PCA. It was originally developed to deal with problems that
were closely related to the cocktail party problem most commonly
known as Blind Source Separation (BSS). It gained lot of popularity
because of its use in wide variety of applications such as signal proc-
essing, pattern recognition, telecommunications, medical imaging,
and financial time series analysis (Hyvarinen and Oja, 2000). PCA
deals with second-order statistics, whereas ICA reduces the higher
order statistical dependencies and tries to make the signal as inde-
pendent as possible. Consider u is the source vector and A is the
mixing matrix. The observation vector x is given by x 5 Au, whereboth A and u are unknown. The aim is to find the demixing matrix
sayW, such that the original vector u can be recovered from the out-
put vector y defined as y 5 Wx. As x 5 Au, therefore y 5 WAu.Here W 5 A21 leads to perfect separation of source signals, i.e., y5 u. Practically, y should be as close to u as possible. We need an
iterative technique for updating the weight matrix W in unsuper-
vised manner that will lead to source separation. Various ICA
approaches were proposed that were mainly based on information
theoretic concepts. Bartlett et al. (Bartlett and Sejnowski, 1997;
Bartlett, et al., 1998, 2002; Bartlett, 1998) developed methods for
representing face images. Two different architectures were proposed
with the assumption that the face images are a linear mixer of an
unknown set of statistically independent source images. Architec-
ture I treated images as random variables and pixels as outcomes,
whereas the pixels are treated as random variables and images as
262 Vol. 20, 261–267 (2010)
outcome in Architecture II. The Infomax algorithm proposed by
Bell and Sejnowski (1995) was used for performing the ICA.
The weight update rule is DW 5 h(I 1 (1 2 2z)yT)W. Z is the
output of the nonlinearity (logistic function) used (Fig. 1). ICA was
performed on both the Architectures I and II.
III. GSOM AND LSOM
A. Introduction. The global processing (GSOM) is the one in
which each and every pixel of the face image is fed into the SOM
networks, whereas in the local processing (LSOM) method, the face
image is divided into blocks and these blocks of pixels are proc-
Figure 1. Maximum entropy method for ICA.
Figure 2. Flowchart for SOM algorithm.
Table I. Total variance contribution rate for different n.
Eigenvalues (n) 199 160 120 100 80 40 20
TVCR 100 98.67 96.06 94.13 91.53 81.72 69.82
Figure 3. (a) Original images, (b) reconstructed images using local
processing, and (c) reconstructed images using global processing.
Vol. 20, 261–267 (2010) 263
essed. Global processing requires substantially larger network as
compared with that required for local processing technique. This is
due to the fact that the usage of pixel blocks effectively results in
reduction of dimensionality of data space that has to be topologi-
cally represented in the SOM space. The training images in both
approaches are mapped to lower dimensions and the weight matrix
of each training image is stored. At the time of recognition, the
training images are reconstructed using the weight matrices and
matching is done with the test image using Euclidean norm (L2
norm) as the similarity measure.
B. Algorithm. The steps are as follows:
1. Consider a face image I of size n 3 n. For GSOM, concate-
nate the face image to form a single vector x of size b 3 1
where b 5 n 3 n. This will form the input for 2D SOM. For
LSOM, the face image is divided into sub-blocks of size say
a 3 a resulting in total of p 5 (n 3 n)/(a 3 a) blocks each of
which contains q5 a 3 a number of elements, concatenation
of which produces a vector to represent one block resulting
in a matrix X 5 [x1,x2,. . .,xp] of size q 3 p. This gives a
stream of training vectors {xi}i51p.
2. Consider 2D (r 3 r) map of neurons each of which is identi-
fied as index jk, j, k 5 1, 2,. . .,r. The j kth neuron has an
incoming weight vector wjk 5 (wl,jk,. . .,wq,jk) at instant i. Thevalue of neighborhood around the winning neuron is hJK at
instant i. Initialize weights wjK, neighborhood hJK, and the
learning rate h0.
3. For GSOM, present the single vector x of size b 3 1 as
obtained in step 1 to a 2D (r 3 r) map of neurons with a total
of z 5 r 3 r neurons. For LSOM, pick a sample vector xi atrandom and present it to a 2D (r 3 r) map of neurons with a
total of z5 r3 r neurons.4. Find out best matching (winning neuron) using following dis-
tance criterion
jjxi � wJKðiÞjj ¼ minjk
fjjxi � wjkðiÞjjg;
where wJK is the best matching weight vector.
5. Update the synaptic weight vectors of only the winning cluster
wjkðiþ1Þ ¼ wjkðiÞ þ hiðxðiÞ � wjkðiÞÞ jk 2 hJKðiÞ;
6. Update learning rate hi and the neighborhood hJK(i).
7. Continue with step 3 until no noticeable changes in the fea-
ture map are observed. Finally a matrix R of size z 3 1 is
obtained for GSOM. In case of LSOM, a matrix M of size z3 q is obtained.
8. Retain the weight matrices for both the methodologies.
9. Repeat the above steps for all training images.
10. Reconstruct the images at the time of recognition and match
with the test image using nearest neighbor classifier.
Figure 2 shows the flowchart. At the start of the algorithm, the
neighborhood hJK(i) usually includes all neurons in the vector field
and its value reduces gradually. During the initial period of adapta-
tion called the ordering phase, the learning rate hi is kept close to
unity and then decreases either linearly or exponentially or inversely
with index i. During the tuning phase which occurs after ordering
phase, it has a very small value but never zero. For the experimenta-
tion purpose ‘‘hextop" topology has been chosen together with
‘‘linkdist’’ as the distance function. The ordering phase learning
rate was kept 0.9 when maintaining the tuning phase rate as 0.02.
For PCA, the total variance contribution rate (TVCR), was com-
puted by retaining only n number of eigenvalues for total of 200
images (200 eigenvalues).
TVCR ¼Pn
i¼1 kiPLi¼1 ki
3100;
L is the total number of eigenvalues. Table I gives TVCR for vari-
ous values of n.
IV. EXPERIMENTAL RESULTS AND DISCUSSIONSThe ORL face database discussed in Section I was used for com-
puter simulations in this article. The original image 92 3 112 was
resized to 80 3 80 before further processing of the face image. Eu-
clidean norm was used as the similarity measure to see which
Table II. Recognition rate vs. block size – (ORL).
Recognition Rate (%)
Method Size of Block
43 4 83 8 163 16
LOCAL SOM (53 5) 96 96 96
GLOBAL SOM (53 5) 98
Table III. Recognition rate vs. block size – (Yale_Illumination).
Recognition Rate (%)
Method Size of Block
43 4 83 8 163 16
LOCAL SOM (53 5) 72 70 74
GLOBAL SOM (53 5) 74
Table IV. Recognition rate vs. block size – (Yale_Pose).
Recognition Rate (%)
Method
Size of Block
43 4 83 8 163 16
LOCAL SOM (53 5) 72.5 67.5 75
GLOBAL SOM (53 5) 75
Table V. Recognition rate vs. SOM size – (ORL).
Recognition Rate (%)
Method
Size of SOM
SOM (33 3) SOM (53 5)
LOCAL SOM 94 96
GLOBAL SOM 98 98
264 Vol. 20, 261–267 (2010)
images are most alike. As many as five training images and the
same number of test images were used for performing the experi-
ments. There is no overlap between training and test sets. The
experiments are as follows:
1. The first experiment was performed to see the effect of global
and local processing on the recognition rate of the face recog-
nition system. Two-dimensional self-organizing map of size
5-by-5 was chosen, for both global and local processing. The
face image of size 80 3 80 was concatenated to form a single
vector of size 1 3 6400. This formed the input for the SOM
and it was trained. After training, a matrix of size 25 3 1 was
obtained and retained. The image was reconstructed with the
help of this matrix at the time of recognition for matching
purpose. As many as five training images and the same num-
ber of test images for the first 10 classes of image database
were used for performing the experiment 2. The same proce-
dure was adopted to get the results for another face database;
Yale-Pose and Yale-Illumination. As there are total of nine
images per subject in former and 10 images per subject in the
latter, as many as five images per subject were taken for
training and remaining four (five in Yale-Illumination) nono-
verlapping images were used for testing. The image was
cropped and resized to 48 3 48 for making the computations
simple. Figure 3 shows the original images and the images
reconstructed using GSOM and LSOM. Table II shows that
there is no change in the recognition rates with respect to the
change in the size of the block, whereas the global processing
system performs better in terms of recognition rate as com-
pared with local processing system. Tables III and IV indi-
cate that the size of block affects the recognition rate which
is more with 4 3 4 block size as compared with that using a
block of size 8 3 8. But, as the size was increased to 16 316, the rate approached to a value that was equal to that
obtained using global processing.
2. The second experiment was performed to see the effect of
changing the SOM size on the performance of recognition
system. For this purpose, maps of two different sizes (3 3 3
and 5 3 5) were chosen and the experiment was performed
for the first 10 classes of the face database using five training
images and the same number of test images and the matching
was done using Euclidean norm. The block size for local
processing was kept as 4 3 4. Table V depicts that the recog-
nition rate remains same for both, 3 3 3 and 5 3 5 sizes if
the global processing method is used whereas local process-
ing method results in the change in recognition rate as the
size of the SOM is changed. There is an increase in recogni-
tion rate as the size of the SOM is increased. This experiment
was also repeated for Yale-Pose and Yale-Illumination face
databases. Tables VI and VII revealed that no change in rec-
ognition rate was observed so far as Yale-Pose was con-
cerned with respect to the change of SOM size, whereas a
change was noticed for Yale-Illumination. For LSOM,
though there was an increase in value yet still less than the
value obtained for GSOM.
3. In the third experiment, the number of classes of the face
database was varied from 10 to 20 to 40. This experiment
was performed to see the effect of local and global processing
methods on changing the number of classes of the face data-
base. The block size was kept as 4 3 4 for local processing.
Table VIII clearly shows that the recognition rate decreases
for both global and local processing systems as the number
of classes is increased. The increase in the number of classes
results in the increase in chances of similarity among the
classes and hence results in the decrease in performance of
the system. The results indicate that global processing still
performs better than the local processing method.
4. In this experiment, the training images were taken in the
form of a matrix, each column of which represented one
image and the number of columns was equal to the number
of images. The eigenvectors and eigenvalues were obtained
from the covariance matrix of the training images and the
80% of total number of eigenvectors, covering almost 99%
energy (Table I), were retained for performing PCA. Recon-
struction of test images was done after finding out the
Table VI. Recognition rate vs. SOM size – (Yale_Illumination).
Recognition Rate (%)
Method
Size of SOM
SOM (33 3) SOM (53 5)
LOCAL SOM 70 72
GLOBAL SOM 76 76
Table VII. Recognition rate vs. SOM size – (Yale_Pose).
Recognition Rate (%)
Method
Size of SOM
SOM (33 3) SOM (53 5)
LOCAL SOM 72.5 72.5
GLOBAL SOM 75 75
Table VIII. Recognition rate vs. number of classes for SOM, PCA, and
ICA – (ORL).
Recognition Rate (%)
Method
Number of Classes
10 20 40
GSOM 98.00 94.00 90.50
LSOM 96.00 90.00 88.00
PCA 94.00 91.67 89.83
ICA-I 94.00 92.00 84.00
ICA-II 90.00 85.00 79.00
Figure 4. Recognition rate for varying number of classes for SOM,
PCA, and ICA2 ORL.
Vol. 20, 261–267 (2010) 265
Karhunen-Loeve (KL) coefficients using the retained eigen-
vectors followed by matching using Euclidean norm. As
many as five training images and the same number of test
images were used for performing the experiments. There was
no overlap between training and test sets. The number of
classes was varied from 10 to 20 to 40 to determine the rec-
ognition rate. To perform ICA, a matrix X was obtained that
had 40% of the total number of principal axes. The data were
first whitened by passing the input matrix X through the whit-
ening matrix WZ ¼ 23ðCovðXÞÞ�12 and ICA was performed.
The weights W were updated as per rule DW 5 h(I 1 (1 22z)yT)W for 1600 iterations. The learning rate was initialized
at 0.001 and annealed down to 0.0001. A comparison among
all the techniques GSOM, LSOM, ICA-I, ICA-II, and PCA
has been given. Table VIII and Figure 4 show the recognition
rate of the techniques as the number of classes is varied.
5. This experiment was performed on the database obtained af-
ter mixing images from ORL, Yale-Pose, and Yale-Illumina-
tion databases, as explained in Section I. The images were
resized to 48 3 48 and as many as four images per subject
were taken for training and the same number was used for
testing. Table IX and Figure 5 depict the results. The Table
IX shows that PCA gives better results for 40 classes. It is
pertinent to mention here that this result has been obtained
when 80% of the total number of eigenvectors was retained.
The change in the recognition rate with respect to the number
of retained eigenvectors has been shown in Figure 6. There is
an increase in former as the latter increases. It has been
observed that normally 40% of the total number of eigenvec-
tors are retained that gives good results and at the same time
results in sufficient reduction in dimensionality.
V. CONCLUSIONS. In this article, an analysis of three unsuper-
vised learning techniques was done. From experimental results it
was found that while training the SOM, the local processing
approach took very less time as compared with global processing
method. This was due to the reason that pixel blocks were used that
reduced the dimensionality of the data space that was to be repre-
sented topologically in the SOM space. The results show that there
was no change in the performance of the recognition system for
ORL face database, whereas a change was observed in case of
Yale-Pose and Yale-Illumination databases as the size of the block
is changed. It was also observed that as the size of the block was
made 16 3 16, it yielded same results for both GSOM and LSOM.
It was further observed that the increase in the size of the SOM
does result in the increase of recognition rate (ORL and Yale-Illu-
mination) so far as local processing is concerned but still less than
that using global processing. Tables VIII and IX highlight compari-
son of all the unsupervised techniques. The simulation results indi-
cate that the performance of face recognition system decreases as
the number of classes (subjects) is increased. The reason for the
decrease in performance of recognition system is attributed to the
fact that as the number of classes (subjects) increase, the chances of
mismatch increase due to more similar faces. The results very
clearly highlight that GSOM outperforms all other techniques.
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