Journal of Signal and Information Processing, 2013, 4, 173-175
doi:10.4236/jsip.2013.43B031 Published Online August 2013 (http://www.scirp.org/journal/jsip)
173
An Overview of Principal Component Analysis
Sasan Karamizadeh1, Shahidan M. Abdullah1, Azizah A. Manaf1, Mazdak Zamani1,
Alireza Hooman2
1Advanced Informatics School(AIS), Universiti Teknologi Malayisa, Kuala Lumpur, Malaysia; 2Faculty of Management (FOM),
Multimedia University (MMU), Cyberjaya, Malaysia.
Received May, 2013.
ABSTRACT
The principal component analysis (PCA) is a kind of algorithms in biometrics. It is a statistics technical and used or-
thogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly
uncorrelated variables. PCA also is a tool to reduce multidimensional data to lower dimensions while retaining most of
the information. It covers standard deviation, covariance, and eigenvectors. This background knowledge is meant to
make the PCA section very straightforward, but can be skipped if the concepts are already familiar.
Keywords: Biometric; PCA; Eigenvector; Covariance; Standard Deviation
1. Introduction
Biometrics is derived from Greek .words “bio” meaning
life and metrics meaning the term biometrics is derived
from the Greek words bio meaning “life” and metrics
meaning “to measure” [1]. Biometrics refers to the iden-
tification or verification of a person based on his/her
physiological and/or behavioral characteristics [2]. Sev-
eral verification and identification based biometrics have
evolved based on various unique aspects of human body,
ease of acquiring the biometric, public acceptance and
the degree of security required [3].
Principal component analysis (PCA), also known as
Karhunen-Loeve expansion, is a classical feature extrac-
tion and data representation technique widely used in the
areas of pattern recognition and computer vision such as
face recognition [4]. The strategy of the Eigenfaces
method consists of extracting the characteristic features
on the face and representing the face in question as a
linear combination of the so called ‘eigenfaces’ obtained
from the feature extraction process [5]. The principal
components of the faces in the training set are calculated.
Recognition is achieved using the projection of the face
into the space formed by the eigenfaces [6]. A compari-
son on the basis of the Euclidian distance of the eigen-
vectors of the eigenfaces and the eigenface of the image
under question is made [7]. If this distance is small
enough, the person is identified [8]. On the other hand, if
the distance is too large, the image is regarded as one that
belongs to an individual for which the system has to be
trained [9]. Principal component analysis is a statistics
technical [10]. PCA used for reduce dimension vector to
better recognize images [11]. PCA is a useful statistical
technique that has found application in fields such as face
recognition and image compression, and is a common
technique for finding patterns in data of high dimension
[12]. Before getting to a description of PCA, this tutorial
first introduces mathematical concepts that will be used
in PCA. It covers standard deviation, covariance, and
eigenvectors [13]. This background knowledge is meant
to make the PCA section very straightforward, but can be
skipped if the concepts are already familiar [10, 14]. The
basis of the eigenfaces method is the Principal Compo-
nent Analysis (PCA). Eigenfaces and PCA have been
used by Sirovich and Kirby to represent the face images
efficiently [15, 16].
2. PCA Algorithm
Following are steps involve;
Step 1: Column or row vector of size N2 represents the
set of M images (B1, B2, B3…BM) with size N*N
Step 2: The training set image average (µ) is described
as
M
n1
1
μBn
m


(1)
Step 3: the average image by vector (W) is different
for each trainee image
Wi = Bi - µ (2)
Step 4: Total Scatter Matrix or Covariance Matrix is
calculated from Φ as shown below:

An Overview of Principal Component Analysis
174
M
n1
Cwnwnt AAT


, (3)
where A= [W1W2W3…Wn]
Step 5: Measure the eigenvectors UL and eigenvalues
λL of the covariance matrix C.
Step6: For image classification, this feature space can
be utilized. Measure the vectors of weights
ΩT = [w1, w2, …, wM'], (4)
whereby,
Hk = UkT (B - µ), k = 1, 2, …, M' (5)
3. The Important of PCA in Face
Recognition
The statistical information published in the area of facial
recognition technology utilizing the PCA method reveals
the significance of using this method for identifying and
verifying facial features [8]. Figure 1 below reveals the
amount of publications that have used the words ‘face
recognition’ and ‘PCA’ in their headings [17]
Figure 1. Number of publication utilizing [15].
Table 1 shows features about principal component
analysis.
4. Advantage and disadvantage of PCA
PCA’s key advantages are its low noise sensitivity, the
decreased requirements for capacity and memory, and
increased efficiency given the processes taking place in a
smaller dimensions; the complete advantages of PCA are
listed below:
1) Lack of redundancy of data given the orthogonal
components [19, 20].
2) Reduced complexity in images’ grouping with the
use of PCA [19, 20]
3) Smaller database representation since only the
trainee images are stored in the form of their projections
on a reduced basis [19].
4) Reduction of noise since the maximum variation
basis is chosen and so the small variations in the back-
ground are ignored automatically [19].
Table 1. The features of PCA are shown in the table below
[18].
Feature Principal component analysis
Discrimination between
classes
PCA manages the entire data for the
principal components analysis without
taking into consideration the
fundamental class structure.
Applications
PCA applications in the significant
fields of criminal investigation are
beneficial
Computation for large
datasets
PCA does not require large
computations
Direction of maximum
discrimination
The directions of the maximum
discrimination are not the same as the
directions of maximum variance as it is
not required to utilize the class
information such as the within class
scatter and between class scatter
Focus PCA examines the directions that
have widest variations
Supervised learning
technique PCA is an unsupervised technique.
Well distributed classes
in small datasets
PCA is not as powerful as other
methods.
Two key disadvantages of PCA are:
1) The covariance matrix is difficult to be evaluated in
an accurate manner [19].
2) Even the simplest invariance could not be captured
by the PCA unless the training data explicitly provides
this information [4].
5. Conclusions
The PCA method is an unsupervised technique of learn-
ing that is mostly suitable for databases that contain im-
ages with no class labels. A detailed description of the
PCA technique utilizing in face recognition has been
provided. As mentioned above, the PCA method’s ad-
vantages and disadvantages have also been explained in
this study.
6. Acknowledgment
The work we presented in this paper has been supported
by the University Technology Malaysia.
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