This document compares Principal Component Analysis (PCA) and Independent Component Analysis (ICA) and their application to facial image analysis. It provides an introduction to both PCA and ICA, including their processes and differences. The document then summarizes previous literature comparing PCA and ICA, describes implementations of PCA for facial recognition on Japanese, African, and Asian datasets in MATLAB, and calculates statistical metrics for the original and recognized images. It concludes that PCA is effective for pattern recognition and dimensionality reduction in facial analysis applications.

1. Standard Statistical Feature analysis of Image
Features for Facial Images using Principal
Component Analysis and its Comparative study
with Independent Component Analysis
Madhav Institute of Technology and Science
Gwalior (M.P.)
By: Bulbul Agrawal

2. Content
Introduction
Literature Review
Principal Component Analysis
Independent Component Analysis
Comparison b/w PCA and ICA
Applications of PCA and ICA
Work Done
References

3. Introduction
• The two most important techniques have been explored here as these approaches are
very useful in many fields. One of the most interesting field, scilicet as face
recognition has become a hot topic in computer vision algorithms. Similarly,
dimensionality reduction, compression, signal separation, image filtering, and many
other statistical approaches are becoming popular and of great use in many fields day
by day.
• In the computer vision, PCA is a popular method and applied mainly in face
recognition whereas ICA was initially originated for distinct and the mixed audio
signals into independent sources[10].
• The literature on the subject is conflicting. Some assert that PCA outperforms ICA
others claim that ICA outperforms PCA and some claims that there is no difference
in their performance statistically[8]. Thus, this paper compares the PCA technique to
a newer technique ICA.

4. Literature Review
• Bing Luo et al This paper discusses about the PCA and ICA and compares them in
face recognition application and gives differences between them. They used PCA
derived from eigen faces and ICA derived from linear representation of non-
gaussian data.
• Bruce A. Draper et al This paper compares principal component analysis (PCA)
and independent component analysis (ICA). Depending upon the task statement,
the ICA algorithm, PCA subspace distance metric relative performance has been
measured. in the context of a baseline face recognition system, a comparison
motivated by contradictory.
• Zaid Abdi Alkareem Alyasseri In this paper, two algorithms are discussed to
recognize a face, namely, Eigenface and ICA. This paper shows how the error rate
between the original face and the recognized face has been improved and the
results are shown by the various graphs.

5. Principal Component Analysis
• The main idea of principal component analysis (PCA) is to reduce the
dimensionality of a data set consisting of many variables correlated with each other.
• The same is done by transforming the variables to a new set of variables, which are
known as the principal components (or simply, the PCs)[2] and are orthogonal.
• The principal components are the eigenvectors of a covariance matrix, and hence
they are orthogonal.
• The direction of the PCA space serves as the direction of the maximum variance of
the given data points[9].

6. Process of computing the PCA space
A. Acquire some data
B. Calculate the covariance matrix
from mean centering data
C. Find the eigenvalues and
eigenvectors of the covariance
matrix
 Plot the eigenvectors / principal
components over the scaled data
Fig 1: Process of computing PCs

7. Independent Component Analysis
• In the method of ICA, not only statistical characteristics in second order or higher
order are considered, but also basis vectors decomposed from face images obtained
by ICA are more localized in distribution space than those by PCA[12].
• Localized characteristics are favorable for face recognition, because human faces
are non-rigid bodies, and because localized characteristics are not easily influenced
by face expression changes, location position, or partial occlusion [11].
• Independent Component Analysis is basically used to solve the Blind Source
Seperation/ Cocktail Party Problem[8].
ICAAmbiguities:
• The two most common ambiguities arise in ICA are that the method to calculate the
variances of the independent components cannot be determined. Another problem is
that the order of the independent components is also cannot be identifiable.

8. Example of ICA
• Imagine that you are a weaver, and you have a loom of
colorful strings. Each string represents a unique pattern in
the data. With actual data, each of these strings would be a
vector of numbers that can be fit with a linear equation. As
we see the strings in fig 1, they are well organized.
• Unfortunately, when we collect data in the real world it
does not come to us neat and organized. Our unique strings
get mixed up with other strings, and random signal such as
noise as shown in fig 2. In our example above, a monkey
has come along and mixed up our strings. How do we
untangle them?
• We could know something special about each string,
maybe a feature like color, and manually unmix, however
it we are dealing with a huge dataset and don’t have a clue
about any special features, we are powerless. This is where
ICA comes in. We start with our mixed data and assume
1) we have mixed up data (our loom) that is
2) comprised of independent signals
Fig 2: Original Data
Fig 3: MIXED UP DATA
INDEPENDENCE

9. • We start with this mixed up data, X, and we know
that it was generated by the monkey applying
some sequence of movements to it (the “monkey
madness”). We call this series of transformations
that the monkey applies to the unmixed data, s our
mixing matrix. This matrix would consist of
vectors of numbers that, when multiplied with s,
produce the observed data X.
X=A x S
• To solve this problem and recover our original
strings from the mixed ones, we just need to solve
this equation for s. We know X, so we just need to
figure out what the inverse of A is. This is
normally referred to as “W” or the un-mixing
matrix. We are going to choose the numbers in
this matrix that maximize the probability of our
data.
S= A-1 x X
Mixed Strings Monkey Madness
(Mixing Matrix)
Original Strings
(Original Data)
Original Strings
(Original Data)
Unmixing
matrix W (A-1)
Mixed Strings
(Observed Data)
Fig 4
Fig 5

10. Comparison between PCA & ICA
S.No. Principal Component Analysis (PCA) Independent Component Analysis (ICA)
1. In the image database, PCA relies only on pairwise
relationships between pixels.
Detecting the component from a multivariate data is
done by ICA.
2. PCA takes details of statistical changes from second
order statistics.
It can have details up to higher order statistics.
3. With the help of PCA, higher order relations cannot be
removed but it is useful for removing correlations.
ICA, on the other hand removes both correlations as
well as higher order dependence.
4. It works with the Gaussian model. ICA works with the non-Gaussian model.
5. Based on their eigenvalues some of the components in
PCA are given more importance with respect to others.
In ICA, all of the components are of equal
importance.
6. It prefers orthogonal vectors. Non-orthogonal vectors are used.
7. PCA performance is based on the task statement, the
subspace distance metric, and the number of subspace
dimensions retained.
The performance of ICA depends on the task, the
algorithm used to approximate ICA, and the number of
subspace dimensions retained.
8. For compression purpose, PCA uses low-rank matrix It uses full rank matrix factorization to eliminate
Table 1: Comparison between PCA & ICA[7][12] :

11. Applications of PCA & ICA:
PCA:
• Dimensionality reduction
• Image compression
• Medical imaging
• Gene expression analysis
• Data classification
• Noise reduction
ICA:
• Artifacts separation in MEG data
• ICA in text mining
• ICA for CDMA communication
• Searching for hidden factors in
Financial Data
• Noise Reduction in natural images
Applications of PCA and ICA are following:

12. Proposed Work
• In this paper, we have implemented the facial recognition system for the different
types of dataset such as Japanese, African and Asian by the principal component
analysis using Euclidean distance.
• In our work, the equivalent tested image is obtained as a output for the
corresponding original input image and the various statistical parameters for
facial input image and recognised equivalent image is computed.
• All the parameters of the different dataset have been calculated in the MATLAB
2018a.
• In addition to the above mentioned points, comparision of both the techniques
(PCA/ICA) along with their application in various field is discussed.

13. Implementation of face recognition system by
PCA using MATLAB
 Analysis on Japanese Dataset
S.No. Parameters Test Image Equivalent
Image
1. Entropy 7.3298 7.2780
2. Standard
Deviation
78.4347 76.4705
3. Mean 127.9513 121.8242
4. Median 152 142
5. Variance 8.8563 8.7447
6. Mode 2 2
7. Correlation 0.9514
8. SSIM 0.5976
Fig 6: Analysis of face recognition system for
Japanese dataset
Table 2: Calculation of different parameters

14. Implementation of face recognition system by
PCA using MATLAB
 Analysis on Africans Dataset
S.No
.
Parameters Test Image Equivalent
Image
1. Entropy 4.8991 4.9450
2. Standard
Deviation
110.4553 109.0322
3. Mean 139.2155 142.5504
4. Median 110 129
5. Variance 10.5097 10.4418
6. Mode 255 255
7. Correlation 0.8993
8. SSIM 0.6804
Fig 7: Analysis of face recognition system for
Africans dataset
Table 3: Calculation of different parameters

15. Implementation of face recognition system by
PCA using MATLAB
 Analysis on Asian Dataset
S.N
o.
Parameters Test Image Equivalent
Image
1. Entropy 4.6686 4.8430
2. Standard
Deviation
97.0983 98.4387
3. Mean 174.5845 169.2308
4. Median 255 252
5. Variance 9.8538 9.9216
6. Mode 255 255
7. Correlation 0.9075
8. SSIM 0.7840
Table 4: Calculation of different parameters
Fig 8: Analysis of face recognition system for Asian
dataset

16. Conclusion
• We have implemented the PCA techniques on different types of datasets namely
African, Japanese and Asian datasets and have calculated various parameters such
as entropy, standard deviation, mean, median, variance, mode, correlation.
• We have also compared PCA and ICA based on certain specifications. In our study,
we have also concluded that face based PCA is a classical fruitful technique and
PCA justifies its strength in pattern recognition and dimensionality reduction.

17. References
1. Swati Goel Akhilesh Verma Savita Goel KomalJuneja, “ICA in Image Processing: A Survey” IEEE International
Conference on Computational Intelligence & Communication Technology (2015).
2. Shlens, Jonathon. "A tutorial on principal component analysis." arXiv preprint arXiv:1404.1100 (2014).
3. Martis, Roshan Joy, U. Rajendra Acharya, and Lim Choo Min. "ECG beat classification using PCA, LDA, ICA and
discrete wavelet transform." Biomedical Signal Processing and Control8.5 (2013): 437-448
4. Chawla, M. P. S. "PCA and ICA processing methods for removal of artifacts and noise in electrocardiograms: A
survey and comparison." Applied Soft Computing 11.2 (2011): 2216-2226.
5. Gupta, Varun, et al. "An introduction to principal component analysis and its importance in biomedical signal
processing." International Conference on Life Science and Technology, IPCBEE. Vol. 3. 2011.
6. Comon, Pierre, and Christian Jutten, eds. Handbook of Blind Source Separation: Independent component analysis
and applications. Academic press, 2010.
7. Bing Luo, Yu-Jie Hao, Wei-Hua Zhang, Zhi-Shen Liu “Comparison of PCA and ICA in Face Recognition.”
8. Simon HaykinZhe Chen, “The Cocktail Party Problem” Neural Computation17, 18751902 (2005).
9. Yang, Jian, et al. "Two-dimensional PCA: a new approach to appearance-based face representation and recognition."
IEEE transactions on pattern analysis and machine intelligence 26.1 (2004): 131-137.
10. Draper, Bruce A., et al. "Recognizing faces with PCA and ICA." Computer vision and image understanding 91.1-2
(2003): 115-137.
11. Ziga Zaplotnik, “Indepenent Component Analysis”, April 2014.
12. Baek, K., Draper, B.A., Beveridge, J.R. and She, K., 2002, March. PCA vs. ICA: A Comparison on the FERET Data
Set. In JCIS (pp. 824-827).

18. CITATION OF THIS PAPER
Agrawal, Bulbul, Shradha Dubey, and Manish Dixit. "Standard Statistical
Feature Analysis of Image Features for Facial Images Using Principal
Component Analysis and Its Comparative Study with Independent Component
Analysis." International Conference on Intelligent Computing and Smart
Communication 2019. Springer, Singapore, 2020.