A clustering is process to identify a homogeneous
groups of object called as cluster. Clustering is one interesting topic
on data mining. A group or class behaves similarly characteristics.
This paper discusses a robust clustering process for data images with
two reduction dimension approaches; i.e. the two dimensional
principal component analysis (2DPCA) and principal component
analysis (PCA). A standard approach to overcome this problem is
dimension reduction, which transforms a high-dimensional data into
a lower-dimensional space with limited loss of information. One of
the most common forms of dimensionality reduction is the principal
components analysis (PCA). The 2DPCA is often called a variant of
principal component (PCA), the image matrices were directly treated
as 2D matrices; they do not need to be transformed into a vector so
that the covariance matrix of image can be constructed directly using
the original image matrices. The decomposed classical covariance
matrix is very sensitive to outlying observations. The objective of
paper is to compare the performance of robust minimizing vector
variance (MVV) in the two dimensional projection PCA (2DPCA)
and the PCA for clustering on an arbitrary data image when outliers
are hiden in the data set. The simulation aspects of robustness and
the illustration of clustering images are discussed in the end of
paper
[1] D.E. Herwindiati, M.A. Djauhari, and M. Mashuri, "Robust
Multivariate Outlier Labeling-, Journal Communication in Statistics -
Simulation And Computation, Vol. 36, No 6, pp 1287-1294, April 2007.
[2] D.E. Herwindiati, S.M. Isa, S.M, "The Robust Principal Component
Using Minimum Vector Variance", Electronic Engineering and
Computing Technology, SpringerLink, Volume 60, pp 397-408, 2010
[3] D.E. Herwindiati, "A Robust Two-Dimensional Principal Component
Analysis for Classification" Civil-Comp Proceedings ISSN 1759-3433,
paper No 108, Valencia, September 2010
[4] F.Anguilla and C. Pizzuti, "Outlier Mining and Large High-
Dimensional Data Sets", IEEE Transaction on Knowledge and Data
Engineering, Vol 17, No 2, pp 203-215, 2005
[5] I.T. Jolliffe, I.T. "Principal Component Analysis", Springer Verlag,
1986
[6] J. Yang, D. Zhang, A.F. Frangi and J-yu Yang, "Two-Dimensional
PCA: A New Approach to Appearance - Based Face Representation
and Recognition", IEEE Transaction on Pattern Analysis and machine
Intelligence, Vol 26, No 1, pp 131 -137, 2004
[7] M.A Djauhari,"Improved Monitoring of Multivariate Process
Variability", Journal of Quality Technology, No 37, pp 32-39, 2005
[8] M. Hubert, P.J. Rousseeuw, K. vanden Branden, "ROBPCA: a New
Approach to Robust Principal Component Analysis", Journal.
Technometrics, 47, pp 64-79, 2003
[9] P.J. Rousseeuw and A.M. Leroy, "Robust Regression and Outlier
Detection", John Wiley, New York, 1987
[10] P.J. Rousseeuw and K.van Driessen, "A Fast Algorithm for The
Minimum Covariance Determinant Estimator", Journal.
Technometrics, 41, pp 212-223, 1999
[11] S.M Kendall and A. Stuart, "The Advanced Theory of Statistics",
Charles Griffin & Co Ltd, Vol. 2, Fourth Edition, London, 1979
[1] D.E. Herwindiati, M.A. Djauhari, and M. Mashuri, "Robust
Multivariate Outlier Labeling-, Journal Communication in Statistics -
Simulation And Computation, Vol. 36, No 6, pp 1287-1294, April 2007.
[2] D.E. Herwindiati, S.M. Isa, S.M, "The Robust Principal Component
Using Minimum Vector Variance", Electronic Engineering and
Computing Technology, SpringerLink, Volume 60, pp 397-408, 2010
[3] D.E. Herwindiati, "A Robust Two-Dimensional Principal Component
Analysis for Classification" Civil-Comp Proceedings ISSN 1759-3433,
paper No 108, Valencia, September 2010
[4] F.Anguilla and C. Pizzuti, "Outlier Mining and Large High-
Dimensional Data Sets", IEEE Transaction on Knowledge and Data
Engineering, Vol 17, No 2, pp 203-215, 2005
[5] I.T. Jolliffe, I.T. "Principal Component Analysis", Springer Verlag,
1986
[6] J. Yang, D. Zhang, A.F. Frangi and J-yu Yang, "Two-Dimensional
PCA: A New Approach to Appearance - Based Face Representation
and Recognition", IEEE Transaction on Pattern Analysis and machine
Intelligence, Vol 26, No 1, pp 131 -137, 2004
[7] M.A Djauhari,"Improved Monitoring of Multivariate Process
Variability", Journal of Quality Technology, No 37, pp 32-39, 2005
[8] M. Hubert, P.J. Rousseeuw, K. vanden Branden, "ROBPCA: a New
Approach to Robust Principal Component Analysis", Journal.
Technometrics, 47, pp 64-79, 2003
[9] P.J. Rousseeuw and A.M. Leroy, "Robust Regression and Outlier
Detection", John Wiley, New York, 1987
[10] P.J. Rousseeuw and K.van Driessen, "A Fast Algorithm for The
Minimum Covariance Determinant Estimator", Journal.
Technometrics, 41, pp 212-223, 1999
[11] S.M Kendall and A. Stuart, "The Advanced Theory of Statistics",
Charles Griffin & Co Ltd, Vol. 2, Fourth Edition, London, 1979
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63061", author = "Dyah E. Herwindiati", title = "The Robust Clustering with Reduction Dimension", abstract = "A clustering is process to identify a homogeneous
groups of object called as cluster. Clustering is one interesting topic
on data mining. A group or class behaves similarly characteristics.
This paper discusses a robust clustering process for data images with
two reduction dimension approaches; i.e. the two dimensional
principal component analysis (2DPCA) and principal component
analysis (PCA). A standard approach to overcome this problem is
dimension reduction, which transforms a high-dimensional data into
a lower-dimensional space with limited loss of information. One of
the most common forms of dimensionality reduction is the principal
components analysis (PCA). The 2DPCA is often called a variant of
principal component (PCA), the image matrices were directly treated
as 2D matrices; they do not need to be transformed into a vector so
that the covariance matrix of image can be constructed directly using
the original image matrices. The decomposed classical covariance
matrix is very sensitive to outlying observations. The objective of
paper is to compare the performance of robust minimizing vector
variance (MVV) in the two dimensional projection PCA (2DPCA)
and the PCA for clustering on an arbitrary data image when outliers
are hiden in the data set. The simulation aspects of robustness and
the illustration of clustering images are discussed in the end of
paper", keywords = "Breakdown point, Consistency, 2DPCA, PCA,
Outlier, Vector Variance", volume = "6", number = "3", pages = "346-6", }