The Robust Clustering with Reduction Dimension
Commenced in January 2007
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The Robust Clustering with Reduction Dimension

Authors: Dyah E. Herwindiati

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082267

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References:


[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