{"title":"The Robust Clustering with Reduction Dimension","authors":"Dyah E. Herwindiati","volume":63,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":199,"pagesEnd":205,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14058","abstract":"A clustering is process to identify a homogeneous\ngroups of object called as cluster. Clustering is one interesting topic\non data mining. A group or class behaves similarly characteristics.\nThis paper discusses a robust clustering process for data images with\ntwo reduction dimension approaches; i.e. the two dimensional\nprincipal component analysis (2DPCA) and principal component\nanalysis (PCA). A standard approach to overcome this problem is\ndimension reduction, which transforms a high-dimensional data into\na lower-dimensional space with limited loss of information. One of\nthe most common forms of dimensionality reduction is the principal\ncomponents analysis (PCA). The 2DPCA is often called a variant of\nprincipal component (PCA), the image matrices were directly treated\nas 2D matrices; they do not need to be transformed into a vector so\nthat the covariance matrix of image can be constructed directly using\nthe original image matrices. The decomposed classical covariance\nmatrix is very sensitive to outlying observations. The objective of\npaper is to compare the performance of robust minimizing vector\nvariance (MVV) in the two dimensional projection PCA (2DPCA)\nand the PCA for clustering on an arbitrary data image when outliers\nare hiden in the data set. The simulation aspects of robustness and\nthe illustration of clustering images are discussed in the end of\npaper","references":"[1] D.E. Herwindiati, M.A. Djauhari, and M. Mashuri, \"Robust\nMultivariate Outlier Labeling-, Journal Communication in Statistics -\nSimulation And Computation, Vol. 36, No 6, pp 1287-1294, April 2007.\n[2] D.E. Herwindiati, S.M. Isa, S.M, \"The Robust Principal Component\nUsing Minimum Vector Variance\", Electronic Engineering and\nComputing Technology, SpringerLink, Volume 60, pp 397-408, 2010\n[3] D.E. Herwindiati, \"A Robust Two-Dimensional Principal Component\nAnalysis for Classification\" Civil-Comp Proceedings ISSN 1759-3433,\npaper No 108, Valencia, September 2010\n[4] F.Anguilla and C. Pizzuti, \"Outlier Mining and Large High-\nDimensional Data Sets\", IEEE Transaction on Knowledge and Data\nEngineering, Vol 17, No 2, pp 203-215, 2005\n[5] I.T. Jolliffe, I.T. \"Principal Component Analysis\", Springer Verlag,\n1986\n[6] J. Yang, D. Zhang, A.F. Frangi and J-yu Yang, \"Two-Dimensional\nPCA: A New Approach to Appearance - Based Face Representation\nand Recognition\", IEEE Transaction on Pattern Analysis and machine\nIntelligence, Vol 26, No 1, pp 131 -137, 2004\n[7] M.A Djauhari,\"Improved Monitoring of Multivariate Process\nVariability\", Journal of Quality Technology, No 37, pp 32-39, 2005\n[8] M. Hubert, P.J. Rousseeuw, K. vanden Branden, \"ROBPCA: a New\nApproach to Robust Principal Component Analysis\", Journal.\nTechnometrics, 47, pp 64-79, 2003\n[9] P.J. Rousseeuw and A.M. Leroy, \"Robust Regression and Outlier\nDetection\", John Wiley, New York, 1987\n[10] P.J. Rousseeuw and K.van Driessen, \"A Fast Algorithm for The\nMinimum Covariance Determinant Estimator\", Journal.\nTechnometrics, 41, pp 212-223, 1999\n[11] S.M Kendall and A. Stuart, \"The Advanced Theory of Statistics\",\nCharles Griffin & Co Ltd, Vol. 2, Fourth Edition, London, 1979","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 63, 2012"}