Outlier Detection Using Minimum Vector Variance Algorithm with Depth Function and Mahalanobis Distance
Bahasa Indonesia
DOI:
https://doi.org/10.20956/j.v17i3.12629Keywords:
Depth, Mahalanobis, MVV, PencilanAbstract
Outliers are observations where the point of observation deviates from the data pattern. The existence of outliers in the data can cause irregularities in the results of data analysis. One solution to this problem is to detect outliers using a statistical approach. The statistical approach method used in this study is the Minimum Vector Variance (MVV) algorithm which has robust characteristics for outliers. The purpose of this research is to detect outliers using the MVV algorithm by changing the data sorting criteria using the Robust Depth Mahalanobis to produce maximum detection. The results obtained from this study are that RDMMVV is superior to the observed value in showing the outliers and the location of the outliers in the data plot compared to DMMVV and MMVV.
References
Ali, Hazlina, 2013. On Robust Mahalanobis Distance issued from minimum vector variance. Universiti Utara Malaysia. Far East Journal of Mathematical Sciences
Barnett, V. and Lewis, T., 1984. Outliers in Statistical Data. 2nd Edition, John Wiley & Sons, Chichester.
Boni, Melda Putri., 2018. Mengelompokkan Subjek Menggunakan Mahalanobis Distance dan PCA. Sumatra Utara. Tesis Magister Jurusan Matematika Universitas Sumatra Utara
Butler RW, Davies PL, Jhun M., 1993. Asymptotics for the Minimum Covariance Determinant estimator. Ann Stat 1993, 21:1385–1400
Djauhari, M.A., 2005. Improved Monitoring of Multivariate Process Variability, Journal of Quality Technology, 37, 32-39.
Djauhari, M.A., Umbara, R. F., 2006. On Mahalanobis Depth Function, paper ini telah dipresentasikan di International Conference on Mathematics and Natural Sciences (ICMNS), Bandung, Indonesia
E T Herdiani, 2017. Modofikasi Penaksir Robust dalam Pelabelan Outlier Multivariat. Jurnal Matematika, Statistika, dan Komputasi Vol. 14, No.1, 46-53
E T Herdiani, P P Sari, and N Sunusi, 2019. Detection of Outliers in Multivariate Data using Minimum Vector Variance Method. Journal of Physics: Conference Series, Volume 1341 Issue 9
Hadi AS., 1992. Identifying Multivariate Outlier in Multivariate Data. Journal of Royal Statistical Society. 3(2):761-771.
Herwindiati, D.E., Djauhari, M.A., and Mashuri, M., 2006. Robust multivariate outlier labeling. Communication in Statistics.
Herwindiati, D. E., 2006. A New Criterion in Robust Estimation for Location and Covariance Matrix and Its Application for Outlier Labeling, Disertasi, Institut Teknologi Bandung.
Herwindiati D.E., and Sani M., 2009. The Robust Principal Component Using Minimum Vector Variance, Proceedings of the World Congress on Engineering 2009. Vol I, 1 – 3 July 2009. London, U.K.
Liu, R. Y., 1990. On a Notion of Data Depth Based on Random Simplices. The Annals of Statistics, 18(1), 405–414. doi:10.1214/aos/1176347507
Mahalanobis PC., 1936. On the generalised distance in statistics. Proceedings of the National Institute of Science India, 2: 4955.
Manoj, K., Senthamarai Kannan, K., 2013. Comparison of Methods for detecting Outliers, International Journal of Scientific and Engineering Research,4(9), 709-714
Rousseeuw, P. J., & Driessen, K. V., 1999. A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics, 41(3), 212–223.doi:10.1080/00401706.1999.10485670
Rousseeuw, P.J. & Van Zomeren, B.C., 1990. Unmasking Multivariate Outlier and Leverage Points. Journal of the American Statistical Association. 85: 633-639.
Singh, K., Parelius, J. M., & Liu, R. Y., 1999. Multivariate analysis by data depth: descriptive statistics, graphics and inference The Annals of Statistics, 27(3), 783–858. doi:10.1214/aos/1018031260
Suwanda Idris, Lisnur Wachidah, Teti Sofiyayanti, Erwin Harahap, 2019. The Control Chart of Data Depth Based on Influence Function of Variance Vector. J. Phys.: Conf. Ser.1366 012125
Syed Yahaya, Sharipah Soaad and Ali, Hazlina and Omar, Zurni, 2011. An alternative hotelling T^2 control chart based on Minimum Vector Variance (MVV). Modern Applied Science, 5 (4). pp. 132-151. ISSN 1913-1844
Ye, N., Chen, Q., 2001. An Anomaly Detection Technique Based on A Chi Square Statistic for Detecting Intrusion into Information Systems, Quality and Realibility Engineering International, Qual. Realb. Engng. Int., 17, 105-112.
Zuo, Y., & Serfling, R., 2000. General notions of statistical depth function. The Annals of Statistics, 28(2), 461–482. doi:10.1214/aos/1016218226
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