메뉴 건너뛰기




Volumn 22, Issue 1, 2012, Pages 325-336

The flood algorithm-a multivariate, self-organizing-map-based, robust location and covariance estimator

Author keywords

Computational complexity; Minimum covariance determinant; Outlier detection

Indexed keywords


EID: 81955161248     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-011-9250-3     Document Type: Article
Times cited : (9)

References (48)
  • 1
    • 21844510157 scopus 로고
    • Fast very robust methods for the detection of multiple outliers
    • Atkinson, A. C.: Fast very robust methods for the detection of multiple outliers. J. Am. Stat. Assoc. 89(428), 1329-1339 (1994).
    • (1994) J. Am. Stat. Assoc. , vol.89 , Issue.428 , pp. 1329-1339
    • Atkinson, A.C.1
  • 3
    • 0347920342 scopus 로고    scopus 로고
    • The grand tour as a method for detecting multivariate outliers
    • Bartkowiak, A., Szustalewicz, A.: The grand tour as a method for detecting multivariate outliers. Mach. Graph. Vis. 6, 487-505 (1997).
    • (1997) Mach. Graph. Vis. , vol.6 , pp. 487-505
    • Bartkowiak, A.1    Szustalewicz, A.2
  • 4
    • 1542742610 scopus 로고    scopus 로고
    • The masking breakdown point of multivariate outlier identification rules
    • Becker, C., Gather, U.: The masking breakdown point of multivariate outlier identification rules. J. Am. Stat. Assoc. 94, 947-955 (1999).
    • (1999) J. Am. Stat. Assoc. , vol.94 , pp. 947-955
    • Becker, C.1    Gather, U.2
  • 5
    • 0035962037 scopus 로고    scopus 로고
    • The largest nonidentifiable outlier: a comparison of multivariate simultaneous outlier identification rules
    • Becker, C., Gather, U.: The largest nonidentifiable outlier: a comparison of multivariate simultaneous outlier identification rules. Comput. Stat. Data Anal. 36(1), 119-127 (2001).
    • (2001) Comput. Stat. Data Anal. , vol.36 , Issue.1 , pp. 119-127
    • Becker, C.1    Gather, U.2
  • 6
    • 81955167169 scopus 로고    scopus 로고
    • MVE, MCD, and MZE: A simulation study comparing convex body minimizers
    • Becker, C., Paris Scholz, S.: MVE, MCD, and MZE: A simulation study comparing convex body minimizers. Allg. Stat. Arch. 88(2), 155-162 (2004).
    • (2004) Allg. Stat. Arch. , vol.88 , Issue.2 , pp. 155-162
    • Becker, C.1    Paris Scholz, S.2
  • 7
    • 81955162454 scopus 로고    scopus 로고
    • Deepest points and least deep points: robustness and outliers with MZE
    • M. Spiliopoulou, R. Kruse, C. Borgelt, A. Nürnberger, and W. Gaul (Eds.), Berlin: Springer
    • Becker, C., Paris Scholz, S.: Deepest points and least deep points: robustness and outliers with MZE. In: Spiliopoulou, M., Kruse, R., Borgelt, C., Nürnberger, A., Gaul, W. (eds.) From Data and Information Analysis to Knowledge Engineering, pp. 254-261. Springer, Berlin (2006).
    • (2006) From Data and Information Analysis to Knowledge Engineering , pp. 254-261
    • Becker, C.1    Paris Scholz, S.2
  • 8
    • 0345404393 scopus 로고    scopus 로고
    • Theoretical aspects of the SOM algorithm
    • Cottrell, M., Fort, J. C., Pagès, G.: Theoretical aspects of the SOM algorithm. Neurocomputing 21(1-3), 119-138 (1998).
    • (1998) Neurocomputing , vol.21 , Issue.1-3 , pp. 119-138
    • Cottrell, M.1    Fort, J.C.2    Pagès, G.3
  • 9
    • 0001088628 scopus 로고    scopus 로고
    • Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies
    • Croux, C., Haesbroeck, G.: Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87(3), 603 (2000).
    • (2000) Biometrika , vol.87 , Issue.3 , pp. 603
    • Croux, C.1    Haesbroeck, G.2
  • 10
    • 0000789842 scopus 로고
    • Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices
    • Davies, P.: Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices. Ann. Stat. 15(3), 1269-1292 (1987).
    • (1987) Ann. Stat. , vol.15 , Issue.3 , pp. 1269-1292
    • Davies, P.1
  • 11
    • 21144467678 scopus 로고
    • The asymptotics of Rousseeuw's minimum volume ellipsoid estimator
    • Davies, P.: The asymptotics of Rousseeuw's minimum volume ellipsoid estimator. Ann. Stat. 20(4), 1828-1843 (1992).
    • (1992) Ann. Stat. , vol.20 , Issue.4 , pp. 1828-1843
    • Davies, P.1
  • 12
    • 23744473058 scopus 로고    scopus 로고
    • Breakdown and groups
    • Davies, P., Gather, U.: Breakdown and groups. Ann. Stat. 33(3), 977-988 (2005).
    • (2005) Ann. Stat. , vol.33 , Issue.3 , pp. 977-988
    • Davies, P.1    Gather, U.2
  • 13
    • 33747178343 scopus 로고    scopus 로고
    • Addendum to the discussion of "breakdown and groups"
    • Davies, P., Gather, U.: Addendum to the discussion of "breakdown and groups". Ann. Stat. 34(3), 1577-1579 (2006).
    • (2006) Ann. Stat. , vol.34 , Issue.3 , pp. 1577-1579
    • Davies, P.1    Gather, U.2
  • 14
    • 8344287578 scopus 로고
    • Convergence properties of self-organizing maps
    • Erwin, E., Obermeyer, K., Schulten, K.: Convergence properties of self-organizing maps. Artif. Neural Netw. 1, 409-414 (1991).
    • (1991) Artif. Neural Netw. , vol.1 , pp. 409-414
    • Erwin, E.1    Obermeyer, K.2    Schulten, K.3
  • 15
    • 0026436795 scopus 로고
    • Self-organizing maps: ordering, convergence properties and energy functions
    • Erwin, E., Obermayer, K., Schulten, K.: Self-organizing maps: ordering, convergence properties and energy functions. Biol. Cybern. 67(1), 47-55 (1992a).
    • (1992) Biol. Cybern. , vol.67 , Issue.1 , pp. 47-55
    • Erwin, E.1    Obermayer, K.2    Schulten, K.3
  • 16
    • 0026462366 scopus 로고
    • Self-organizing maps: stationary states, metastability and convergence rate
    • Erwin, E., Obermayer, K., Schulten, K.: Self-organizing maps: stationary states, metastability and convergence rate. Biol. Cybern. 67(1), 35-45 (1992b).
    • (1992) Biol. Cybern. , vol.67 , Issue.1 , pp. 35-45
    • Erwin, E.1    Obermayer, K.2    Schulten, K.3
  • 17
    • 33746622513 scopus 로고    scopus 로고
    • SOM's mathematics
    • Advances in Self Organising Maps-WSOM'05
    • Fort, J.: SOM's mathematics. Neural Netw. 19(6-7), 812-816 (2006). Advances in Self Organising Maps-WSOM'05.
    • (2006) Neural Netw , vol.19 , Issue.6-7 , pp. 812-816
    • Fort, J.1
  • 18
    • 21144473392 scopus 로고
    • Unmasking outliers and leverage points: a confirmation
    • Fung, W.-K.: Unmasking outliers and leverage points: a confirmation. J. Am. Stat. Assoc. 88(422), 515-519 (1993).
    • (1993) J. Am. Stat. Assoc. , vol.88 , Issue.422 , pp. 515-519
    • Fung, W.-K.1
  • 19
    • 0005454084 scopus 로고    scopus 로고
    • Outlier identification and robust methods
    • Handbook of Statistics, G. Maddala and C. Rao (Eds.)
    • Gather, U., Becker, C.: Outlier identification and robust methods. In: Maddala, G., Rao, C. (eds.) Robust Inference. Handbook of Statistics, vol. 15, pp. 123-143 (1997).
    • (1997) Robust Inference , vol.15 , pp. 123-143
    • Gather, U.1    Becker, C.2
  • 21
    • 29544436837 scopus 로고    scopus 로고
    • The distribution of robust distances
    • Hardin, J., Rocke, D.: The distribution of robust distances. J. Comput. Graph. Stat. 14(4), 928-946 (2005).
    • (2005) J. Comput. Graph. Stat. , vol.14 , Issue.4 , pp. 928-946
    • Hardin, J.1    Rocke, D.2
  • 24
    • 49749129645 scopus 로고    scopus 로고
    • High-breakdown robust multivariate methods
    • Hubert, M., Rousseeuw, P., Aelst, S.: High-breakdown robust multivariate methods. Stat. Sci. 23(1), 92-119 (2008).
    • (2008) Stat. Sci. , vol.23 , Issue.1 , pp. 92-119
    • Hubert, M.1    Rousseeuw, P.2    Aelst, S.3
  • 25
    • 7444265318 scopus 로고    scopus 로고
    • Bibliography of self-organizing map (SOM) papers: 1981-1997
    • Kaski, S., Kangas, J., Kohonen, T.: Bibliography of self-organizing map (SOM) papers: 1981-1997. Neural Comput. Surv. 1(3&4), 1-176 (1998).
    • (1998) Neural Comput. Surv. , vol.1 , Issue.3-4 , pp. 1-176
    • Kaski, S.1    Kangas, J.2    Kohonen, T.3
  • 26
    • 0020068152 scopus 로고
    • Self-organized formation of topologically correct feature maps
    • Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cybern. 43(1), 59-69 (1982).
    • (1982) Biol. Cybern. , vol.43 , Issue.1 , pp. 59-69
    • Kohonen, T.1
  • 29
    • 0031482783 scopus 로고    scopus 로고
    • Zonoid trimming for multivariate distributions
    • Koshevoy, G., Mosler, K.: Zonoid trimming for multivariate distributions. Ann. Stat. 25(5), 1998-2017 (1997).
    • (1997) Ann. Stat. , vol.25 , Issue.5 , pp. 1998-2017
    • Koshevoy, G.1    Mosler, K.2
  • 30
    • 0007773105 scopus 로고    scopus 로고
    • Lift zonoids, random convex hulls, and the variability of random vectors
    • Koshevoy, G., Mosler, K.: Lift zonoids, random convex hulls, and the variability of random vectors. Bernoulli 4(3), 377-399 (1998).
    • (1998) Bernoulli , vol.4 , Issue.3 , pp. 377-399
    • Koshevoy, G.1    Mosler, K.2
  • 31
    • 10744230913 scopus 로고    scopus 로고
    • A scatter matrix estimate based on the zonotope
    • Koshevoy, G., Möttönen, J., Oja, H.: A scatter matrix estimate based on the zonotope. Ann. Stat. 31(5), 1439-1459 (2003).
    • (2003) Ann. Stat. , vol.31 , Issue.5 , pp. 1439-1459
    • Koshevoy, G.1    Möttönen, J.2    Oja, H.3
  • 33
    • 0033233738 scopus 로고    scopus 로고
    • Asymptotics of reweighted estimators of multivariate location and scatter
    • Lopuhaä, H.: Asymptotics of reweighted estimators of multivariate location and scatter. Ann. Stat. 27(5), 1638-1665 (1999).
    • (1999) Ann. Stat. , vol.27 , Issue.5 , pp. 1638-1665
    • Lopuhaä, H.1
  • 34
    • 0001352378 scopus 로고
    • Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
    • Lopuhaä, H., Rousseeuw, P.: Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. Ann. Stat. 19(1), 229-248 (1991).
    • (1991) Ann. Stat. , vol.19 , Issue.1 , pp. 229-248
    • Lopuhaä, H.1    Rousseeuw, P.2
  • 35
    • 33746037215 scopus 로고    scopus 로고
    • Multiple outlier detection in multivariate data using self-organizing maps title
    • Nag, A., Mitra, A., Mitra, S.: Multiple outlier detection in multivariate data using self-organizing maps title. Comput. Stat. 20(2), 245-264 (2005).
    • (2005) Comput. Stat. , vol.20 , Issue.2 , pp. 245-264
    • Nag, A.1    Mitra, A.2    Mitra, S.3
  • 36
    • 7444265318 scopus 로고    scopus 로고
    • Bibliography of self-organizing map (SOM) papers: 1998-2001 addendum
    • Oja, M., Kaski, S., Kohonen, T.: Bibliography of self-organizing map (SOM) papers: 1998-2001 addendum. Neural Comput. Surv. 1, 1-176 (2002).
    • (2002) Neural Comput. Surv. , vol.1 , pp. 1-176
    • Oja, M.1    Kaski, S.2    Kohonen, T.3
  • 38
    • 0036383073 scopus 로고    scopus 로고
    • Small sample corrections for LTS and MCD
    • Pison, G., van Aelst, S., Willems, G.: Small sample corrections for LTS and MCD. Metrika 55, 111-123 (2002).
    • (2002) Metrika , vol.55 , pp. 111-123
    • Pison, G.1    van Aelst, S.2    Willems, G.3
  • 41
    • 0030500928 scopus 로고    scopus 로고
    • Robustness properties of S-estimators of multivariate location and shape in high dimension
    • Rocke, D.: Robustness properties of S-estimators of multivariate location and shape in high dimension. Ann. Stat. 24(3), 1327-1345 (1996).
    • (1996) Ann. Stat. , vol.24 , Issue.3 , pp. 1327-1345
    • Rocke, D.1
  • 42
    • 0030344143 scopus 로고    scopus 로고
    • Identification of outliers in multivariate data
    • Rocke, D. M., Woodruff, D. L.: Identification of outliers in multivariate data. J. Am. Stat. Assoc. 91(435), 1047-1061 (1996).
    • (1996) J. Am. Stat. Assoc. , vol.91 , Issue.435 , pp. 1047-1061
    • Rocke, D.M.1    Woodruff, D.L.2
  • 44
    • 0002564033 scopus 로고
    • Multivariate estimation with high breakdown point
    • Rousseeuw, P.: Multivariate estimation with high breakdown point. Math. Stat. Appl. 8, 283-297 (1985).
    • (1985) Math. Stat. Appl. , vol.8 , pp. 283-297
    • Rousseeuw, P.1
  • 46
    • 0032680362 scopus 로고    scopus 로고
    • A fast algorithm for the minimum covariance determinant estimator
    • Rousseeuw, P., van Driessen, K.: A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212-223 (1999).
    • (1999) Technometrics , vol.41 , pp. 212-223
    • Rousseeuw, P.1    van Driessen, K.2
  • 47
    • 84950439147 scopus 로고
    • Unmasking multivariate outliers and leverage points
    • Rousseeuw, P., van Zomeren, B.: Unmasking multivariate outliers and leverage points. J. Am. Stat. Assoc. 85(411), 633-639 (1990).
    • (1990) J. Am. Stat. Assoc. , vol.85 , Issue.411 , pp. 633-639
    • Rousseeuw, P.1    van Zomeren, B.2
  • 48
    • 0002535204 scopus 로고
    • Self-organizing neural networks for visualization and classification
    • O. Opitz, B. Lausen, and R. Klar (Eds.), Berlin: Springer
    • Ultsch, A.: Self-organizing neural networks for visualization and classification. In: Opitz, O., Lausen, B., Klar, R. (eds.) Information and Classification: Concepts, Methods and Applications, pp. 307-313. Springer, Berlin (1993).
    • (1993) Information and Classification: Concepts, Methods and Applications , pp. 307-313
    • Ultsch, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.