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. Author manuscript; available in PMC: 2015 Aug 6.
Published in final edited form as: J Am Stat Assoc. 2011;106(495):1075–1084. doi: 10.1198/jasa.2011.tm10183

Table 1.

Misclassification rate (averaged over 50 simulations with standard errors given in parentheses)

Spherical, ℓ2 Spherical, ℓ1 Elliptical, ℓ2 Elliptical, ℓ1 Outliers, ℓ2 Outliers, ℓ1
Minimax M3 0.36 (0.01) 0.38 (0.01) 0.49 (0.00) 0.50 (0.00) 0.40 (0.01) 0.38 (0.01)
Complete M3 0.32 (0.01) 0.37 (0.01) 0.49 (0.00) 0.50 (0.00) 0.38 (0.01) 0.38 (0.01)
Average M3 0.64 (0.01) 0.66 (0.00) 0.54 (0.01) 0.55 (0.01) 0.65 (0.01) 0.66 (0.00)
Single M3 0.66 (0.00) 0.66 (0.00) 0.66 (0.00) 0.66 (0.00) 0.66 (0.00) 0.66 (0.00)
Centroid M3 0.66 (0.00) 0.66 (0.00) 0.60 (0.01) 0.60 (0.01) 0.66 (0.00) 0.66 (0.00)
Minimax Mk̂ 0.29 (0.00) 0.30 (0.00) 0.28 (0.00) 0.31 (0.00) 0.29 (0.00) 0.30 (0.00)
k̂ 11.0 (1.5) 13.2 (1.3) 25.1 (0.5) 38.8 (1.0) 10.7 (1.5) 13.2 (1.5)
Complete Mk̂ 0.28 (0.00) 0.30 (0.00) 0.29 (0.00) 0.31 (0.00) 0.28 (0.00) 0.30 (0.00)
k̂ 7.2 (0.7) 9.6 (0.8) 27.8 (0.4) 40.4 (1.0) 7.7 (0.7) 11.2 (0.9)
Average Mk̂ 0.26 (0.00) 0.27 (0.00) 0.28 (0.00) 0.30 (0.00) 0.26 (0.00) 0.28 (0.00)
k̂ 15.4 (1.1) 18.7 (1.0) 25.6 (0.4) 42.1 (0.9) 17.6 (1.2) 20.4 (1.3)
Single Mk̂ 0.33 (0.00) 0.33 (0.00) 0.25 (0.01) 0.31 (0.00) 0.33 (0.00) 0.33 (0.00)
k̂ 224.9 (3.9) 231.7 (3.3) 61.9 (2.4) 88.7 (2.0) 225.5 (4.0) 232.1 (3.3)
Centroid Mk̂ 0.33 (0.00) 0.33 (0.00) 0.28 (0.00) 0.31 (0.00) 0.33 (0.00) 0.33 (0.00)
k̂ 270.7 (2.1) 272.6 (1.7) 42.1 (1.0) 71.7 (1.3) 271.0 (2.1) 272.8 (1.7)

NOTE: Mk denotes the misclassification rate for a size-k clustering and k̂= arg mink Mk.