Table 1.
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.