Table 17 Sparsity of classifiers in the test for Bimodal, CSTH, Iris-setosa and versicolor data sets on the noise level (standard deviation in parentheses)

From: Norm ball classifier for one-class classification

Classifier 0% 5% 10% 15% 20%
Bimodal
Two norm 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00)
Max norm 2.0 (0.00) 2.0 (0.00) 3.3 (0.64) 3.8 (0.75) 2.0 (0.00)
One norm 2.2 (0.40) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00)
Mix norm 2.0 (0.00) 2.0 (0.00) 12.1 (0.94) 8.0 (0.63) 2.0 (0.00)
MoG* 4 4 6 3 3
PDE** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
1-NN** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
k-NN ** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
SVDD 6.2 (0.60) 7.8 (0.60) 17.2 (0.75) 21.7 (1.00) 23.2 (1.83)
CSTH
Two norm 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.3 (0.72)
Max norm 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.6 (0.49)
One norm 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00) 2.0 (0.00)
Mix norm 2.0 (0.00) 2.0 (0.00) 2.6 (0.70) 2.0 (0.00) 2.6 (0.49)
MoG* 2 2 2 2 2
PDE ** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
1-NN** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
k-NN** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
SVDD 2.1 (0.30) 6.9 (0.94) 7.3 (0.90) 4.4 (0.80) 8.5 (0.50)
Iris-setosa
Two norm 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00)
Max norm 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00)
One norm 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00)
Mix norm 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00)
MoG* 1 1 1 1 1
PDE ** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
1-NN** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
k-NN ** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
SVDD 2.0 (0.00) 4.0 (0.89) 11.6 (0.49) 12.8 (0.74) 16.4 (1.02)
Iris-versicolor
Two norm 2.0 (0.00) 2.6 (0.75) 1.0 (0.00) 1.0 (0.00) 1.0 (0.00)
Max norm 3.8 (0.80) 2.6 (0.49) 1.6 (0.55) 3.0 (0.89) 3.2 (1.60)
One norm 2.2 (0.40) 2.0 (0.00) 1.6 (0.49) 4.2 (1.17) 2.6 (0.49)
Mix norm 14.6 (3.38) 3.6 (1.02) 3.2 (1.30) 3.0 (1.10) 2.2 (0.98)
MoG* 1 2 1 2 2
PDE ** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
1-NN** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
k-NN** \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\) \(|\mathrm{N}|\)
SVDD 3.4 (1.2) 7.2 (0.40) 11.8 (0.75) 11.6 (0.49) 12.0 (0.00)
  1. *The number of Gaussian functions is pre-specified beforehand by parameter
  2. **The model has the non-zero terms as many as all the training points