Table 5.
Average (Standard Deviation) of L1 Distance to True Subspace for m = 10 Gaussian Noise/Error 100 Replications for Each Configuration
| q | p | μ | L1-PCA* | L2-PCA | pcaPP | L1-PCA |
|---|---|---|---|---|---|---|
| 2 | 0 | 0 | 313.8 ( 61.6 ) | 253.1 ( 50.6 ) | 3312.2 ( 637.9 ) | 323.9 ( 64.9 ) |
| 2 | 1 | 25 | 342.2 ( 64.0 ) | 921.6 ( 408.7 ) | 4104.5 ( 870.0 ) | 323.4 ( 58.4 ) |
| 2 | 2 | 25 | 368.2 ( 75.4 ) | 6540.2 ( 373.4 ) | 5663.8 ( 1261.7 ) | 6675.4 ( 347.8 ) |
| 2 | 3 | 25 | 315.2 ( 56.2 ) | 9014.0 ( 161.8 ) | 7188.9 ( 1276.1 ) | 9019.2 ( 157.6 ) |
| 2 | 1 | 50 | 327.5 ( 66.1 ) | 5945.0 ( 60.8 ) | 6342.9 ( 923.5 ) | 5979.1 ( 68.3 ) |
| 2 | 2 | 50 | 4569.8 ( 5343.7 ) | 11188.4 ( 53.3 ) | 7725.0 ( 887.7 ) | 11262.7 ( 72.0 ) |
| 2 | 3 | 50 | 16428.7 ( 55.0 ) | 16400.3 ( 48.2 ) | 8622.2 ( 991.6 ) | 16433.2 ( 54.6 ) |
| 2 | 1 | 75 | 8464.7 ( 55.3 ) | 8420.7 ( 43.4 ) | 6804.2 ( 847.4 ) | 8470.5 ( 64.4 ) |
| 2 | 2 | 75 | 16217.4 ( 58.2 ) | 16181.2 ( 50.1 ) | 7650.8 ( 774.2 ) | 16230.9 ( 60.9 ) |
| 2 | 3 | 75 | 23914.2 ( 54.6 ) | 23886.2 ( 46.1 ) | 7743.1 ( 837.0 ) | 23923.6 ( 51.1 ) |
| 5 | 0 | 0 | 342.9 ( 43.3 ) | 272.7 ( 37.2 ) | 3323.9 ( 525.1 ) | 337.0 ( 46.9 ) |
| 5 | 1 | 25 | 378.1 ( 53.4 ) | 1381.1 ( 337.0 ) | 4747.7 ( 837.0 ) | 340.8 ( 51.2 ) |
| 5 | 2 | 25 | 416.6 ( 72.6 ) | 6544.6 ( 390.3 ) | 7142.7 ( 1021.1 ) | 6751.3 ( 402.9 ) |
| 5 | 3 | 25 | 309.7 ( 48.3 ) | 8961.2 ( 166.0 ) | 9876.1 ( 1164.5 ) | 9023.1 ( 155.9 ) |
| 5 | 1 | 50 | 340.6 ( 56.7 ) | 5963.8 ( 59.9 ) | 8629.7 ( 645.3 ) | 6030.6 ( 79.1 ) |
| 5 | 2 | 50 | 10909.0 ( 1875.4 ) | 11189.1 ( 46.9 ) | 11456.6 ( 699.8 ) | 11262.6 ( 58.8 ) |
| 5 | 3 | 50 | 16383.4 ( 49.1 ) | 16357.3 ( 37.6 ) | 12814.8 ( 705.6 ) | 16392.5 ( 53.4 ) |
| 5 | 1 | 75 | 8495.9 ( 48.2 ) | 8438.6 ( 40.6 ) | 9399.0 ( 755.7 ) | 8501.7 ( 52.6 ) |
| 5 | 2 | 75 | 16221.3 ( 49.0 ) | 16178.6 ( 39.4 ) | 11348.0 ( 1056.0 ) | 16229.8 ( 47.0 ) |
| 5 | 3 | 75 | 23878.3 ( 38.5 ) | 23854.2 ( 37.3 ) | 11995.8 ( 871.1 ) | 23884.5 ( 45.6 ) |
q: dimension of “true” underlying subspace
p: number of outlier-contaminated dimensions
μ: outlier magnitude