Table 4.
Average (Standard Deviation) of L1 Distance to True Subspace for m = 100 Laplacian Noise/Error 100 Replications for Each Configuration
| q | p | μ | L1-PCA* | L2-PCA | pcaPP | L1-PCA |
|---|---|---|---|---|---|---|
| 2 | 0 | 0 | 5012.0 ( 294.1 ) | 4054.7 ( 223.0 ) | 42876.7 ( 2733.3 ) | 2965.2 ( 167.5 ) |
| 2 | 1 | 25 | 5079.1 ( 306.8 ) | 4379.2 ( 276.9 ) | 43127.7 ( 2088.2 ) | 2991.8 ( 164.3 ) |
| 2 | 2 | 25 | 5055.7 ( 272.7 ) | 5210.7 ( 754.1 ) | 45059.6 ( 2644.3 ) | 3001.6 ( 161.7 ) |
| 2 | 3 | 25 | 6069.4 ( 727.1 ) | 13567.6 ( 2811.4 ) | 46975.9 ( 2926.5 ) | 8774.4 ( 4563.1 ) |
| 2 | 1 | 50 | 5127.4 ( 295.5 ) | 9842.0 ( 500.7 ) | 46602.8 ( 2507.1 ) | 8628.0 ( 453.7 ) |
| 2 | 2 | 50 | 5052.1 ( 305.0 ) | 14850.5 ( 237.8 ) | 49793.2 ( 2478.7 ) | 13998.4 ( 339.3 ) |
| 2 | 3 | 50 | 6668.7 ( 4793.3 ) | 20106.7 ( 217.6 ) | 52352.1 ( 2922.9 ) | 19140.3 ( 144.6 ) |
| 2 | 1 | 75 | 5036.1 ( 260.9 ) | 11868.0 ( 213.0 ) | 49244.6 ( 2666.6 ) | 10923.4 ( 165.8 ) |
| 2 | 2 | 75 | 20649.4 ( 262.5 ) | 19790.3 ( 217.9 ) | 52503.2 ( 2703.2 ) | 18913.6 ( 155.2 ) |
| 2 | 3 | 75 | 28369.1 ( 262.8 ) | 27549.7 ( 211.9 ) | 54090.3 ( 3307.9 ) | 26720.3 ( 436.8 ) |
| 5 | 0 | 0 | 8590.3 ( 278.1 ) | 6933.6 ( 202.9 ) | 70283.2 ( 3071.5 ) | 5182.5 ( 187.5 ) |
| 5 | 1 | 25 | 8603.1 ( 285.1 ) | 7451.2 ( 326.7 ) | 71539.1 ( 3933.4 ) | 5178.2 ( 171.3 ) |
| 5 | 2 | 25 | 8663.4 ( 314.3 ) | 9014.1 ( 712.9 ) | 73553.8 ( 3275.1 ) | 5194.2 ( 213.9 ) |
| 5 | 3 | 25 | 10326.2 ( 922.5 ) | 18144.2 ( 1251.5 ) | 76066.9 ( 3690.2 ) | 15035.6 ( 2951.7 ) |
| 5 | 1 | 50 | 8682.2 ( 291.9 ) | 12879.5 ( 439.0 ) | 75432.8 ( 3286.9 ) | 11186.4 ( 420.0 ) |
| 5 | 2 | 50 | 8623.1 ( 306.7 ) | 18030.7 ( 251.3 ) | 82312.4 ( 3241.5 ) | 16459.9 ( 242.5 ) |
| 5 | 3 | 50 | 12340.6 ( 6879.0 ) | 23276.8 ( 257.7 ) | 86927.0 ( 4196.8 ) | 21677.5 ( 231.0 ) |
| 5 | 1 | 75 | 8564.1 ( 287.2 ) | 15107.4 ( 213.0 ) | 81899.0 ( 3897.0 ) | 13488.4 ( 192.7 ) |
| 5 | 2 | 75 | 24608.9 ( 292.8 ) | 22979.6 ( 216.2 ) | 87993.7 ( 3899.2 ) | 21373.5 ( 203.4 ) |
| 5 | 3 | 75 | 32371.0 ( 299.4 ) | 30743.9 ( 242.8 ) | 90029.9 ( 3800.5 ) | 29097.8 ( 194.9 ) |
q: dimension of “true” underlying subspace
p: number of outlier-contaminated dimensions
μ: outlier magnitude