Table 3.
Average (Standard Deviation) of L1 Distance to True Subspace for m = 10 Laplacian Noise/Error 100 Replications for Each Configuration
| q | p | μ | L1-PCA* | L2-PCA | pcaPP | L1-PCA |
|---|---|---|---|---|---|---|
| 2 | 0 | 0 | 339.8 ( 66.0 ) | 329.1 ( 60.2 ) | 4600.2 ( 978.6 ) | 244.5 ( 46.2 ) |
| 2 | 1 | 25 | 328.5 ( 60.0 ) | 640.7 ( 185.9 ) | 5556.0 ( 1216.1 ) | 253.1 ( 48.7 ) |
| 2 | 2 | 25 | 371.5 ( 73.7 ) | 1515.7 ( 681.4 ) | 7456.1 ( 1711.5 ) | 253.9 ( 47.1 ) |
| 2 | 3 | 25 | 872.4 ( 427.8 ) | 8974.9 ( 3298.1 ) | 9145.1 ( 1852.6 ) | 5520.1 ( 4965.3 ) |
| 2 | 1 | 50 | 358.4 ( 75.6 ) | 6521.5 ( 393.8 ) | 8085.5 ( 1045.0 ) | 6211.4 ( 248.6 ) |
| 2 | 2 | 50 | 337.4 ( 60.4 ) | 11637.9 ( 111.2 ) | 10010.6 ( 1091.2 ) | 11611.9 ( 107.5 ) |
| 2 | 3 | 50 | 3644.8 ( 6662.5 ) | 16912.9 ( 80.8 ) | 11097.6 ( 1090.0 ) | 16850.1 ( 63.8 ) |
| 2 | 1 | 75 | 329.3 ( 61.8 ) | 8698.4 ( 88.5 ) | 8835.1 ( 940.1 ) | 8606.3 ( 58.0 ) |
| 2 | 2 | 75 | 16599.0 ( 75.1 ) | 16584.4 ( 71.7 ) | 9940.4 ( 1130.2 ) | 16538.7 ( 75.5 ) |
| 2 | 3 | 75 | 24372.2 ( 61.9 ) | 24371.8 ( 68.2 ) | 10288.8 ( 1297.9 ) | 24329.6 ( 56.6 ) |
| 5 | 0 | 0 | 347.5 ( 51.8 ) | 370.4 ( 56.0 ) | 4555.6 ( 716.1 ) | 273.3 ( 39.4 ) |
| 5 | 1 | 25 | 330.1 ( 50.2 ) | 884.1 ( 191.1 ) | 5819.6 ( 986.1 ) | 271.3 ( 40.9 ) |
| 5 | 2 | 25 | 386.3 ( 72.1 ) | 2503.5 ( 785.3 ) | 8258.3 ( 1549.5 ) | 286.0 ( 44.6 ) |
| 5 | 3 | 25 | 1644.9 ( 947.7 ) | 11485.5 ( 1308.1 ) | 10510.0 ( 1727.2 ) | 9581.7 ( 3963.4 ) |
| 5 | 1 | 50 | 395.5 ( 75.8 ) | 6447.3 ( 308.8 ) | 9985.7 ( 1142.8 ) | 6379.1 ( 269.2 ) |
| 5 | 2 | 50 | 326.1 ( 52.5 ) | 11636.4 ( 129.0 ) | 14075.7 ( 1017.2 ) | 11629.6 ( 110.4 ) |
| 5 | 3 | 50 | 3944.9 ( 6881.0 ) | 16882.8 ( 65.8 ) | 16555.9 ( 1136.5 ) | 16845.3 ( 78.1 ) |
| 5 | 1 | 75 | 325.3 ( 55.1 ) | 8719.7 ( 76.3 ) | 11983.1 ( 996.1 ) | 8659.6 ( 85.6 ) |
| 5 | 2 | 75 | 16554.3 ( 60.0 ) | 16584.5 ( 63.3 ) | 15153.7 ( 1198.3 ) | 16546.4 ( 67.5 ) |
| 5 | 3 | 75 | 24330.9 ( 64.1 ) | 24351.5 ( 56.6 ) | 16541.6 ( 1179.0 ) | 24327.3 ( 59.0 ) |
q: dimension of “true” underlying subspace
p: number of outlier-contaminated dimensions
μ: outlier magnitude