Timeline for Robust PCA vs. robust Mahalanobis distance for outlier detection
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 28, 2017 at 8:07 | history | bounty ended | Mustafa Eisa | ||
| Oct 27, 2017 at 17:59 | vote | accept | Mustafa Eisa | ||
| Oct 27, 2017 at 1:37 | comment | added | Mustafa Eisa | Sorry I mean Robust PCA is not invariant due to the entry-wise penalty. However replacing that with a sum of row norms makes it so. | |
| Oct 27, 2017 at 1:35 | comment | added | David J. Harris | Now I'm confused. PCA is already rotationally invariant, right? | |
| Oct 26, 2017 at 19:59 | comment | added | Mustafa Eisa | No it’s just an extension of PCA that incorporates rotational invariance. | |
| Oct 26, 2017 at 19:28 | comment | added | David J. Harris | Oh, I see. Would that be a special case of Mahalanobis distance? | |
| Oct 26, 2017 at 18:22 | comment | added | Mustafa Eisa | If your answer is, “No” that’s totally fine I’m just wondering. | |
| Oct 26, 2017 at 18:21 | comment | added | Mustafa Eisa | In your answer, you distinguish between the two methods by pointing out that the $\ell_1$ penalty in robust PCA is not rotationally-invariant and so is better suited to corruptions in the canonical basis. I’m just asking if you’ve considered or thought about the case in which a sum of (Euclidean) row norms is used in place of the $\ell_1$ coordinate penalties. | |
| Oct 26, 2017 at 18:09 | comment | added | David J. Harris | I'm not sure I understand your question. Are you asking me to compare the two approaches you discussed in your question with a different robust PCA approach? | |
| Oct 26, 2017 at 17:27 | comment | added | Mustafa Eisa | Thanks for this David, I will take a look at the paper. However, there is a version of robust PCA which imposes a rotationally-invariant penalty on the datum (rows of the data matrix) instead of a penalty on coordinates (such as in the Candes case). Thoughts? | |
| Oct 26, 2017 at 15:21 | history | answered | David J. Harris | CC BY-SA 3.0 |