Dual Principal Component Pursuit
By Manolis C. Tsakiris, René Vidal. 2015
104 citations recorded by the source corpus.
We consider the problem of outlier rejection in single subspace learning. Classical approaches work directly with a low-dimensional representation of the subspace. Our approach works with a dual representation of the subspace and hence aims to find its orthogonal complement. We pose this problem as an l1-minimization problem on the sphere and show that, under certain conditions on the distribution of the data, any global minimizer of this non-convex problem gives a vector orthogonal to the subspace. Moreover, we show that such a vector can still be found by relaxing the non-convex problem with a sequence of linear programs. Experiments on synthetic and real data show that the proposed approach, which we call Dual Principal Component Pursuit (DPCP), outperforms state-of-the art methods, especially in the case of high-dimensional subspaces.
Subfields: Artificial Intelligence, Computational Mechanics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Gianfranco Doretto
- Mohammad Sabokrou
- Mahmood Fathy
- D. Adjeroh
- Ehsan Adeli
- Ranya Almohsen
- Mohammad Khalooei
- Stanislav Pidhorskyi
In Computational Mechanics
- Mahmood Fathy
- D. Adjeroh
- Gianfranco Doretto
- Ehsan Adeli
- Mohammad Sabokrou
- Ranya Almohsen
- Mohammad Khalooei
- Stanislav Pidhorskyi
Citations in the corpus
- The Ideal Continual Learner: An Agent That Never Forgets (2023, neutral): “…subspace and its orthogonal complement, respectively, then UU> +BB> is the identity matrix, and we have ‖UU>Yt − Yt‖2F = ‖BB>Yt‖2F = ‖Y >t B‖2F. (33) Note that relation (33) was discussed by Tsakiris & Vidal (2018) in a different context, in comparison to the algorithm of Lerman et al. (2015).”
- Generative Probabilistic Novelty Detection with Adversarial Autoencoders (2018, methodology): “OutRank[55,56] CoP[57] REAPER[58] OutlierPursuit[59] LRR[60] DPCP [61] ℓ 1 thresholding[25] Coil-100 dataset.”
- Adversarially Learned One-Class Classifier for Novelty Detection (2018, methodology): “CoP [32] REAPER [22] OutlierPursuit [50] LRR [24] DPCP [45] them.”