Thresholding Based Efficient Outlier Robust PCA

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Description: Thresholding Based Efficient Outlier Robust PCA Yeshwanth Cherapanamjeri, Prateek Jain, Praneeth Netrapalli Microsoft Research India Vanilla PCA Vanilla PCA Outlier Robust PCA Our Contributions Outlier Effects Blatant Outliers Outliers

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slide1. Thresholding Based Efficient Outlier Robust PCA Yeshwanth Cherapanamjeri, Prateek Jain, Praneeth Netrapalli
Microsoft Research India<br>
slide2. Vanilla PCA<br>
slide3. Vanilla PCA<br>
slide4. Outlier Robust PCA<br>
slide5. Our Contributions<br>
slide6. Outlier Effects – Blatant Outliers Outliers with
large contribution<br>
slide7. Outlier Effects – Subtle Outliers Outlier with small contribution to principal subspace

Earlier strategy doesn’t work<br>
slide8. Outlier Effects – Subtle Outliers Outliers generally have larger residual than inliers<br>
slide9. Algorithm (TORP) Threshold Points<br>
slide10. Algorithm (TORP) Threshold
Points<br>
slide11. Algorithm (TORP)<br>
slide12. Theorem - Noiseless Case<br>
slide13. Theorem - Noiseless Case<br>
slide14. Theorem - Noisy Case<br>
slide15. Theorem - Noisy Case<br>
slide16. Prior Work<br>
slide17. Theorem Gaussian Case<br>
slide18. Prior Work (Gaussian Noise Case)<br>
slide19. Application to Anomaly Detection Given a set of URLs, separate good from bad
Hypothesis: Good ones belong to a low dimensional space
Results:<br>
slide20. Conclusions<br>
slide21. Thank You<br>
slide22. Algorithm – First Pass<br>
slide23. Algorithm 1 – Coherence Based Thresholding<br>
slide24. Adversarial Example<br>
slide25. Adversarial Example – Iteration 1<br>
slide26. Adversarial Example – Iteration 2<br>
slide27. Adversarial Example – Contd<br>
slide28. Proof Overview<br>
slide29. Proof Overview<br>
slide30. Proof of Theorem<br>
slide31. Proof of Theorem<br>
slide33. Appendix and Extra Slides<br>
slide34. Convex Relaxation (Outlier Pursuit)<br>
slide35. Theorem - TORP<br>