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Low-rank modeling
Published on 2011-10-1224599 Views
Inspired by the success of compressive sensing, the last three years have seen an explosion of research in the theory of low-rank modeling. By now, we have results stating that it is possible to recov
Presentation
Some Recent Advances in the Theory of Low-rank Modeling00:00
Objective08:51:34
Agenda18:51:19
Matrix Completion22:45:31
The Net ix problem (1)23:30:54
The Net ix problem (2)42:27:53
The Net ix problem (3)52:57:03
Global positioning from local distances (1)80:42:11
Global positioning from local distances (2)98:23:08
Other problems of this kind111:23:10
Matrix completion (1)122:47:15
Matrix completion (2)128:27:35
Massive high-dimensional data130:03:56
Low-rank matrix completion? (1)142:54:44
Low-rank matrix completion? (2)167:58:12
Low-rank matrix completion? (3)198:04:29
Low-rank matrix completion? (4)222:29:20
Which entries do we get to see? (1)222:59:20
Which entries do we get to see? (2)235:34:24
Which matrices can we complete? (1)241:54:01
Which matrices can we complete? (3)270:52:07
Which matrices can we complete? (4)289:24:10
Which matrices can we complete? (2)297:48:42
Coherence308:02:45
What is information theoretically possible?347:06:09
Recovery algorithm (1)375:44:21
Recovery algorithm (2)402:46:10
Recovery algorithm (3)472:56:45
Near-optimal matrix completion480:13:06
Related work511:18:03
Geometry (1)527:42:58
Geometry (2)556:44:15
General formulation575:14:10
Example: C. and Recht '08 (1)598:45:13
Example: C. and Recht '08 (2)599:53:14
Quantum-state tomography (1)600:47:57
Quantum-state tomography (2)601:08:58
General statement (1)601:19:16
General statement (2)602:05:51
Robust PCA641:37:48
Matrix completion from noisy entries (1)645:21:02
Matrix completion from noisy entries (2)658:07:04
Matrix completion from noisy entries (3)662:36:17
Gross errors669:08:06
The separation problem (2)701:43:33
Classical PCA (1)708:17:33
Classical PCA (2)731:46:57
PCA and corruptions/outliers (1)733:55:08
PCA and corruptions/outliers (2)744:26:24
Robust PCA752:05:46
Example: Face recognition under varying illuminations761:33:51
Occlusions and other corruptions in computer vision768:27:34
The separation problem (1)784:32:40
When does separation make sense? (1)791:27:09
When does separation make sense? (2)808:35:14
What if the sparse component has low-rank? (1)818:23:37
What if the sparse component has low-rank? (2)825:14:35
Principal Component Pursuit (PCP) (1)834:02:11
Principal Component Pursuit (PCP) (2)838:17:42
Main result: M = L + E863:25:25
Connections with matrix completion (MC)881:28:43
Phase transitions in probability of success892:24:10
Other works918:10:15
Tying it together (1)927:55:38
Tying it together (2)930:44:35
Gross errors + noise (1)937:07:43
Gross errors + noise (2)940:31:30
Empirical performance944:28:06
Implementation status953:52:16
Some Applications963:57:06
Application to video surveillance964:43:41
Background modeling from surveillance video (1)980:20:19
Background modeling from surveillance video (2)999:31:25
Repairing vintage movies (1)1009:20:39
Repairing vintage movies (2)1014:20:42
Repairing vintage movies (3)1015:41:44
Repairing vintage movies (4)1016:07:22
Repairing vintage movies (5)1017:17:19
Repairing vintage movies (6)1017:58:05
Repairing vintage movies (7)1018:14:07
Faces under varying illumination (1)1021:18:16
Faces under varying illumination (2)1040:47:11
Robust batch image alignment (Ma et al.) (1)1045:15:40
Robust batch image alignment (Ma et al.) (2)1052:54:09
2D image matching and 3D modeling1059:26:52
Batch face alignment: accuracy evaluation1070:34:37
Simultaneous Alignment and Repairing1083:35:00
Celebri5es from the Internet1102:31:22
Face recognition with less controlled data?1109:32:15
Aligning handwritten digits1112:25:38
The world we see (through camera) is tilted!1120:55:22
Transform Invariant Low-rank Textures (TILT)1127:44:36
TILT via Iterative RPCA-‐Like Convex Optimization1135:40:35
TILT: Examples of Symmetric Patterns and Textures1141:52:23
TILT – Robust to Background, Occlusion, and Corruption1154:48:39
TILT: All Types of Regular Geometric Structures in Images1155:06:04
TILT: Examples of Characters, Signs, and Texts1159:17:23
TILT: More Examples1167:51:32
TILT – 3D Geometry from a Single Image1175:11:24
TILT Applications: Augmented Reality1182:32:39
Other Applications: Web Document Corpus Analysis1190:55:11
Other Applications: Sparse Keywords Extracted1211:26:08
Summary1220:19:10