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Low-rank modeling
Published on Oct 12, 201124604 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
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Chapter list
Some Recent Advances in the Theory of Low-rank Modeling00:00
Objective00:31
Agenda01:07
Matrix Completion01:21
The Net ix problem (1)01:24
The Net ix problem (2)02:32
The Net ix problem (3)03:10
Global positioning from local distances (1)04:50
Global positioning from local distances (2)05:54
Other problems of this kind06:40
Matrix completion (1)07:22
Matrix completion (2)07:42
Massive high-dimensional data07:48
Low-rank matrix completion? (1)08:34
Low-rank matrix completion? (2)10:04
Low-rank matrix completion? (3)11:53
Low-rank matrix completion? (4)13:20
Which entries do we get to see? (1)13:22
Which entries do we get to see? (2)14:08
Which matrices can we complete? (1)14:30
Which matrices can we complete? (3)16:15
Which matrices can we complete? (4)17:21
Which matrices can we complete? (2)17:52
Coherence18:28
What is information theoretically possible?20:49
Recovery algorithm (1)22:32
Recovery algorithm (2)24:09
Recovery algorithm (3)28:22
Near-optimal matrix completion28:48
Related work30:40
Geometry (1)31:39
Geometry (2)33:24
General formulation34:30
Example: C. and Recht '08 (1)35:55
Example: C. and Recht '08 (2)35:59
Quantum-state tomography (1)36:02
Quantum-state tomography (2)36:04
General statement (1)36:04
General statement (2)36:07
Robust PCA38:29
Matrix completion from noisy entries (1)38:43
Matrix completion from noisy entries (2)39:29
Matrix completion from noisy entries (3)39:45
Gross errors40:08
The separation problem (2)42:06
Classical PCA (1)42:29
Classical PCA (2)43:54
PCA and corruptions/outliers (1)44:02
PCA and corruptions/outliers (2)44:39
Robust PCA45:07
Example: Face recognition under varying illuminations45:41
Occlusions and other corruptions in computer vision46:06
The separation problem (1)47:04
When does separation make sense? (1)47:29
When does separation make sense? (2)48:30
What if the sparse component has low-rank? (1)49:06
What if the sparse component has low-rank? (2)49:30
Principal Component Pursuit (PCP) (1)50:02
Principal Component Pursuit (PCP) (2)50:17
Main result: M = L + E51:48
Connections with matrix completion (MC)52:53
Phase transitions in probability of success53:32
Other works55:05
Tying it together (1)55:40
Tying it together (2)55:50
Gross errors + noise (1)56:13
Gross errors + noise (2)56:25
Empirical performance56:40
Implementation status57:13
Some Applications57:50
Application to video surveillance57:53
Background modeling from surveillance video (1)58:49
Background modeling from surveillance video (2)59:58
Repairing vintage movies (1)01:00:33
Repairing vintage movies (2)01:00:51
Repairing vintage movies (3)01:00:56
Repairing vintage movies (4)01:00:58
Repairing vintage movies (5)01:01:02
Repairing vintage movies (6)01:01:04
Repairing vintage movies (7)01:01:05
Faces under varying illumination (1)01:01:16
Faces under varying illumination (2)01:02:26
Robust batch image alignment (Ma et al.) (1)01:02:42
Robust batch image alignment (Ma et al.) (2)01:03:10
2D image matching and 3D modeling01:03:34
Batch face alignment: accuracy evaluation01:04:14
Simultaneous Alignment and Repairing01:05:00
Celebri5es from the Internet01:06:09
Face recognition with less controlled data?01:06:34
Aligning handwritten digits01:06:44
The world we see (through camera) is tilted!01:07:15
Transform Invariant Low-rank Textures (TILT)01:07:39
TILT via Iterative RPCA-‐Like Convex Optimization01:08:08
TILT: Examples of Symmetric Patterns and Textures01:08:30
TILT – Robust to Background, Occlusion, and Corruption01:09:17
TILT: All Types of Regular Geometric Structures in Images01:09:18
TILT: Examples of Characters, Signs, and Texts01:09:33
TILT: More Examples01:10:04
TILT – 3D Geometry from a Single Image01:10:30
TILT Applications: Augmented Reality01:10:57
Other Applications: Web Document Corpus Analysis01:11:27
Other Applications: Sparse Keywords Extracted01:12:41
Summary01:13:13