Department of Mathematics

MTH 995-001: Introduction to Compressive Sensing and the Analysis of Big Data

Schedule and Topics Covered

L Date Topic References and Further Reading
1/13Class Canceled-- Attend Jameson Cahill's talk at
10:20 am in C304 WH
-- Read Book Chapter 1
1 1/15Introduction and OverviewBook Chapter 1, & Instructor notes
1/16Seminar Talk-- Attend Matthew Hirn's talk at
10:20 am in C304 WH
2 1/20PCA, SVD, & Weyl's BoundsBook Appendix A.2, Shlens, & Stewart.
Notes: Parts of S2014 lectures 3 & 5.
3 1/22John's EllipsoidsHoward and [TY'07].
Notes: They are here.
4 1/27Semidefinite ProgrammingBook Appendix B, [VB'96], Epel-
man's Notes, Gallier's Notes.
Notes: S2014 lectures 3, 4, & 5.
5 1/29Semidefinite ProgrammingBook Appendix B, [VB'96], Epel-
man's Notes, Gallier's Notes.
Notes: S2014 lectures 3, 4, & 5.
6 2/3The RIP and Basis Pursuit
HW 1 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		Book Sec's 4.1 - 4.3, 6.1, & 6.2
Notes: S2014 lectures 15 & 16.
7 2/5The RIP and BP cont'd,
Coherence		Book Sec's 4.1 - 4.3, 6.1, & 6.2
Book Sections 5.1 & 5.2
Notes: S2014 lectures 15, 16, & 25.
8 2/10Coherence cont'd,
Deterministic Constructions		Book Sec's 5.1, 5.2, [D'07], & [I'09]
Notes: S2014 lectures 25 & 26.
9 2/12Combinatorial Properties[BIS'12]
Notes: S2014 lecture 27.
10 2/17Combinatorial Props cont'd,
Fast Recovery Algorithms
HW 2 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		[CM'06], [GSTV'07], [GLPS'10],
[BIS'12], & [I'14]
Notes: S2014 lectures 27 and 28.
11 2/19Fast Recovery Algs cont'd[CM'06], [GSTV'07], [GLPS'10],
[BIS'12], & [I'14]
Notes: S2014 lectures 28 and 29.
12 2/24Locality-Sensitive Hashing[DIIM'04], [IM'98], & [DKS'11]
Notes: S2014 lectures 8 and 9.
13 2/26LSH cont'd"
14 3/3Large Deviation Inequalities
HW 3 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		Book Chapter 7
Notes: S2014 lectures 10 and 11.
15 3/5Large Deviation InequalitiesBook Chapter 7
Notes: S2014 lectures 10, 11, and 11a.
3/10Spring Break - no class
3/12Spring Break - no class
3/14 AMS Meeting Attend one of my sessions
3/15 AMS Meeting Attend one of my sessions
16 3/17Subgaussian ConcentrationBook Chapter 7, & Section 9.1
Notes: S2014 lectures 11, 12, & 13.
17 3/19Subgaussian ConcentrationBook Chapter 7, & Section 9.1
Notes: S2014 lectures 11, 12, & 13.
18 3/24Semidefinite Programming
HW 4 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		Notes: Optimization Part 1
19 3/26Semidefinite ProgrammingNotes: Optimization Part 2
20 3/31Johnson-Lindenstrauss Lem.
Implies the RIP		[BDDW'08], Book Appendix C,
[DG'02], & [A'01]
Notes: S2014 lectures 14 & 15.
21 4/2Lower BoundsBook Section 10.2
Notes: Lower Bounds
22 4/7The RIP Implies the
Johnson-Lindenstrauss Lem.
HW 5 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		Book Sections 9.5 and 8.4
Notes: They are here.
23 4/9The RIP Implies the
Johnson-Lindenstrauss Lem.		Book Sections 9.5 and 8.4
Notes: They are here.
24 4/14The RIP Implies the
Johnson-Lindenstrauss Lem.		Book Sections 9.5 and 8.4
Notes: They are here.
25 4/16The RIP and BONSBook Chapter 12
Notes: S2014 lecture 19.
26 4/21Applications in Numerical L.A.
HW 6 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		[RT'08], & [HMT'09]
Notes: S2014 lecture 20.
27 4/23Manifold Models for Data[F'59], [NSW'08], [BSLT'00],
[BW'07], [IM'13], & [EW'13]
Notes: S2014 lectures 21, 22, 23, & 24.
28 4/28Manifold Models cont'd[F'59], [NSW'08], [BSLT'00],
[BW'07], [IM'13], & [EW'13]
Notes: S2014 lectures 21, 22, 23, & 24.
29 4/30Manifold Models cont'd
HW 7 DUE, IF NOT
WORKING ON A PROJECT
OR SCRIBING.		[F'59], [NSW'08], [BSLT'00],
[BW'07], [IM'13], & [EW'13]
Notes: S2014 lectures 21, 22, 23, & 24.