Statistics 322
Object Oriented Data Analysis
Class Meetings:
Tuesday, August 30
Organizational matters - What is OODA? -
Visualization by Projection -
Object Space & Feature Space - Curves as Data
- Data Representation Issues - PCA visualization
Thursday,
September 1
Matlab Software - Time
Series of Curves - Chemometrics Data -
Mortality Data
Tuesday,
September 6
Gene
Cell Cycle Data - Microarrays and HDLSS visualization
- DWD bias adjustment - NCI 60 Data
Thursday,
September 8
Finish NCI 60 Data - Linear Algebra Review -
Multivariate Probability Review - PCA as an optimization
Problem - PCA Mathematics and Graphics
Tuesday,
September 13
PCA
Redistribution of Energy - PCA Data Representation
- Alternate PCA Computation & SVD
- Primal - Dual PCA
- Connections between
discrete and continuous curve data
Thursday,
September 15
Finished
Primal-Dual PCA vs. SVD - PCA for Corpora
Callosa - Fourier Boundary Representation -
Medial Representation
- Movies for Visualization
Tuesday,
September 20
Cornea
Data - Robust
HDLSS (Spherical) PCA
Thursday, September 22 Out of Town
Tuesday,
September 27
Elliptical PCA - Cluster & PCA -
Revisit NCI60 Data - Mass Flux Data - SiZer
Thursday,
September 29
SiZer - Revisit Mass
Flus Data - SiZer
Analysis
of Cell Cycle Data - Data Representation
Tuesday,
October 4
Euclidean
data, not near
subspace - M-reps - Bladder
Prostate
Rectum - Data on manifolds -
Mildly Non-Euclidean data - Trees as Data -
Strongly Non-Euclidean Data
Thursday, October 6
Participant Presentations: Lingsong Zhang, Travis Gaydos, Ja-Yeon
Jeong, Marcel Prastawa
Tuesday,
October 11
Discrimination - Fisher Linear Discrimination
(Nonparametric
& Parametric)
Thursday, October 13
Participant Presentations: Martin Styner, Isabelle Corouge, Joshua
Stough, Surajit Ray
Tuesday, October 18
Participant Presentations: Myung Hee Lee, Chihoon Lee, Brad
Davis, Peter Lorenzen
Thursday, October 20 Fall Break
Tuesday, October 25 Class Cancelled
Thursday, October 27
Participant Presentations: Xuxin Liu, Sushant Rewaskar, Alok Shriram,
Abhishek Singh
Tuesday, November 1
Sarang Joshi
Thursday, November 3
Participant Presentations: Josh Levy, Jeongyoun Ahn, Fernando Silva,
Christine Xu
Tuesday, November 8 Generalizations
of FLD - HDLSS Discrimination - Maximal Data
Piling
Thursday, November 10
Participant Presentations: Yufeng Liu, Jiancheng Jiang, Haipeng
Shen, Christine Xu
Tuesday, November 15
Participant Presentations: Hua Yang, Dan Samarov, Jie Zhou, Qiong Han
Thursday, November 17
Class Cancelled
Tuesday, November 22
Participant Presentations: Changwon Lin, Xin Fu, Luke Huan, Mihee Lee
Thursday, November 24 Thanksgiving
Tuesday, November 29
Participant Presentations: Xuanyao He, Miao Xie, Fangfang Wang, Ipek
Oguz
Thursday, December 1 Embedding and Kernel
Spaces
- Support
Vector Machines - Distance Weighted Discrimination -
Revisit micro-array data - Face Data
Tuesday, December 6
Participant Presentations: Vangelis Evangelou, Suman Sen, Ping Bai, Eli
Broadhurst
Thursday,
December 8
Revisit NCI 60 data - HDLSS Hypothesis Testing:
DiProPerm
Test - HDLSS
Geometric
Representation
-
Independent
Component Analysis -
ICA for checking Gaussianity
Course Information:
Fall Semester, 2005
Class Meetings: Tuesday-Thursday 12:30 - 1:45, Smith 107
Taught by:
J. S. Marron
Office: Smith 309
Office Hours: Thursday, 2:00 - 3:30
Email: marron@email.unc.edu
Office Telephone: (919)
962-2188
Home Telephone: (919) 493-2844
Class Email Listserv:
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the UNC Listerver: http://mail.unc.edu/lists/
and the "visit" the list Stat322-2005, from which you can join.
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Course Description:
Object Oriented Data Analysis is the statistical
analysis of populations of complex objects. In the special case
of Functional Data Analysis, these data objects are curves, where
standard Euclidean approaches, such as principal components analysis,
have been very successful. Recent developments in medical image
analysis motivate the statistical analysis of populations of more
complex data objects which are elements of mildly non-Euclidean spaces,
such as Lie Groups and Symmetric Spaces, or of strongly non-Euclidean
spaces, such as spaces of tree-structured data objects. These new
contexts for Object Oriented Data Analysis create several potentially
large new interfaces between mathematics and statistics. Even in
situations where Euclidean analysis makes sense, there are statistical
challenges because of the High Dimension Low Sample Size problem, which
motivates a new type of asymptotics leading to non-standard
mathematical statistics.
Prerequisite is some type of course experience with notions of
probability, expectation, variance, covariance, and the multivariate
normal distribution, e.g. as in Stat 164 (but there are a number of
other courses that will work as well). Most fundamental
statistical concepts that are needed (e.g. Principal Component
Analysis) will be developed during the course.
Course grading will be done on the basis of student
presentations. The presentation will be either about the
student's own related work (rather broadly defined), or else about a
recent paper in the area.
Enrollment is encouraged, but auditors are also welcome.
Grading:
- Based only
upon an in class presentation
- Could be your work, or I can suggest something
- Will ask auditors
to present as well
- Thus, why not
enroll in the course?
- Enrolling will increase
frequency with which
courses like this are offered.
Class Discussion:
- Heartily encouraged
- Dialogs at various levels are enjoyable and useful
- Please jump in with questions of clarity
- Questions like "what are you talking about?" are
encouraged
- As are requests of the from "please summarize what
has been discussed"