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Data Analysis on Hilbert Manifolds and their Applications

The theoretical focus of this Working Group is nonparametric statistics on Hilbert manifolds and dimensionality reduction from infinity to low dimension as small as 1. This will include an extension of CLT for iid variables to infinite dimensional Hilbert manifolds and beyond -- to infinite dimensional stratified spaces -- as well as the neighborhood hypothesis testing methodology, extending recent results to two or multiple samples on Hilbert manifolds or even to infinite dimensional stratified spaces.

Applications to Hilbert manifolds data analysis that will be potentially discussed, depending on the WG participants, could be to any of the following:

i. MRI imaging including MRI, DTI, or f-MRI;
ii. CT imaging;
iii. eye medical imaging, including stereo imaging;
iv. 2D and 3D scene recognition from similarity shapes of curves and surfaces;
v. projective shape of 3D scenes reconstructed from digital camera imaging;
vi. color and texture imaging data;
vii. spatial and temporal data on the geoid;
viii. plate tectonics data and continental drift;
ix. paths of eyes of storms on planet Earth;
x. volcanic activity, earthquakes, and other Earth Sciences data;
xi. astronomy data;
xii. solar system data;
xiii. DNA based data.

Lizhen's picture

Group meeting-April 22

Bijan Afsari (http://www.cis.jhu.edu/~bijan/) is going to give a talk in our group meeting next week. Here is the tentative title for his talk: "Quotient Geometries on Certain Spaces of High-dimensional Linear Stochastic Processes." Afsari did some solid work on conditions for the existence of unique intrinsic Frechet mean etc. Please plan to attend the meeting.

Best,

Lizhen

Meeting Date: 
April 22, 2014 - 12:30pm - 2:30pm
Lizhen's picture

Group meeting-April 15

Nikhil will continue his presentation from last week remotely for about 30mins (12:30pm-1pm) on April 15. We can use the rest of time to discuss other topics.

Meeting Date: 
April 15, 2014 - 12:30pm - 2:30pm
htzhu's picture

DTI chapter and data sets

Sue McDonald's picture

Weekly Meeting Info Through April 22, 2014

Topic: Hilbert WG Meeting
Date: Every Tuesday, from Tuesday, February 11, 2014 to Tuesday, April 22, 2014
Time: 12:30 pm, Eastern Standard Time (New York, GMT-05:00)
Meeting Number: 687 732 576
Meeting Password: Himeet-1

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To join the online meeting (Now from mobile devices!)
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1. Go to https://samsi.webex.com/samsi/j.php?MTID=mb771d61582ccaec2759dc09707c2ce04
2. If requested, enter your name and email address.

Meeting Date: 
February 11, 2014 - 12:30pm - April 22, 2014 - 2:30am
Fabian Telschow's picture

Nonlinear functional principal components

Leif Ellingson's picture

Neighborhood hypothesis test for extrinsic mean shape presentation

kdy's picture

Analysis on Global Economical Data

Victor Patrangenaru's picture

Palais (classical stuff)- index of a Morse function and topology of Hilbert manifolds

Valentina Staneva's picture

Papers on Kernel Estimation

Lizhen's picture

No group meeting on November the 5th

Dear All,

Due to the approaching deadlines for grant submissions etc, we decided during our last group meeting to take a break this week. We'll resume our meeting on November the 12th.

Best,

Lizhen

Meeting Date: 
November 4, 2013 - 7:50pm