Science topics: Geometry and Topology Information Geometry

Science topic

Information Geometry - Science topic

This is a group for discussing information geometry. That is the field of study that uses tools from geometry to study statistics. Geometric methods can lead to greater insights in statistical estimation algorithms and understanding of various statistical tests from a new perspective. Will be of interest for geometers wishing to learn about statistics or vice versa.

Md Golam Sarowar

asked a question related to Information Geometry

What actually expectation maximization, KL divergence and Information Geometry perform.

Question

2 answers

Jul 13, 2017

How those algorithms mentioned above performs if we consider a long DNA sequence as input. what actually happens and what will be the outcome?

Relevant answer

William Obeng-Denteh

Aug 28, 2017

Answer

It is a system designed to capture, store, manipulate, analyze, manage, and present spatial or geographic data.

2 Recommendations

Muhittin Evren Aydin

asked a question related to Information Geometry

Is it false that ∇*J=0 on any Kaehlerian manifold?

Question

5 answers

Feb 4, 2016

Let (M,g,∇,J) be a Kaehlerian manifold with almost complex structure J and ∇ a torsion free affine connection of M. The dual (conjugate) connection ∇* of ∇ is defined by Xg(Y,Z)=g(∇_XY,Z)+g(X,∇^*_YZ).
The question is whether J is ∇*-parallel.
A remark: ∇_XJY=J∇*_YZ.
Many thanks in advance for your contributions.

Relevant answer

Gabriel-Eduard Vilcu

Feb 6, 2016

Answer

Let (M,g,J) be an almost Hermitian manifold and ∇ a torsion free affine connection on M. Then we have:

g(JX,Y)+g(X,JY)=0. (1)

Using now (1) and the definition of the conjugate connection ∇* of ∇, namely

Xg(Y,Z)=g(∇_XY,Z)+g(X,∇*_YZ), (2)

it follows easily that

g((∇_zJ)X,Y)+g(X,(∇*_ZJ)Y)=0. (3)

Hence we derive from (3) that J is parallel with respect to ∇ if and only if J is parallel with respect to ∇*.

6 Recommendations

Muhammad Zubair Ahmad

asked a question related to Information Geometry

Can someone describe the use of differential geometry in signal processing?

Question

9 answers

Jun 13, 2015

I have no introduction to differential geometry so kindly point out some works aimed at beginners

Relevant answer

Jun 14, 2015

Answer

This is a good question.

An introduction to differential geometry in signal processing (complete with many important references to related works) is given in

Speical issue, IEEE Journal of Selected Topics in Signal Processing 7, 2013, no. 4:

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6559200

Differential geometry in low-dimensional signal models is covered in

M.B. Wakin, The Geometry of Low-Dimensional Signal Models, Ph.D. thesis, Rice University, 2006:

http://inside.mines.edu/~mwakin/papers/mbwPhdThesis.pdf

9 Recommendations

Suresh K. Shukla

asked a question related to Information Geometry

Which software would you recommend for handling computations in differential geometry of manifolds (or other related software)?

Question

2 answers

Sep 6, 2013

I want to purchase software related to differential geometry of manifolds. Also, please suggest related manuals. Thanks in advance

Relevant answer

Sep 13, 2013

Answer

Apparently there is a package under development in SAGE, the free and open source symbolic package. Don't know how usable it is but they claim to have tensor calculus implemented: http://www.u-cergy.fr/_attachments/anr-aarg-first-meeting-actualite/Gourgoulhon-sagemanifolds.pdf, and http://trac.sagemath.org/ticket/14865

4 Recommendations