Tensor decomposition

[kastnerkyle]

Pierre Comon - Lots of tensor work!

http://www.stat.rice.edu/~gallen/reg_tensor_jsm_talk.pdf

http://www.slideshare.net/yokotatsuya/principal-component-analysis-for-tensor-analysis-and-eeg-classification

http://www.slideshare.net/KentaOono/tensordecomposition

http://www.slideshare.net/KoheiHayashi1/talk-in-jokyonokai-12989223

http://math.berkeley.edu/~oeding/RTG/Navasca.pdf

http://www.cs.huji.ac.il/~shashua/papers/ICML07-Tutorial.pdf

http://www.wu.ac.at/statmath/resseminar/wt11-12/files/slidesfreudenthaler.pdf

http://www.cs.yale.edu/homes/mmahoney/pubs/tensorSVD_LAA.pdf

http://www.mcs.anl.gov/~jiechen/pub/tensorSVD.pdf

http://www.cs.ucdavis.edu/~bai/ECS231/returnsfinal/Kuo.pdf

ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/ida/reports/12-37.pdf

http://issnla2010.ba.cnr.it/TheSVDs.pdf

Merging other issue...

http://www.slideshare.net/yokotatsuya/independent-component-analysis-11359849

http://dl.acm.org/citation.cfm?id=1776792

http://arxiv.org/abs/1305.0395

http://books.google.com/books?id=sA_WYuU1rS4C&pg=PA484&lpg=PA484&dq=Plant+Classification+Based+on+Multilinear+Independent+Component+Analysis&source=bl&ots=OCbrkI2Mvk&sig=0tLZHY_GMN5JerG1cl4VXrzYdL8&hl=en&sa=X&ei=5uuaU4_KBKTJ8wGDtoHgBg&ved=0CD4Q6AEwAw#v=onepage&q=Plant%20Classification%20Based%20on%20Multilinear%20Independent%20Component%20Analysis&f=false

http://alumni.media.mit.edu/~maov/classes/vision09/syllabus.html

http://www.dsp.toronto.edu/~haiping/Publication/MPCA_TNN07.pdf

http://alumni.media.mit.edu/~maov/classes/pra/index.html

http://alumni.media.mit.edu/~maov/classes/vision09/lect/08_face_recognition_mica_mprojection_09.pdf

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=0EC381BC42F5B1433BA477987A78472C?doi=10.1.1.87.7604&rep=rep1&type=pdf

https://dro.deakin.edu.au/eserv/DU:30044579/venkatesh-recognisingfaces-2008.pdf

http://www.comp.hkbu.edu.hk/~haiping/MSL.html#code

(MPCA) http://www.mathworks.com/matlabcentral/fileexchange/26168-multilinear-principal-component-analysis--mpca-

(Japanese) http://www.slideshare.net/taki0313/tensor-decomposition-and-its-applications

http://arxiv.org/pdf/1305.0395v1.pdf

http://issnla2010.ba.cnr.it/DecompositionsI.pdf

http://www4.ncsu.edu/~smsulli2/tensors.html

http://arxiv.org/pdf/1403.4462v1.pdf

http://www.slideshare.net/KentaOono/tensordecomposition

http://arxiv.org/abs/1304.8087

[kastnerkyle]

Code:

ShiftCP for Neuroimaging Data and Tutorial Code

CP Decomposition and BCD

http://www.mathworks.com/matlabcentral/fileexchange/25514-tp-tool/content/tptool/array/hosvd.m

http://code.google.com/p/beta-ntf/source/browse/beta_ntf.py

http://www.caam.rice.edu/~optimization/bcu/ncp/index.html

http://www.caam.rice.edu/~optimization/bcu/ncpc/index.html

http://www.caam.rice.edu/~optimization/bcu/ntd/index.html

[kastnerkyle]

From: http://www.cs.unc.edu/~coombe/research/code/

function [U1,U2,U3,S] = svd3(rank, A)
% Compute the HOSVD of a 3­way tensor A 
% [U1,U2,U3,S] = svd3(rank, A)
%
% Computes a Higher-Order SVD using the online SVD. Truncates
% the SVD after a certain number of terms (constant across all
% dimensions, i.e. a rank-R approximation). This is known to be
% sub-optimal, as shown in "On the Best Rank-1 and 
% Rank-(R1,R2...,Rn) Approximation of Higer-Order Tensors".
%
% From notes by Martin Holmberg
%
% Author: Greg Coombe
% Date: Aug 5, 2003
%

disp('Dimension 1');
fA = flatten(A, 1);
size(fA)
[U1, s, v] = svd( fA );
U1 = U1(:, 1:rank);

s = s(1:rank, 1:rank);
v = v(:,1:rank);
compare( U1*s*v', fA, '1st');

disp('Dimension 2');
fA = flatten(A, 2);
size(fA)
[U2, s, v] = svd( fA );
U2 = U2(:, 1:rank);

s = s(1:rank, 1:rank);
v = v(:,1:rank);
compare( U2*s*v', fA, '2nd');

disp('Dimension 3');
fA = flatten(A, 3);
size(fA)
[U3, s, v] = svd( fA );
U3 = U3(:, 1:rank);

s = s(1:rank, 1:rank);
v = v(:,1:rank);
compare( U3*s*v', fA, '3rd');

% Compute the scaling tensor S = A * U1' * U2' * U3'
S = tmul(A, U1', 1);
S = tmul(S, U2', 2);
S = tmul(S, U3', 3); 

% Reconstruct the full tensor
%F = tmul( tmul( tmul( S, U1, 1), U2, 2), U3, 3);

[kastnerkyle]

Numerical Approaches to CP-ALS Decomposition

Overview of CP-ALS Methods

Tensor Decomposition Overview

[kastnerkyle]

Tutorials: A book on tensor applications in statistics by Peter McCullagh An excellent slideshow on linked data and tensors by Maximillian Nickel A nice page with links to several good papers

[kastnerkyle]

NLP applications: Thesis by Tim van den Cruys