Tensor Factorization of large scale linked datasets

http://www.cip.ifi.lmu.de/~nickel/iswc2012-slides/

Results from running: Ext-Rescalhttps://github.com/nzhiltsov/Ext-RESCAL

For inspiration see:http://videolectures.net/lsoldm2013_nickel_tensor_factorization/


A Three-Way Model for Collective Learning on Multi-Relational Data
http://www.icml-2011.org/papers/438_icmlpaper.pdf
http://www.cip.ifi.lmu.de/~nickel/data/slides-icml2011.pdf

Logistic Tensor Factorization for Multi-Relational Datahttps://arxiv.org/pdf/1306.2084.pdf
Factorizing YAGO Scalable Machine Learning for Linked Data
http://www.dbs.ifi.lmu.de/%7Etresp/papers/p271.pdf


Machine Learning on Linked Data: Tensors and Their Applications in Graph Structured Domains
http://www.cip.ifi.lmu.de/~nickel/iswc2012-slides/


cat rescal.log

DEBUG:RESCAL:[Config] rank: 2 | maxIter: 50 | conv: 1.0e-05 | lmbda: 0.0e+00
DEBUG:RESCAL:[Algorithm] The tensor norm: 3.00000
DEBUG:RESCAL:[Algorithm] The eigenvector based initialization will be performed.
DEBUG:RESCAL:Initializing tensor slices by summation required secs: 0.00045
DEBUG:RESCAL:eigenvector decomposition required secs: 0.00073
DEBUG:RESCAL:[Algorithm] Finished initialization.
DEBUG:RESCAL:[Algorithm] Preheating is going on.
DEBUG:RESCAL:[  0] total fit: 0.0000000000 | delta: 0.0000000000 | secs: 0.00090
DEBUG:RESCAL:[  1] total fit: 0.1717171717 | delta: 0.1717171717 | secs: 0.00095
DEBUG:RESCAL:[  2] total fit: 0.1679586563 | delta: 0.0037585154 | secs: 0.00067
DEBUG:RESCAL:[  3] total fit: 0.1669915530 | delta: 0.0009671034 | secs: 0.00076
DEBUG:RESCAL:[  4] total fit: 0.1667480072 | delta: 0.0002435458 | secs: 0.00081
DEBUG:RESCAL:[  5] total fit: 0.1666870092 | delta: 0.0000609979 | secs: 0.00077
DEBUG:RESCAL:[  6] total fit: 0.1666717528 | delta: 0.0000152565 | secs: 0.00075
DEBUG:RESCAL:[  7] total fit: 0.1666679382 | delta: 0.0000038146 | secs: 0.00067

cat extrescal.log

DEBUG:EXT-RESCAL:[Config] rank: 2 | maxIter: 50 | conv: 1.0e-05 | lmbda: 1.0e-03
DEBUG:EXT-RESCAL:[Algorithm] The tensor norm: 6.00000
DEBUG:EXT-RESCAL:[Algorithm] The extended matrix norm: 6.00000
DEBUG:EXT-RESCAL:[Algorithm] The eigenvector based initialization will be performed.
DEBUG:EXT-RESCAL:Initializing tensor slices by summation required secs: 0.00823
DEBUG:EXT-RESCAL:eigenvector decomposition required secs: 0.00459
DEBUG:EXT-RESCAL:[Algorithm] Finished initialization.
DEBUG:EXT-RESCAL:[Algorithm] Preheating is going on.
DEBUG:EXT-RESCAL:[  0] total fit: 0.0000000000 | tensor fit: 0.0000000000 | matrix fit: 0.0000000000 | delta: 0.0000000000 | secs: 0.00558
DEBUG:EXT-RESCAL:[  1] total fit: 0.4747103411 | tensor fit: 3.3519407763 | matrix fit: 2.3283205125 | delta: 0.4747103411 | secs: 0.00630
DEBUG:EXT-RESCAL:[  2] total fit: 0.4712640986 | tensor fit: 3.3643886333 | matrix fit: 2.2744289865 | delta: 0.0034462424 | secs: 0.00621
DEBUG:EXT-RESCAL:[  3] total fit: 0.4703993646 | tensor fit: 3.3703803959 | matrix fit: 2.2580441655 | delta: 0.0008647340 | secs: 0.01467
DEBUG:EXT-RESCAL:[  4] total fit: 0.4701842063 | tensor fit: 3.3730443071 | matrix fit: 2.2528058256 | delta: 0.0002151584 | secs: 0.00705
DEBUG:EXT-RESCAL:[  5] total fit: 0.4701298575 | tensor fit: 3.3741804443 | matrix fit: 2.2510327404 | delta: 0.0000543488 | secs: 0.00657
DEBUG:EXT-RESCAL:[  6] total fit: 0.4701152048 | tensor fit: 3.3746532816 | matrix fit: 2.2504019270 | delta: 0.0000146527 | secs: 0.00668
DEBUG:EXT-RESCAL:[  7] total fit: 0.4701103686 | tensor fit: 3.3748470868 | matrix fit: 2.2501688141 | delta: 0.0000048362 | secs: 0.00661

cat entity.embeddings.csv 

5.287400282344740798e-01 -2.648288074937905172e-17
6.472985753526332431e-01 -1.883524571199644730e-17
6.472985753526332431e-01 -1.883524571199644730e-17
2.528510059971223606e-03 -8.399779633628449750e-20
9.723663381107547794e-17 7.118437655042088030e-01
9.723718319815804104e-17 7.118437655042088030e-01

cat term.embeddings.csv 

4.730825851270915039e-01 -6.977337002813972351e-17
1.157697052140589156e+00 -1.451761439325526721e-16
4.522254109924176389e-03 -5.860147020766050828e-19
4.822701779013331954e-17 1.404572401961088790e+00

cat latent.factors.csv 

5.476271649231128080e-01 -1.168831819383593920e-16
-6.070133651429397840e-17 1.295001708078205427e-32
1.069584306490454703e-03 -1.659206118320981211e-19
-2.282874647233581876e-19 3.540155448418387818e-35
1.741390346565283288e-33 5.092367925378079864e-17
5.092333426231983632e-17 1.478663144852583988e+00