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License: Other
Pairwise Perturbation: an efficient numerical algorithm for alternating least squares in tensor decompositions
License: Other
As to a random tensor, the relation between decomposition residual and Tucker rank is interesting:
residual drops a lot when rank is 1 and rank is the size of the tensor, while change little in the middle. For example, as to a random tensor with size 4 and F-norm 50, the decomposition residual is as follows:
rank 1 : res = 9.03
rank 2 : res = 8.875
rank 3 : res = 7.965
rank 4 : res = 0.0
Interesting topic to investigate in the future
Running ./test_ALS -model CP -tensor r2 -pp 0 -dim 5 -size 5 -maxiter 250 will make ctf produce edge length doesn't match error.
When the update_rank is larger than the mode size, ALS blows up.
commands:
mpirun -np 4 ./run -model CP -tensor r -pp 0 -dim 6 -size 12 -rank 100 -maxiter 100 -resprint 10
mpirun -np 4 ./run -model CP -tensor r -pp 2 -dim 6 -size 12 -rank 100 -maxiter 100 -updaterank 20 -resprint 10
Even when the CP rank is equal to the update rank, DT_LR results are not exactly the same as DT results.
command:
mpirun -np 4 ./run -model CP -tensor r -pp 0 -dim 6 -size 12 -rank 10 -maxiter 10 -updaterank 10 -resprint 10
mpirun -np 4 ./run -model CP -tensor r -pp 2 -dim 6 -size 12 -rank 10 -maxiter 10 -updaterank 10 -resprint 10
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