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Incremental Approaches for Matrix Approximation

Experimental code and results of:

T. Kitazawa, T. Matsuo, Incremental Approaches for Matrix Approximation: Performance Evaluations and Their Possible Applications, (in Japanese), The Japanese Society for Artificial Intelligence SIG-FPAI-B501, Aug. 2015.

Dataset

Training data of USPS normalized handwritten dataset.

http://statweb.stanford.edu/~tibs/ElemStatLearn/data.html

1) Brute Force

Running Time: around 4000 sec.

2) Incremental SVD (iSVD)

Running Time: around 750 sec.

k Covariance Error Projection Error
2 0.0657172694621 1.0
4 0.0491418902379 1.0
8 0.0256682270686 1.0
16 0.0122495458957 1.0
32 0.0052127371377 1.0
64 0.00168276318593 1.0
128 0.000446738422159 1.0
256 6.82607484728e-13 5228.83140371

3) Frequent Directions

ell Projection Error Running Time (sec.)
4 1.9043975495 0.591689
8 1.53392089235 0.877754
16 1.14943840055 2.401179
32 1.00044963427 6.108395
64 1.00000728168 17.863258
128 1.00000006729 84.104562
256 1.0 304.967199

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Implementation and evaluation of several incremental matrix approximation algorithms

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