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Decomposition
vene edited this page Jul 2, 2012 · 2 revisions
The design in FastICA's callable nonlinear functions G and G' was suboptimal by being separated. Very often the derivative can be computed faster if it's computed at the same time as the function, and this fits FastICA, because they are always computed at the same time.
For small datasets, the calls to g and gprime sometimes overthrow the costs to np.dot and eigh.
For a random X of shape (500, 500), here is the before and after. This is a small but consistent speedup, and for certain functions it could make more of a difference.
ncalls tottime percall cumtime percall filename:lineno(function) 1599 30.089 0.019 30.089 0.019 {numpy.core._dotblas.dot} 200 25.427 0.127 25.788 0.129 decomp.py:196(eigh) 1 1.678 1.678 59.546 59.546 fastica_.py:94(_ica_par) 199 1.490 0.007 1.490 0.007 fastica_.py:229(g) 200 0.284 0.001 41.156 0.206 fastica_.py:40(_sym_decorrelation) ncalls tottime percall cumtime percall filename:lineno(function) 1599 28.578 0.018 28.578 0.018 {numpy.core._dotblas.dot} 200 27.604 0.138 27.944 0.140 decomp.py:196(eigh) 1 1.615 1.615 61.189 61.189 fastica_.py:88(_ica_par) 199 1.569 0.008 1.570 0.008 fastica_.py:219(gprime) 199 0.995 0.005 0.995 0.005 fastica_.py:215(g) 200 0.272 0.001 42.587 0.213 fastica_.py:40(_sym_decorrelation) And the output of %timeit:
import numpy as np from sklearn.decomposition import fastica from fastica_ import fastica as new_ica np.random.seed(0) X = np.random.randn(200, 200) for algorithm in ('deflation', 'parallel'): for fun in ('logcosh', 'exp', 'cube'): print '%s %s:' % (algorithm, fun) print 'old: ', %timeit -r10 fastica(X, algorithm=algorithm, fun=fun) print 'new: ', %timeit -r10 new_ica(X, algorithm=algorithm, fun=fun) deflation logcosh: old: 1 loops, best of 10: 1.38 s per loop new: 1 loops, best of 10: 1.25 s per loop deflation exp: old: 1 loops, best of 10: 2.26 s per loop new: 1 loops, best of 10: 2.13 s per loop deflation cube: old: 1 loops, best of 10: 463 ms per loop new: 1 loops, best of 10: 465 ms per loop parallel logcosh: old: 1 loops, best of 10: 23.9 s per loop new: 1 loops, best of 10: 23.3 s per loop parallel exp: old: 1 loops, best of 10: 23.1 s per loop new: 1 loops, best of 10: 22.8 s per loop parallel cube: old: 1 loops, best of 10: 1.22 s per loop new: 1 loops, best of 10: 1.11 s per loop