From 531f25f96cfef084631acda9bb44dc0c690de884 Mon Sep 17 00:00:00 2001
From: Olivier Grisel <olivier.grisel@ensta.org>
Date: Sun, 28 Nov 2010 18:55:06 +0100
Subject: [PATCH] more documentation on fast SVD + missing reference
---
scikits/learn/utils/extmath.py | 17 ++++++++++++++---
1 file changed, 14 insertions(+), 3 deletions(-)
diff --git a/scikits/learn/utils/extmath.py b/scikits/learn/utils/extmath.py
index aad0789942..1ec6cc1858 100644
--- a/scikits/learn/utils/extmath.py
+++ b/scikits/learn/utils/extmath.py
@@ -94,7 +94,7 @@ def _sparsedot(a, b):
else:
return np.dot(a,b)
-def fast_svd(M, k, p=10, rng=0, q=0):
+def fast_svd(M, k, p=None, rng=0, q=0):
"""Computes the k-truncated SVD using random projections
Parameters
@@ -105,10 +105,14 @@ def fast_svd(M, k, p=10, rng=0, q=0):
k: int
Number of singular values and vectors to extract.
- p: int (default is 10)
+ p: int (default is k)
Additional number of samples of the range of M to ensure proper
conditioning. See the notes below.
+ q: int (default is 0)
+ Number of power iterations (can be used to deal with very noisy
+ problems).
+
rng: RandomState or an int seed (0 by default)
A random number generator instance to make behavior
@@ -123,10 +127,14 @@ def fast_svd(M, k, p=10, rng=0, q=0):
checked by ensuring that the lowest extracted singular value is on
the order of the machine precision of floating points.
- References: Finding structure with randomness: Stochastic
+ References
+ ==========
+ Finding structure with randomness: Stochastic
algorithms for constructing approximate matrix decompositions,
Halko, et al., 2009 (arXiv:909)
+ A randomized algorithm for the decomposition of matrices
+ Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert
"""
if rng is None:
rng = np.random.RandomState()
@@ -143,6 +151,9 @@ def fast_svd(M, k, p=10, rng=0, q=0):
# sampling the range of M using by linear projection of r
Y = _sparsedot(M, r)
del r
+
+ # apply q power iterations on Y to make to further 'imprint' the top
+ # singular values of M in Y
for i in xrange(q):
Y = _sparsedot(M, _sparsedot(M.T, Y))
--
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