From 7e2777d43412fa6c4d2f8459b576b472723a7260 Mon Sep 17 00:00:00 2001
From: Olivier Grisel <olivier.grisel@ensta.org>
Date: Wed, 8 Dec 2010 11:11:43 +0100
Subject: [PATCH] switch whintening off in PCA by default + ensure unit scale +
better docstring
---
scikits/learn/pca.py | 16 +++++++++++-----
scikits/learn/tests/test_pca.py | 30 ++++++++++++++++++------------
2 files changed, 29 insertions(+), 17 deletions(-)
diff --git a/scikits/learn/pca.py b/scikits/learn/pca.py
index e8bb5120d4..1a19ebfaca 100644
--- a/scikits/learn/pca.py
+++ b/scikits/learn/pca.py
@@ -127,10 +127,15 @@ class PCA(BaseEstimator):
explained variances is equal to 1.0
whiten: bool, optional
- If True (default) the components_ vectors are divided by the
- singular values to ensure uncorrelated outputs with identical
+ When True (False by default) the components_ vectors are divided
+ by the singular values to ensure uncorrelated outputs with unit
component-wise variances.
+ Whitening will remove some information from the transformed signal
+ (the relative variance scales of the components) but can sometime
+ improve the predictive accuracy of the downstream estimators by
+ making there data respect some hard-wired assumptions.
+
iterated_power: int, optional
Number of iteration for the power method if do_fast_svd is True. 3 by
default.
@@ -147,7 +152,7 @@ class PCA(BaseEstimator):
>>> from scikits.learn.pca import PCA
>>> pca = PCA(n_comp=2)
>>> pca.fit(X)
- PCA(do_fast_svd=False, n_comp=2, copy=True, whiten=True, iterated_power=3)
+ PCA(do_fast_svd=False, n_comp=2, copy=True, whiten=False, iterated_power=3)
>>> print pca.explained_variance_ratio_
[ 0.99244289 0.00755711]
@@ -157,7 +162,7 @@ class PCA(BaseEstimator):
"""
def __init__(self, n_comp=None, copy=True, do_fast_svd=False,
- iterated_power=3, whiten=True):
+ iterated_power=3, whiten=False):
self.n_comp = n_comp
self.copy = copy
self.do_fast_svd = do_fast_svd
@@ -188,7 +193,8 @@ class PCA(BaseEstimator):
self.explained_variance_.sum()
if self.whiten:
- self.components_ = np.dot(V.T, np.diag(1.0 / S))
+ n = X.shape[0]
+ self.components_ = np.dot(V.T, np.diag(1.0 / S)) * np.sqrt(n)
else:
self.components_ = V.T
diff --git a/scikits/learn/tests/test_pca.py b/scikits/learn/tests/test_pca.py
index f65694e774..1282213625 100644
--- a/scikits/learn/tests/test_pca.py
+++ b/scikits/learn/tests/test_pca.py
@@ -26,31 +26,37 @@ def test_pca():
def test_whitening():
"""Check that PCA output has unit-variance"""
np.random.seed(0)
+ n_samples = 100
+ n_features = 80
+ n_components = 30
+ rank = 50
# some low rank data with correlated features
- X = np.dot(randn(100, 50),
- np.dot(np.diag(np.linspace(10.0, 1.0, 50)),
- randn(50, 80)))
+ X = np.dot(randn(n_samples, rank),
+ np.dot(np.diag(np.linspace(10.0, 1.0, rank)),
+ randn(rank, n_features)))
# the component-wise variance of the first 50 features is 3 times the
# mean component-wise variance of the remaingin 30 features
X[:, :50] *= 3
- assert_equal(X.shape, (100, 80))
+ assert_equal(X.shape, (n_samples, n_features))
# the component-wise variance is thus highly varying:
assert_almost_equal(X.std(axis=0).std(), 43.9, 1)
- # whiten by default
- X_whitened = PCA(n_comp=30).fit(X).transform(X)
- assert_equal(X_whitened.shape, (100, 30))
+ # whiten the data while projecting to the lower dim subspace
+ pca = PCA(n_comp=n_components, whiten=True).fit(X)
+ X_whitened = pca.transform(X)
+ assert_equal(X_whitened.shape, (n_samples, n_components))
- # all output component have identical variance
- assert_almost_equal(X_whitened.std(axis=0).std(), 0.0, 3)
+ # all output component have unit variances
+ assert_almost_equal(X_whitened.std(axis=0), np.ones(n_components))
# is possible to project on the low dim space without scaling by the
# singular values
- X_unwhitened = PCA(n_comp=30, whiten=False).fit(X).transform(X)
- assert_equal(X_unwhitened.shape, (100, 30))
+ pca = PCA(n_comp=n_components, whiten=False).fit(X)
+ X_unwhitened = pca.transform(X)
+ assert_equal(X_unwhitened.shape, (n_samples, n_components))
# in that case the output components still have varying variances
assert_almost_equal(X_unwhitened.std(axis=0).std(), 74.1, 1)
@@ -182,7 +188,7 @@ def test_probabilistic_pca_4():
Xt = randn(n, p) + randn(n, 1)*np.array([3, 4, 5]) + np.array([1, 0, 7])
ll = np.zeros(p)
for k in range(p):
- ppca = ProbabilisticPCA(n_comp=k, whiten=False)
+ ppca = ProbabilisticPCA(n_comp=k)
ppca.fit(Xl)
ll[k] = ppca.score(Xt).mean()
--
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