def test_fastica_nowhiten():
m = [[0, 1], [1, 0]]
ica = FastICA(whiten=False, random_state=0)
ica.fit(m)
ica.get_mixing_matrix()
# test for issue #697
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
ica = FastICA(n_components=1, whiten=False, random_state=0)
ica.fit(m) # should raise warning
assert_true(len(w) == 1) # 1 warning should be raised
def test_fastica_nowhiten():
m = [[0, 1], [1, 0]]
ica = FastICA(whiten=False, random_state=0)
ica.fit(m)
ica.get_mixing_matrix()
# test for issue #697
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
ica = FastICA(n_components=1, whiten=False, random_state=0)
ica.fit(m) # should raise warning
assert_true(len(w) == 1) # 1 warning should be raised
def ICAFilter(signal=None):
# EEG filtering based on Independent Component Analysis
# ICA decomposition
ica = FastICA(whiten=True)
IC = ica.fit(signal).transform(signal)
A = ica.get_mixing_matrix() # signal = np.dot(IC, A.T)
# noise metrics
sigma2 = IC.std(ddof=1, axis=0)**2
f1 = np.abs(IC).max(axis=0) / sigma2
f2 = np.abs(stats.skew(IC, bias=False, axis=0))
f = np.hstack((f1.reshape((len(f1), 1)), f2.reshape((len(f2), 1))))
fr = f.copy()
f /= f.max(axis=0)
norm = np.sqrt(np.dot(f, f.T)).diagonal()
# remove noisy IC
ind = norm.argmax()
IC_ = IC.copy()
IC_[:, ind] = 0
# recompute signal
signalF = np.dot(IC_, A.T)
return signalF, IC, fr
def independent_component(x, y):
clf = FastICA(random_state=1)
clf.fit(x.reshape(-1, 1), y)
comp = clf.components_[0][0]
mm = clf.get_mixing_matrix()[0][0]
sources = clf.sources_.flatten()
src_max = max(sources)
src_min = min(sources)
return [comp, mm, src_max, src_min]
def independent_component((x, y)):
lenX = len(x)
newX = np.array(x).reshape(lenX, 1)
g = FastICA()
g.fit(newX, y)
ret = [0.0, 0.0, 0.0, 0.0]
ret[0] = g.components_[0][0]
ret[1] = g.get_mixing_matrix()[0][0]
sources = g.sources_.flatten()
ret[2] = max(sources)
ret[3] = min(sources)
return ret
def independent_component( (x, y) ):
lenX = len(x)
newX = np.array(x).reshape(lenX, 1)
g = FastICA()
g.fit(newX, y)
ret = [0.0, 0.0, 0.0, 0.0]
ret[0] = g.components_[0][0]
ret[1] = g.get_mixing_matrix()[0][0]
sources = g.sources_.flatten()
ret[2] = max(sources)
ret[3] = min(sources)
return ret
def RunICAScikit(q):
totalTimer = Timer()
# Load input dataset.
data = np.genfromtxt(self.dataset, delimiter=',')
s = re.search('-s (\d+)', options)
s = 0 if not s else int(s.group(1))
try:
# Perform ICA.
with totalTimer:
model = FastICA(random_state=s)
ic = model.fit(data).transform(data)
mixing = model.get_mixing_matrix()
except Exception as e:
q.put(-1)
return -1
time = totalTimer.ElapsedTime()
q.put(time)
return time
def RunICAScikit(q):
totalTimer = Timer()
# Load input dataset.
data = np.genfromtxt(self.dataset, delimiter=',')
s = re.search('-s (\d+)', options)
s = 0 if not s else int(s.group(1))
try:
# Perform ICA.
with totalTimer:
model = FastICA(random_state=s)
ic = model.fit(data).transform(data)
mixing = model.get_mixing_matrix()
except Exception as e:
q.put(-1)
return -1
time = totalTimer.ElapsedTime()
q.put(time)
return time
class ICA(object):
"""M/EEG signal decomposition using Independent Component Analysis (ICA)
This object can be used to estimate ICA components and then
remove some from Raw or Epochs for data exploration or artifact
correction.
Parameters
----------
n_components : int | float | None
The number of components used for ICA decomposition. If int, it must be
smaller then max_n_components. If None, all PCA components will be
used. If float between 0 and 1 components can will be selected by the
cumulative percentage of explained variance.
max_n_components : int | None
The number of components used for PCA decomposition. If None, no
dimension reduction will be applied and max_n_components will equal
the number of channels supplied on decomposing data.
noise_cov : None | instance of mne.cov.Covariance
Noise covariance used for whitening. If None, channels are just
z-scored.
random_state : None | int | instance of np.random.RandomState
np.random.RandomState to initialize the FastICA estimation.
As the estimation is non-deterministic it can be useful to
fix the seed to have reproducible results.
algorithm : {'parallel', 'deflation'}
Apply parallel or deflational algorithm for FastICA
fun : string or function, optional. Default: 'logcosh'
The functional form of the G function used in the
approximation to neg-entropy. Could be either 'logcosh', 'exp',
or 'cube'.
You can also provide your own function. It should return a tuple
containing the value of the function, and of its derivative, in the
point.
fun_args: dictionary, optional
Arguments to send to the functional form.
If empty and if fun='logcosh', fun_args will take value
{'alpha' : 1.0}
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Attributes
----------
last_fit : str
Flag informing about which type was last fit.
ch_names : list-like
Channel names resulting from initial picking.
n_components : int
The number of components used for ICA decomposition.
max_n_components : int
The number of PCA dimensions computed.
verbose : bool, str, int, or None
See above.
"""
@verbose
def __init__(self, n_components, max_n_components=100, noise_cov=None,
random_state=None, algorithm='parallel', fun='logcosh',
fun_args=None, verbose=None):
try:
from sklearn.decomposition import FastICA # to avoid strong dep.
except ImportError:
raise Exception('the scikit-learn package is missing and '
'required for ICA')
self.noise_cov = noise_cov
# sklearn < 0.11 does not support random_state argument for FastICA
kwargs = {'algorithm': algorithm, 'fun': fun, 'fun_args': fun_args}
if random_state is not None:
aspec = inspect.getargspec(FastICA.__init__)
if 'random_state' not in aspec.args:
warnings.warn('random_state argument ignored, update '
'scikit-learn to version 0.11 or newer')
else:
kwargs['random_state'] = random_state
if max_n_components is not None and n_components > max_n_components:
raise ValueError('n_components must be smaller than '
'max_n_components')
if isinstance(n_components, float):
if not 0 < n_components <= 1:
raise ValueError('For selecting ICA components by the '
'explained variance of PCA components the'
' float value must be between 0.0 and 1.0 ')
self._explained_var = n_components
logger.info('Selecting pca_components via explained variance.')
else:
self._explained_var = 1.1
logger.info('Selecting pca_components directly.')
self._ica = FastICA(**kwargs)
self.current_fit = 'unfitted'
self.verbose = verbose
self.n_components = n_components
self.max_n_components = max_n_components
self.ch_names = None
self._mixing = None
def __repr__(self):
s = 'ICA '
if self.current_fit == 'unfitted':
msg = '(no'
elif self.current_fit == 'raw':
msg = '(raw data'
else:
msg = '(epochs'
msg += ' decomposition, '
s += msg + ('%s components' % str(self.n_components) if
self.n_components else 'no dimension reduction') + ')'
return s
@verbose
def decompose_raw(self, raw, picks=None, start=None, stop=None,
verbose=None):
"""Run the ICA decomposition on raw data
Parameters
----------
raw : instance of mne.fiff.Raw
Raw measurements to be decomposed.
picks : array-like
Channels to be included. This selection remains throughout the
initialized ICA session. If None only good data channels are used.
start : int
First sample to include (first is 0). If omitted, defaults to the
first sample in data.
stop : int
First sample to not include. If omitted, data is included to the
end.
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Defaults to self.verbose.
Returns
-------
self : instance of ICA
Returns the modified instance.
"""
if self.current_fit != 'unfitted':
raise RuntimeError('ICA decomposition has already been fitted. '
'Please start a new ICA session.')
logger.info('Computing signal decomposition on raw data. '
'Please be patient, this may take some time')
if picks is None: # just use good data channels
picks = pick_types(raw.info, meg=True, eeg=True, eog=False,
ecg=False, misc=False, stim=False,
exclude=raw.info['bads'])
if self.max_n_components is None:
self.max_n_components = len(picks)
logger.info('Inferring max_n_components from picks.')
self.ch_names = [raw.ch_names[k] for k in picks]
data, self._pre_whitener = self._pre_whiten(raw[picks, start:stop][0],
raw.info, picks)
to_ica, self._pca = self._prepare_pca(data, self.max_n_components)
self._ica.fit(to_ica)
self._mixing = self._ica.get_mixing_matrix().T
self.current_fit = 'raw'
return self
@verbose
def decompose_epochs(self, epochs, picks=None, verbose=None):
"""Run the ICA decomposition on epochs
Parameters
----------
epochs : instance of Epochs
The epochs. The ICA is estimated on the concatenated epochs.
picks : array-like
Channels to be included relative to the channels already picked on
epochs-initialization. This selection remains throughout the
initialized ICA session.
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Defaults to self.verbose.
Returns
-------
self : instance of ICA
Returns the modified instance.
"""
if self.current_fit != 'unfitted':
raise RuntimeError('ICA decomposition has already been fitted. '
'Please start a new ICA session.')
logger.info('Computing signal decomposition on epochs. '
'Please be patient, this may take some time')
if picks is None: # just use epochs good data channels and avoid
picks = pick_types(epochs.info, include=epochs.ch_names, # double
exclude=epochs.info['bads']) # picking
meeg_picks = pick_types(epochs.info, meg=True, eeg=True, eog=False,
ecg=False, misc=False, stim=False,
exclude=epochs.info['bads'])
# filter out all the channels the raw wouldn't have initialized
picks = np.intersect1d(meeg_picks, picks)
self.ch_names = [epochs.ch_names[k] for k in picks]
if self.max_n_components is None:
self.max_n_components = len(picks)
logger.info('Inferring max_n_components from picks.')
data, self._pre_whitener = self._pre_whiten(
np.hstack(epochs.get_data()[:, picks]),
epochs.info, picks)
to_ica, self._pca = self._prepare_pca(data, self.max_n_components)
self._ica.fit(to_ica)
self._mixing = self._ica.get_mixing_matrix().T
self.current_fit = 'epochs'
return self
def get_sources_raw(self, raw, start=None, stop=None):
"""Estimate raw sources given the unmixing matrix
Parameters
----------
raw : instance of Raw
Raw object to draw sources from.
start : int
First sample to include (first is 0). If omitted, defaults to the
first sample in data.
stop : int
First sample to not include.
If omitted, data is included to the end.
Returns
-------
sources : array, shape = (n_components, n_times)
The ICA sources time series.
"""
if self._mixing is None:
raise RuntimeError('No fit available. Please first fit ICA '
'decomposition.')
return self._get_sources_raw(raw, start, stop)[0]
def _get_sources_raw(self, raw, start, stop):
picks = [raw.ch_names.index(k) for k in self.ch_names]
data, _ = self._pre_whiten(raw[picks, start:stop][0], raw.info, picks)
pca_data = self._pca.transform(data.T)
raw_sources = self._ica.transform(pca_data[:, self._comp_idx]).T
return raw_sources, pca_data
def get_sources_epochs(self, epochs, concatenate=False):
"""Estimate epochs sources given the unmixing matrix
Parameters
----------
epochs : instance of Epochs
Epochs object to draw sources from.
concatenate : bool
If true, epochs and time slices will be concatenated.
Returns
-------
epochs_sources : ndarray of shape (n_epochs, n_sources, n_times)
The sources for each epoch
"""
if self._mixing is None:
raise RuntimeError('No fit available. Please first fit ICA '
'decomposition.')
return self._get_sources_epochs(epochs, concatenate)[0]
def _get_sources_epochs(self, epochs, concatenate):
picks = pick_types(epochs.info, include=self.ch_names,
exclude=epochs.info['bads'])
# special case where epochs come picked but fit was 'unpicked'.
if len(picks) != len(self.ch_names):
raise RuntimeError('Epochs don\'t match fitted data: %i channels '
'fitted but %i channels supplied. \nPlease '
'provide Epochs compatible with '
'ica.ch_names' % (len(self.ch_names),
len(picks)))
data, _ = self._pre_whiten(np.hstack(epochs.get_data()[:, picks]),
epochs.info, picks)
pca_data = self._pca.transform(data.T)
sources = self._ica.transform(pca_data[:, self._comp_idx]).T
sources = np.array(np.split(sources, len(epochs.events), 1))
if concatenate:
sources = np.hstack(sources)
return sources, pca_data
def export_sources(self, raw, picks=None, start=None, stop=None):
"""Export sources as raw object
Parameters
----------
raw : instance of Raw
Raw object to export sources from.
picks : array-like
Channels to be included in addition to the sources. If None,
artifact and stimulus channels will be included.
start : int
First sample to include (first is 0). If omitted, defaults to the
first sample in data.
stop : int
First sample to not include. If omitted, data is included to the
end.
Returns
-------
out : instance of mne.Raw
Container object for ICA sources
"""
if not raw._preloaded:
raise ValueError('raw data should be preloaded to have this '
'working. Please read raw data with '
'preload=True.')
# include 'reference' channels for comparison with ICA
if picks is None:
picks = pick_types(raw.info, meg=False, eeg=False, misc=True,
ecg=True, eog=True, stim=True)
# merge copied instance and picked data with sources
out = raw.copy()
out.fids = []
sources = self.get_sources_raw(raw, start=start, stop=stop)
out._data = np.r_[sources, raw[picks, start:stop][0]]
# update first and last samples
out.first_samp = raw.first_samp + (start if start else 0)
out.last_samp = out.first_samp + stop if stop else raw.last_samp
# set channel names and info
ch_names = out.info['ch_names'] = []
ch_info = out.info['chs'] = []
for i in xrange(self.n_components):
ch_names.append('ICA %03d' % (i + 1))
ch_info.append(dict(ch_name='ICA %03d' % (i + 1), cal=1,
logno=i + 1, coil_type=FIFF.FIFFV_COIL_NONE,
kind=FIFF.FIFFV_MISC_CH, coord_Frame=FIFF.FIFFV_COORD_UNKNOWN,
loc=np.array([0., 0., 0., 1., 0., 0., 0., 1.,
0., 0., 0., 1.], dtype=np.float32),
unit=FIFF.FIFF_UNIT_NONE, eeg_loc=None, range=1.0,
scanno=i + 1, unit_mul=0, coil_trans=None))
# re-append additionally picked ch_names
ch_names += [raw.ch_names[k] for k in picks]
# re-append additionally picked ch_info
ch_info += [raw.info['chs'][k] for k in picks]
# update number of channels
out.info['nchan'] = len(picks) + self.n_components
return out
def plot_sources_raw(self, raw, order=None, start=None, stop=None,
n_components=None, source_idx=None, ncol=3, nrow=10,
show=True):
"""Create panel plots of ICA sources. Wrapper around viz.plot_ica_panel
Parameters
----------
raw : instance of mne.fiff.Raw
Raw object to plot the sources from.
order : ndarray | None.
Index of length n_components. If None, plot will show the sources
in the order as fitted.
Example: arg_sort = np.argsort(np.var(sources)).
start : int
X-axis start index. If None from the beginning.
stop : int
X-axis stop index. If None to the end.
n_components : int
Number of components fitted.
source_idx : array-like
Indices for subsetting the sources.
ncol : int
Number of panel-columns.
nrow : int
Number of panel-rows.
show : bool
If True, plot will be shown, else just the figure is returned.
Returns
-------
fig : instance of pyplot.Figure
"""
sources = self.get_sources_raw(raw, start=start, stop=stop)
if order is not None:
if len(order) != sources.shape[0]:
raise ValueError('order and sources have to be of the '
'same length.')
else:
sources = sources[order]
fig = plot_ica_panel(sources, start=0 if start is not None else start,
stop=(stop - start) if stop is not None else stop,
n_components=n_components, source_idx=source_idx,
ncol=ncol, nrow=nrow)
if show:
import matplotlib.pylab as pl
pl.show()
return fig
def plot_sources_epochs(self, epochs, epoch_idx=None, order=None,
start=None, stop=None, n_components=None,
source_idx=None, ncol=3, nrow=10, show=True):
"""Create panel plots of ICA sources. Wrapper around viz.plot_ica_panel
Parameters
----------
epochs : instance of mne.Epochs
Epochs object to plot the sources from.
epoch_idx : int
Index to plot particular epoch.
order : ndarray | None.
Index of length n_components. If None, plot will show the sources
in the order as fitted.
Example: arg_sort = np.argsort(np.var(sources)).
sources : ndarray
Sources as drawn from self.get_sources.
start : int
X-axis start index. If None from the beginning.
stop : int
X-axis stop index. If None to the end.
n_components : int
Number of components fitted.
source_idx : array-like
Indices for subsetting the sources.
ncol : int
Number of panel-columns.
nrow : int
Number of panel-rows.
show : bool
If True, plot will be shown, else just the figure is returned.
Returns
-------
fig : instance of pyplot.Figure
"""
sources = self.get_sources_epochs(epochs, concatenate=True if epoch_idx
is None else False)
source_dim = 1 if sources.ndim > 2 else 0
if order is not None:
if len(order) != sources.shape[source_dim]:
raise ValueError('order and sources have to be of the '
'same length.')
else:
sources = (sources[:, order] if source_dim
else sources[order])
fig = plot_ica_panel(sources[epoch_idx], start=start, stop=stop,
n_components=n_components, source_idx=source_idx,
ncol=ncol, nrow=nrow)
if show:
import matplotlib.pylab as pl
pl.show()
return fig
def find_sources_raw(self, raw, target=None, score_func='pearsonr',
start=None, stop=None):
"""Find sources based on own distribution or based on similarity to
other sources or between source and target.
Parameters
----------
raw : instance of Raw
Raw object to draw sources from.
target : array-like | ch_name | None
Signal to which the sources shall be compared. It has to be of
the same shape as the sources. If some string is supplied, a
routine will try to find a matching channel. If None, a score
function expecting only one input-array argument must be used,
for instance, scipy.stats.skew (default).
score_func : callable | str label
Callable taking as arguments either two input arrays
(e.g. pearson correlation) or one input
array (e. g. skewness) and returns a float. For convenience the
most common score_funcs are available via string labels: Currently,
all distance metrics from scipy.spatial and all functions from
scipy.stats taking compatible input arguments are supported. These
function have been modified to support iteration over the rows of a
2D array.
start : int
First sample to include (first is 0). If omitted, defaults to the
first sample in data.
stop : int
First sample to not include.
If omitted, data is included to the end.
scores : ndarray
Scores for each source as returned from score_func.
Returns
-------
scores : ndarray
scores for each source as returned from score_func
"""
# auto source drawing
sources = self.get_sources_raw(raw=raw, start=start, stop=stop)
# auto target selection
if target is not None:
if hasattr(target, 'ndim'):
if target.ndim < 2:
target = target.reshape(1, target.shape[-1])
if isinstance(target, str):
pick = _get_target_ch(raw, target)
target, _ = raw[pick, start:stop]
if sources.shape[1] != target.shape[1]:
raise ValueError('Source and targets do not have the same'
'number of time slices.')
target = target.ravel()
return _find_sources(sources, target, score_func)
def find_sources_epochs(self, epochs, target=None, score_func='pearsonr'):
"""Find sources based on relations between source and target
Parameters
----------
epochs : instance of Epochs
Epochs object to draw sources from.
target : array-like | ch_name | None
Signal to which the sources shall be compared. It has to be of
the same shape as the sources. If some string is supplied, a
routine will try to find a matching channel. If None, a score
function expecting only one input-array argument must be used,
for instance, scipy.stats.skew (default).
score_func : callable | str label
Callable taking as arguments either two input arrays
(e.g. pearson correlation) or one input
array (e. g. skewness) and returns a float. For convenience the
most common score_funcs are available via string labels: Currently,
all distance metrics from scipy.spatial and all functions from
scipy.stats taking compatible input arguments are supported. These
function have been modified to support iteration over the rows of a
2D array.
Returns
-------
scores : ndarray
scores for each source as returned from score_func
"""
sources = self.get_sources_epochs(epochs=epochs)
# auto target selection
if target is not None:
if hasattr(target, 'ndim'):
if target.ndim < 3:
target = target.reshape(1, 1, target.shape[-1])
if isinstance(target, str):
pick = _get_target_ch(epochs, target)
target = epochs.get_data()[:, pick]
if sources.shape[2] != target.shape[2]:
raise ValueError('Source and targets do not have the same'
'number of time slices.')
target = target.ravel()
return _find_sources(np.hstack(sources), target, score_func)
def pick_sources_raw(self, raw, include=None, exclude=None,
n_pca_components=64, start=None, stop=None,
copy=True):
"""Recompose raw data including or excluding some sources
Parameters
----------
raw : instance of Raw
Raw object to pick to remove ICA components from.
include : list-like | None
The source indices to use. If None all are used.
exclude : list-like | None
The source indices to remove. If None all are used.
n_pca_components:
The number of PCA components to be unwhitened, where n_components
is the lower bound and max_n_components the upper bound.
If greater than self.n_components, the PCA components that were not
supplied to the ICA will get re-attached. This can be used to take
back the PCA dimension reduction.
start : int | None
The first time index to include.
stop : int | None
The first time index to exclude.
copy: bool
modify raw instance in place or return modified copy.
Returns
-------
raw : instance of Raw
raw instance with selected ICA components removed
"""
if not raw._preloaded:
raise ValueError('raw data should be preloaded to have this '
'working. Please read raw data with '
'preload=True.')
if self.current_fit != 'raw':
raise ValueError('Currently no raw data fitted.'
'Please fit raw data first.')
sources, pca_data = self._get_sources_raw(raw, start=start, stop=stop)
recomposed = self._pick_sources(sources, pca_data, include, exclude,
n_pca_components)
if copy is True:
raw = raw.copy()
picks = [raw.ch_names.index(k) for k in self.ch_names]
raw[picks, start:stop] = recomposed
return raw
def pick_sources_epochs(self, epochs, include=None, exclude=None,
n_pca_components=64, copy=True):
"""Recompose epochs
Parameters
----------
epochs : instance of Epochs
Epochs object to pick to remove ICA components from.
include : list-like | None
The source indices to use. If None all are used.
exclude : list-like | None
The source indices to remove. If None all are used.
n_pca_components:
The number of PCA components to be unwhitened, where n_components
is the lower bound and max_n_components the upper bound.
If greater than self.n_components, the PCA components that were not
supplied to the ICA will get re-attached. This can be used to take
back the PCA dimension reduction.
copy : bool
Modify Epochs instance in place or return modified copy.
Returns
-------
epochs : instance of Epochs
Epochs with selected ICA components removed.
"""
if not epochs.preload:
raise ValueError('raw data should be preloaded to have this '
'working. Please read raw data with '
'preload=True.')
sources, pca_data = self._get_sources_epochs(epochs, True)
picks = pick_types(epochs.info, include=self.ch_names,
exclude=epochs.info['bads'])
if copy is True:
epochs = epochs.copy()
# put sources-dimension first for selection
recomposed = self._pick_sources(sources, pca_data, include, exclude,
n_pca_components)
# restore epochs, channels, tsl order
epochs._data[:, picks] = np.array(np.split(recomposed,
len(epochs.events), 1))
epochs.preload = True
return epochs
def _pre_whiten(self, data, info, picks):
"""Helper function"""
if self.noise_cov is None: # use standardization as whitener
pre_whitener = np.std(data) ** -1
data *= pre_whitener
else: # pick cov
ncov = deepcopy(self.noise_cov)
if ncov.ch_names != self.ch_names:
ncov['data'] = ncov.data[picks][:, picks]
assert data.shape[0] == ncov.data.shape[0]
pre_whitener, _ = compute_whitener(ncov, info, picks)
data = np.dot(pre_whitener, data)
return data, pre_whitener
def _prepare_pca(self, data, max_n_components):
""" Helper Function """
from sklearn.decomposition import RandomizedPCA
# sklearn < 0.11 does not support random_state argument
kwargs = {'n_components': max_n_components, 'whiten': False}
aspec = inspect.getargspec(RandomizedPCA.__init__)
if 'random_state' not in aspec.args:
warnings.warn('RandomizedPCA does not support random_state '
'argument. Use scikit-learn to version 0.11 '
'or newer to get reproducible results.')
else:
kwargs['random_state'] = 0
pca = RandomizedPCA(**kwargs)
pca_data = pca.fit_transform(data.T)
if self._explained_var > 1.0:
if self.n_components is not None: # normal n case
self._comp_idx = np.arange(self.n_components)
to_ica = pca_data[:, self._comp_idx]
else: # None case
to_ica = pca_data
self.n_components = pca_data.shape[1]
self._comp_idx = np.arange(self.n_components)
else: # float case
expl_var = pca.explained_variance_ratio_
self._comp_idx = (np.where(expl_var.cumsum() <
self._explained_var)[0])
to_ica = pca_data[:, self._comp_idx]
self.n_components = len(self._comp_idx)
return to_ica, pca
def _pick_sources(self, sources, pca_data, include, exclude,
n_pca_components):
"""Helper function"""
if not(self.n_components <= n_pca_components <= self.max_n_components):
raise ValueError('n_pca_components must be between n_components'
' and max_n_components.')
if include not in (None, []):
mute = [i for i in xrange(len(sources)) if i not in include]
sources[mute, :] = 0. # include via exclusion
elif exclude not in (None, []):
sources[exclude, :] = 0. # just exclude
# restore pca data
mixing = self._mixing.copy()
pca_restored = np.dot(sources.T, mixing)
# re-append deselected pca dimension if desired
if n_pca_components - self.n_components > 0:
add_components = np.arange(self.n_components, n_pca_components)
pca_reappend = pca_data[:, add_components]
pca_restored = np.c_[pca_restored, pca_reappend]
# restore sensor space data
out = _inverse_t_pca(pca_restored, self._pca)
# restore scaling
pre_whitener = self._pre_whitener.copy()
if self.noise_cov is None: # revert standardization
pre_whitener **= -1
out *= pre_whitener
else:
out = np.dot(out, linalg.pinv(pre_whitener))
return out.T
scale=6,
color=color)
pl.hlines(0, -3, 3)
pl.vlines(0, -3, 3)
pl.xlim(-3, 3)
pl.ylim(-3, 3)
pl.xlabel('x')
pl.ylabel('y')
pl.subplot(2, 2, 1)
plot_samples(S / S.std())
pl.title('True Independent Sources')
axis_list = [pca.components_.T, ica.get_mixing_matrix()]
pl.subplot(2, 2, 2)
plot_samples(X / np.std(X), axis_list=axis_list)
pl.legend(['PCA', 'ICA'], loc='upper left')
pl.title('Observations')
pl.subplot(2, 2, 3)
plot_samples(S_pca_ / np.std(S_pca_, axis=0))
pl.title('PCA scores')
pl.subplot(2, 2, 4)
plot_samples(S_ica_ / np.std(S_ica_))
pl.title('ICA estimated sources')
pl.subplots_adjust(0.09, 0.04, 0.94, 0.94, 0.26, 0.26)
class ICA(object):
"""
Wrapper for sklearn package. Performs fast ICA (Independent Component Analysis)
ICA has 4 methods:
- fit(waveforms)
update class instance with ICA fit
- fit_transform()
do what fit() does, but additionally return the projection onto ICA space
- inverse_transform(A)
inverses the decomposition, returns waveforms for an input A, using Z
- get_params()
returns metadata used for fits.
"""
def __init__(self,
num_components=10,
catalog_name='unknown',
whiten=True,
fun='logcosh',
fun_args=None,
max_iter=600,
tol=.00001,
w_init=None,
random_state=None,
algorithm='parallel'):
self._decomposition = 'Fast ICA'
self._num_components = num_components
self._catalog_name = catalog_name
self._whiten = whiten
self._fun = fun
self._fun_args = fun_args
self._max_iter = max_iter
self._tol = tol
self._w_init = w_init
self._random_state = random_state
self._algorithm = algorithm
self._ICA = FastICA(n_components=self._num_components,
whiten=self._whiten,
fun=self._fun,
fun_args=self._fun_args,
max_iter=self._max_iter,
tol=self._tol,
w_init=self._w_init,
random_state=self._random_state,
algorithm=self._algorithm)
def fit(self, waveforms):
# TODO make sure there are more columns than rows (transpose if not)
# normalize waveforms
self._waveforms = waveforms
self._ICA.fit(self._waveforms)
def fit_transform(self, waveforms):
# TODO make sure there are more columns than rows (transpose if not)
# normalize waveforms
self._waveforms = waveforms
self._A = self._ICA.fit_transform(self._waveforms)
return self._A
def inverse_transform(self, A):
# convert basis back to waveforms using fit
new_waveforms = self._ICA.inverse_transform(A)
return new_waveforms
def get_params(self):
# TODO know what catalog was used! (include waveform metadata)
params = self._ICA.get_params()
params['num_components'] = params.pop('n_components')
params['Decompositon'] = self._decomposition
return params
def get_basis(self):
""" Return the ICA basis vectors (Z^\dagger)"""
return self._ICA.get_mixing_matrix()
class ICA(object):
"""
Wrapper for sklearn package. Performs fast ICA (Independent Component Analysis)
ICA has 4 methods:
- fit(waveforms)
update class instance with ICA fit
- fit_transform()
do what fit() does, but additionally return the projection onto ICA space
- inverse_transform(A)
inverses the decomposition, returns waveforms for an input A, using Z
- get_params()
returns metadata used for fits.
"""
def __init__(self, num_components=10,
catalog_name='unknown',
whiten=True,
fun = 'logcosh',
fun_args = None,
max_iter = 600,
tol = .00001,
w_init = None,
random_state = None,
algorithm = 'parallel'):
self._decomposition = 'Fast ICA'
self._num_components = num_components
self._catalog_name = catalog_name
self._whiten = whiten
self._fun = fun
self._fun_args = fun_args
self._max_iter = max_iter
self._tol = tol
self._w_init = w_init
self._random_state = random_state
self._algorithm = algorithm
self._ICA = FastICA(n_components=self._num_components,
whiten = self._whiten,
fun = self._fun,
fun_args = self._fun_args,
max_iter = self._max_iter,
tol = self._tol,
w_init = self._w_init,
random_state = self._random_state,
algorithm = self._algorithm)
def fit(self,waveforms):
# TODO make sure there are more columns than rows (transpose if not)
# normalize waveforms
self._waveforms = waveforms
self._ICA.fit(self._waveforms)
def fit_transform(self,waveforms):
# TODO make sure there are more columns than rows (transpose if not)
# normalize waveforms
self._waveforms = waveforms
self._A = self._ICA.fit_transform(self._waveforms)
return self._A
def inverse_transform(self,A):
# convert basis back to waveforms using fit
new_waveforms = self._ICA.inverse_transform(A)
return new_waveforms
def get_params(self):
# TODO know what catalog was used! (include waveform metadata)
params = self._ICA.get_params()
params['num_components'] = params.pop('n_components')
params['Decompositon'] = self._decomposition
return params
def get_basis(self):
""" Return the ICA basis vectors (Z^\dagger)"""
return self._ICA.get_mixing_matrix()
import numpy as np
import os
from sklearn.decomposition import FastICA
# Load the data.
data = np.genfromtxt('../data/radical.csv', delimiter=',')
# Peform FastICA
ica = FastICA()
S = ica.fit(data).transform(data)
A = ica.get_mixing_matrix()
# show the results.
print S
print A
if not x==y: # skip diagonal
plt.text(x-0.3,y,'%.2f'%cc_pcorr[x,y],size=6,color='red')
plt.savefig(basedir+'9_correlation_analysis/pcorr_corrcoefs.pdf',format='pdf')
#do clustering
if 1==1:
dst=pdist(data_pcorr[2:,:])
Z=linkage(dst,method='complete')
plt.figure(figsize=(14,12))
dendrogram(Z,labels=tasknames_pcorr)
plt.savefig(basedir+'9_correlation_analysis/pcorr_task_cluster.pdf',format='pdf')
# decompose connections using ICA and save adjacency matrices
data_pcorr_fmri=data_pcorr[2:,:]
if 1==0:
ica = FastICA(n_components=20)
S_ = ica.fit(data_pcorr_fmri.T).transform(data_pcorr_fmri.T) # Get the estimated sources
A_ = ica.get_mixing_matrix() # Get estimated mixing matrix
#ncomps=20
#nmf=decomposition.ProjectedGradientNMF(n_components=ncomps,sparseness='components',init='nndsvd')
#nmf.fit(data_pcorr_fmri+100)
#comps=nmf.components_
import numpy as np
import os
from sklearn.decomposition import FastICA
# Load the data.
data = np.genfromtxt('../data/radical.csv', delimiter=',')
# Peform FastICA
ica = FastICA()
S = ica.fit(data).transform(data)
A = ica.get_mixing_matrix()
# show the results.
print S
print A
def test_fastica_simple(add_noise=False):
""" Test the FastICA algorithm on very simple data.
"""
rng = np.random.RandomState(0)
# scipy.stats uses the global RNG:
np.random.seed(0)
n_samples = 1000
# Generate two sources:
s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
s2 = stats.t.rvs(1, size=n_samples)
s = np.c_[s1, s2].T
center_and_norm(s)
s1, s2 = s
# Mixing angle
phi = 0.6
mixing = np.array([[np.cos(phi), np.sin(phi)], [np.sin(phi), -np.cos(phi)]])
m = np.dot(mixing, s)
if add_noise:
m += 0.1 * rng.randn(2, 1000)
center_and_norm(m)
# function as fun arg
def g_test(x):
return x ** 3, 3 * x ** 2
algos = ["parallel", "deflation"]
nls = ["logcosh", "exp", "cube", g_test]
whitening = [True, False]
for algo, nl, whiten in itertools.product(algos, nls, whitening):
if whiten:
k_, mixing_, s_ = fastica(m.T, fun=nl, algorithm=algo)
assert_raises(ValueError, fastica, m.T, fun=np.tanh, algorithm=algo)
else:
X = PCA(n_components=2, whiten=True).fit_transform(m.T)
k_, mixing_, s_ = fastica(X, fun=nl, algorithm=algo, whiten=False)
assert_raises(ValueError, fastica, X, fun=np.tanh, algorithm=algo)
s_ = s_.T
# Check that the mixing model described in the docstring holds:
if whiten:
assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
center_and_norm(s_)
s1_, s2_ = s_
# Check to see if the sources have been estimated
# in the wrong order
if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
s2_, s1_ = s_
s1_ *= np.sign(np.dot(s1_, s1))
s2_ *= np.sign(np.dot(s2_, s2))
# Check that we have estimated the original sources
if not add_noise:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
else:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
# Test FastICA class
ica = FastICA(fun=nl, algorithm=algo, random_state=0)
ica.fit(m.T)
ica.get_mixing_matrix()
assert_true(ica.components_.shape == (2, 2))
assert_true(ica.sources_.shape == (1000, 2))
for fn in [np.tanh, "exp(-.5(x^2))"]:
ica = FastICA(fun=fn, algorithm=algo, random_state=0)
assert_raises(ValueError, ica.fit, m.T)
assert_raises(TypeError, FastICA(fun=xrange(10)).fit, m.T)
def clusterize_dirichlet(*args, **kwargs):
# TODO plotting when the classifier is NOT learned in the PCA(2-best) space (ellipses are wrong)
""" Clustering and plotting with Dirichlet process GMM """
### Clustering
try:
from sklearn import mixture
from scipy import linalg
import pylab as pl
import matplotlib as mpl
from sklearn.decomposition import PCA, FastICA
except:
print "You need SciPy and scikit-learn"
sys.exit(-1)
models = []
for arg in args:
if apply_ica:
for featurenb in range(len(arg[0])):
if sum(arg[:, featurenb]) == 0.0:
arg = arg[:, range(featurenb+1)+range(featurenb+1, len(arg[0]))]
if kwargs.get('em_gmm', False):
dpgmm = mixture.GMM(n_components = 4, cvtype='full')
else:
dpgmm = mixture.DPGMM(n_components = 100, cvtype='full', alpha=1000.0)
if kwargs.get('clf_on_pca', False):
pca = PCA(2)
dpgmm.fit(pca.fit(arg).transform(arg))
else:
dpgmm.fit(arg)
print dpgmm
models.append(copy.deepcopy(dpgmm))
print raw_input("press any key to pass")
### Plotting
color_iter = itertools.cycle (['r', 'g', 'b', 'c', 'm'])
for i, (clf, data) in enumerate(zip(models, args)):
if apply_ica:
ica = FastICA(2)
X_r = ica.fit(data).transform(data)
print ica.get_mixing_matrix()
else:
pca = PCA(2)
X_r = pca.fit(data).transform(data)
print data
print X_r
print raw_input("press any key to pass")
splot = pl.subplot((len(args)+1)/ 2, 2, 1+i)
pl.scatter(X_r[:,0], X_r[:,1])
if kwargs.get('clf_on_pca', False):
Y_ = clf.predict(X_r)
else:
Y_ = clf.predict(data)
for i, (mean, covar, color) in enumerate(zip(clf.means, clf.covars,
color_iter)):
v, w = linalg.eigh(covar)
u = w[0] / linalg.norm(w[0])
# as the DP will not use every component it has access to
# unless it needs it, we shouldn't plot the redundant
# components.
if not np.any(Y_ == i):
continue
#pl.scatter(data[Y_== i, 0], data[Y_== i, 1], .8, color=color)
pl.scatter(X_r[Y_== i, 0], X_r[Y_== i, 1], .8, color=color)
# Plot an ellipse to show the Gaussian component
angle = np.arctan(u[1]/u[0])
angle = 180 * angle / np.pi # convert to degrees
ell = mpl.patches.Ellipse(mean, v[0], v[1], 180 + angle, color=color)
ell.set_clip_box(splot.bbox)
ell.set_alpha(0.5)
splot.add_artist(ell)
pl.xlim(X_r[:, 0].min(), X_r[:, 0].max())
pl.ylim(X_r[:, 1].min(), X_r[:, 1].max())
pl.xticks(())
pl.yticks(())
pl.title("Dirichlet process GMM")
pl.show()
def test_fastica(add_noise=False):
""" Test the FastICA algorithm on very simple data.
"""
# scipy.stats uses the global RNG:
rng = np.random.RandomState(0)
n_samples = 1000
# Generate two sources:
s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
s2 = stats.t.rvs(1, size=n_samples)
s = np.c_[s1, s2].T
center_and_norm(s)
s1, s2 = s
# Mixing angle
phi = 0.6
mixing = np.array([[np.cos(phi), np.sin(phi)], [np.sin(phi),
-np.cos(phi)]])
m = np.dot(mixing, s)
if add_noise:
m += 0.1 * rng.randn(2, 1000)
center_and_norm(m)
algos = ['parallel', 'deflation']
nls = ['logcosh', 'exp', 'cube']
whitening = [True, False]
for algo, nl, whiten in itertools.product(algos, nls, whitening):
if whiten:
k_, mixing_, s_ = fastica(m.T, fun=nl, algorithm=algo)
else:
X = PCA(n_components=2, whiten=True).fit_transform(m.T)
k_, mixing_, s_ = fastica(X, fun=nl, algorithm=algo, whiten=False)
s_ = s_.T
# Check that the mixing model described in the docstring holds:
if whiten:
assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
center_and_norm(s_)
s1_, s2_ = s_
# Check to see if the sources have been estimated
# in the wrong order
if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
s2_, s1_ = s_
s1_ *= np.sign(np.dot(s1_, s1))
s2_ *= np.sign(np.dot(s2_, s2))
# Check that we have estimated the original sources
if add_noise == False:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
else:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
# Test FastICA class
ica = FastICA(fun=nl, algorithm=algo, random_state=0)
ica.fit(m.T)
ica.get_mixing_matrix()
assert_true(ica.components_.shape == (2, 2))
assert_true(ica.sources_.shape == (1000, 2))
np.random.seed(0)
n_samples = 2000
time = np.linspace(0, 10, n_samples)
s1 = np.sin(2 * time) # Signal 1 : sinusoidal signal
s2 = np.sign(np.sin(3 * time)) # Signal 2 : square signal
S = np.c_[s1, s2]
S += 0.2 * np.random.normal(size=S.shape) # Add noise
S /= S.std(axis=0) # Standardize data
# Mix data
A = np.array([[1, 1], [0.5, 2]]) # Mixing matrix
X = np.dot(S, A.T) # Generate observations
# Compute ICA
ica = FastICA()
S_ = ica.fit(X).transform(X) # Get the estimated sources
A_ = ica.get_mixing_matrix() # Get estimated mixing matrix
assert np.allclose(X, np.dot(S_, A_.T))
###############################################################################
# Plot results
pl.figure()
pl.subplot(3, 1, 1)
pl.plot(S)
pl.title('True Sources')
pl.subplot(3, 1, 2)
pl.plot(X)
pl.title('Observations (mixed signal)')
pl.subplot(3, 1, 3)
pl.plot(S_)
pl.title('ICA estimated sources')
pl.subplots_adjust(0.09, 0.04, 0.94, 0.94, 0.26, 0.36)
# pl.quiver(x_axis, y_axis, x_axis, y_axis, zorder=11, width=0.01,
pl.quiver(0, 0, x_axis, y_axis, zorder=11, width=0.01, scale=6,
color=color)
pl.hlines(0, -3, 3)
pl.vlines(0, -3, 3)
pl.xlim(-3, 3)
pl.ylim(-3, 3)
pl.xlabel('x')
pl.ylabel('y')
pl.subplot(2, 2, 1)
plot_samples(S / S.std())
pl.title('True Independent Sources')
axis_list = [pca.components_.T, ica.get_mixing_matrix()]
pl.subplot(2, 2, 2)
plot_samples(X / np.std(X), axis_list=axis_list)
pl.legend(['PCA', 'ICA'], loc='upper left')
pl.title('Observations')
pl.subplot(2, 2, 3)
plot_samples(S_pca_ / np.std(S_pca_, axis=0))
pl.title('PCA scores')
pl.subplot(2, 2, 4)
plot_samples(S_ica_ / np.std(S_ica_))
pl.title('ICA estimated sources')
pl.subplots_adjust(0.09, 0.04, 0.94, 0.94, 0.26, 0.26)
def test_fastica(add_noise=False):
""" Test the FastICA algorithm on very simple data.
"""
# scipy.stats uses the global RNG:
rng = np.random.RandomState(0)
n_samples = 1000
# Generate two sources:
s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
s2 = stats.t.rvs(1, size=n_samples)
s = np.c_[s1, s2].T
center_and_norm(s)
s1, s2 = s
# Mixing angle
phi = 0.6
mixing = np.array([[np.cos(phi), np.sin(phi)],
[np.sin(phi), -np.cos(phi)]])
m = np.dot(mixing, s)
if add_noise:
m += 0.1 * rng.randn(2, 1000)
center_and_norm(m)
algos = ['parallel', 'deflation']
nls = ['logcosh', 'exp', 'cube']
whitening = [True, False]
for algo, nl, whiten in itertools.product(algos, nls, whitening):
if whiten:
k_, mixing_, s_ = fastica(m.T, fun=nl, algorithm=algo)
else:
X = PCA(n_components=2, whiten=True).fit_transform(m.T)
k_, mixing_, s_ = fastica(X, fun=nl, algorithm=algo,
whiten=False)
s_ = s_.T
# Check that the mixing model described in the docstring holds:
if whiten:
assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
center_and_norm(s_)
s1_, s2_ = s_
# Check to see if the sources have been estimated
# in the wrong order
if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
s2_, s1_ = s_
s1_ *= np.sign(np.dot(s1_, s1))
s2_ *= np.sign(np.dot(s2_, s2))
# Check that we have estimated the original sources
if add_noise == False:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
else:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
# Test FastICA class
ica = FastICA(fun=nl, algorithm=algo, random_state=0)
ica.fit(m.T)
ica.get_mixing_matrix()
assert_true(ica.components_.shape == (2, 2))
assert_true(ica.sources_.shape == (1000, 2))
def main(addNoise = 0, savedir = None, doFastICA = False):
N = 200
tt = linspace(0, 10, N)
# make sources
s1 = 4 + cos(tt*5)
s2 = tt % 2
s1 -= mean(s1)
s1 /= std(s1)
s2 -= mean(s2)
s2 /= std(s2)
pyplot.figure(1)
pyplot.subplot(4,1,1)
pyplot.title('original sources')
pyplot.plot(tt, s1, 'bo-')
pyplot.subplot(4,1,2)
pyplot.plot(tt, s2, 'bo-')
A = array([[3, 1], [-2, .3]])
S = vstack((s1, s2)).T
#print 'S', S
print 'kurt(s1) =', kurt(s1)
print 'kurt(s2) =', kurt(s2)
print ' negentropy(s1) =', negentropy(s1)
print ' negentropy(s2) =', negentropy(s2)
print ' logcosh10(s1) =', logcosh10(s1)
print ' logcosh10(s2) =', logcosh10(s2)
print ' logcosh15(s1) =', logcosh15(s1)
print ' logcosh15(s2) =', logcosh15(s2)
print ' logcosh20(s1) =', logcosh20(s1)
print ' logcosh20(s2) =', logcosh20(s2)
print ' negexp(s1) =', negexp(s1)
print ' negexp(s2) =', negexp(s2)
X = dot(S, A)
if addNoise > 0:
print 'Adding noise!'
X += random.normal(0, addNoise, X.shape)
#print 'X', X
x1 = X[:,0]
x2 = X[:,1]
#print 'kurt(x1) =', kurt(x1)
#print 'kurt(x2) =', kurt(x2)
pyplot.subplot(4,1,3)
pyplot.title('observed signal')
pyplot.plot(tt, x1, 'ro-')
pyplot.subplot(4,1,4)
pyplot.plot(tt, x2, 'ro-')
pyplot.figure(2)
pyplot.subplot(4,1,1)
pyplot.title('original sources')
pyplot.hist(s1)
pyplot.subplot(4,1,2)
pyplot.hist(s2)
pyplot.subplot(4,1,3)
pyplot.title('observed signal')
pyplot.hist(x1)
pyplot.subplot(4,1,4)
pyplot.hist(x2)
pca = PCA(X)
#W = pca.toWhitePC(X)
W = pca.toZca(X)
w1 = W[:,0]
w2 = W[:,1]
print 'kurt(w1) =', kurt(w1)
print 'kurt(w2) =', kurt(w2)
pyplot.figure(3)
pyplot.subplot(4,2,1)
pyplot.title('observed signal')
pyplot.hist(x1)
pyplot.subplot(4,2,3)
pyplot.hist(x2)
pyplot.subplot(2,2,2)
pyplot.plot(x1, x2, 'bo')
pyplot.subplot(4,2,5)
pyplot.title('whitened observed signal')
pyplot.hist(w1)
pyplot.subplot(4,2,7)
pyplot.hist(w2)
pyplot.subplot(2,2,4)
pyplot.plot(w1, w2, 'bo')
# Compute kurtosis at different angles
thetas = linspace(0, pi, 100)
kurt1 = 0 * thetas
for ii, theta in enumerate(thetas):
kurt1[ii] = kurt(dot(rotMat(theta)[0,:], W.T).T)
# functions of data
minfnK = lambda data: -kurt(data)**2
minfnNEnt = lambda data: -negentropy(data)
minfnLC10 = lambda data: -logcosh10(data)
minfnLC15 = lambda data: -logcosh15(data)
minfnLC20 = lambda data: -logcosh20(data)
minfnNExp = lambda data: -negexp(data)
# functions of the rotation angle, given W as the data
minAngleFnK = lambda theta: minfnK(dot(rotMat(theta)[0,:], W.T).T)
minAngleFnNEnt = lambda theta: minfnNEnt(dot(rotMat(theta)[0,:], W.T).T)
minAngleFnLC10 = lambda theta: minfnLC10(dot(rotMat(theta)[0,:], W.T).T)
minAngleFnLC15 = lambda theta: minfnLC15(dot(rotMat(theta)[0,:], W.T).T)
minAngleFnLC20 = lambda theta: minfnLC20(dot(rotMat(theta)[0,:], W.T).T)
minAngleFnNExp = lambda theta: minfnNExp(dot(rotMat(theta)[0,:], W.T).T)
#########
# Chosen objective function. Change this line to change which objective is used.
#########
minDataFn = minfnK
minAngleFn = lambda theta: minDataFn(dot(rotMat(theta)[0,:], W.T).T)
if doFastICA:
# Use FastICA from sklearn
#pdb.set_trace()
from sklearn.decomposition import FastICA
rng = random.RandomState(1)
ica = FastICA(random_state = rng, whiten = False)
ica.fit(W)
Recon = ica.transform(W) # Estimate the sources
#S_fica /= S_fica.std(axis=0) # (should already be done)
Ropt = ica.get_mixing_matrix()
else:
# Manually fit angle using fmin_bfgs
angle0 = 0
xopt = fmin_bfgs(minAngleFn, angle0)
xopt = xopt[0] % pi
Ropt = rotMat(xopt)
Recon = dot(W, Ropt.T)
mnval = array([minAngleFn(aa) for aa in thetas])
pyplot.figure(4)
pyplot.title('objective vs. angle')
#pyplot.plot(thetas, kurt1, 'bo-', thetas, mnval, 'k', xopt, minAngleFn(xopt), 'ko')
pyplot.plot(thetas, mnval, 'b')
if not doFastICA:
pyplot.hold(True)
pyplot.plot(xopt, minAngleFn(xopt), 'ko')
pyplot.figure(5)
pyplot.title('different gaussianness measures vs. angle')
pyplot.subplot(6,1,1); pyplot.title('Kurt'); pyplot.plot(thetas, array([minAngleFnK(aa) for aa in thetas]))
pyplot.subplot(6,1,2); pyplot.title('NegEnt'); pyplot.plot(thetas, array([minAngleFnNEnt(aa) for aa in thetas]))
pyplot.subplot(6,1,3); pyplot.title('LogCosh10'); pyplot.plot(thetas, array([minAngleFnLC10(aa) for aa in thetas]))
pyplot.subplot(6,1,4); pyplot.title('LogCosh15'); pyplot.plot(thetas, array([minAngleFnLC15(aa) for aa in thetas]))
pyplot.subplot(6,1,5); pyplot.title('LogCosh20'); pyplot.plot(thetas, array([minAngleFnLC20(aa) for aa in thetas]))
pyplot.subplot(6,1,6); pyplot.title('NegExp'); pyplot.plot(thetas, array([minAngleFnNExp(aa) for aa in thetas]))
print 'kurt(r1) =', kurt(Recon[:,0])
print 'kurt(r2) =', kurt(Recon[:,1])
print
print 'objective(s1) =', minDataFn(s1)
print 'objective(s2) =', minDataFn(s2)
print 'objective(w1) =', minDataFn(w1)
print 'objective(w2) =', minDataFn(w2)
print 'objective(r1) =', minDataFn(Recon[:,0])
print 'objective(r2) =', minDataFn(Recon[:,1])
print 'optimal theta:',
if doFastICA:
print '<not computed with FastICA>'
else:
print xopt, '(+pi/2 =', (xopt+pi/2)%pi, ')'
print 'Optimal rotation matrix:\n', Ropt
pyplot.figure(6)
pyplot.subplot(4,1,1)
pyplot.title('original sources')
pyplot.plot(tt, s1, 'bo-')
pyplot.subplot(4,1,2)
pyplot.plot(tt, s2, 'bo-')
pyplot.subplot(4,1,3)
pyplot.title('reconstructed sources')
pyplot.plot(tt, Recon[:,0], 'go-')
pyplot.subplot(4,1,4)
pyplot.plot(tt, Recon[:,1], 'go-')
#pyplot.show()
if savedir:
figname = lambda ii : os.path.join(savedir, 'figure_%02d.png' % ii)
for ii in range(6):
pyplot.figure(ii+1)
pyplot.savefig(figname(ii+1))
print 'plots saved in', savedir
else:
import ipdb; ipdb.set_trace()
def main(addNoise=0, savedir=None, doFastICA=False):
N = 200
tt = linspace(0, 10, N)
# make sources
s1 = 4 + cos(tt * 5)
s2 = tt % 2
s1 -= mean(s1)
s1 /= std(s1)
s2 -= mean(s2)
s2 /= std(s2)
pyplot.figure(1)
pyplot.subplot(4, 1, 1)
pyplot.title('original sources')
pyplot.plot(tt, s1, 'bo-')
pyplot.subplot(4, 1, 2)
pyplot.plot(tt, s2, 'bo-')
A = array([[3, 1], [-2, .3]])
S = vstack((s1, s2)).T
#print 'S', S
print 'kurt(s1) =', kurt(s1)
print 'kurt(s2) =', kurt(s2)
print ' negentropy(s1) =', negentropy(s1)
print ' negentropy(s2) =', negentropy(s2)
print ' logcosh10(s1) =', logcosh10(s1)
print ' logcosh10(s2) =', logcosh10(s2)
print ' logcosh15(s1) =', logcosh15(s1)
print ' logcosh15(s2) =', logcosh15(s2)
print ' logcosh20(s1) =', logcosh20(s1)
print ' logcosh20(s2) =', logcosh20(s2)
print ' negexp(s1) =', negexp(s1)
print ' negexp(s2) =', negexp(s2)
X = dot(S, A)
if addNoise > 0:
print 'Adding noise!'
X += random.normal(0, addNoise, X.shape)
#print 'X', X
x1 = X[:, 0]
x2 = X[:, 1]
#print 'kurt(x1) =', kurt(x1)
#print 'kurt(x2) =', kurt(x2)
pyplot.subplot(4, 1, 3)
pyplot.title('observed signal')
pyplot.plot(tt, x1, 'ro-')
pyplot.subplot(4, 1, 4)
pyplot.plot(tt, x2, 'ro-')
pyplot.figure(2)
pyplot.subplot(4, 1, 1)
pyplot.title('original sources')
pyplot.hist(s1)
pyplot.subplot(4, 1, 2)
pyplot.hist(s2)
pyplot.subplot(4, 1, 3)
pyplot.title('observed signal')
pyplot.hist(x1)
pyplot.subplot(4, 1, 4)
pyplot.hist(x2)
pca = PCA(X)
#W = pca.toWhitePC(X)
W = pca.toZca(X)
w1 = W[:, 0]
w2 = W[:, 1]
print 'kurt(w1) =', kurt(w1)
print 'kurt(w2) =', kurt(w2)
pyplot.figure(3)
pyplot.subplot(4, 2, 1)
pyplot.title('observed signal')
pyplot.hist(x1)
pyplot.subplot(4, 2, 3)
pyplot.hist(x2)
pyplot.subplot(2, 2, 2)
pyplot.plot(x1, x2, 'bo')
pyplot.subplot(4, 2, 5)
pyplot.title('whitened observed signal')
pyplot.hist(w1)
pyplot.subplot(4, 2, 7)
pyplot.hist(w2)
pyplot.subplot(2, 2, 4)
pyplot.plot(w1, w2, 'bo')
# Compute kurtosis at different angles
thetas = linspace(0, pi, 100)
kurt1 = 0 * thetas
for ii, theta in enumerate(thetas):
kurt1[ii] = kurt(dot(rotMat(theta)[0, :], W.T).T)
# functions of data
minfnK = lambda data: -kurt(data)**2
minfnNEnt = lambda data: -negentropy(data)
minfnLC10 = lambda data: -logcosh10(data)
minfnLC15 = lambda data: -logcosh15(data)
minfnLC20 = lambda data: -logcosh20(data)
minfnNExp = lambda data: -negexp(data)
# functions of the rotation angle, given W as the data
minAngleFnK = lambda theta: minfnK(dot(rotMat(theta)[0, :], W.T).T)
minAngleFnNEnt = lambda theta: minfnNEnt(dot(rotMat(theta)[0, :], W.T).T)
minAngleFnLC10 = lambda theta: minfnLC10(dot(rotMat(theta)[0, :], W.T).T)
minAngleFnLC15 = lambda theta: minfnLC15(dot(rotMat(theta)[0, :], W.T).T)
minAngleFnLC20 = lambda theta: minfnLC20(dot(rotMat(theta)[0, :], W.T).T)
minAngleFnNExp = lambda theta: minfnNExp(dot(rotMat(theta)[0, :], W.T).T)
#########
# Chosen objective function. Change this line to change which objective is used.
#########
minDataFn = minfnK
minAngleFn = lambda theta: minDataFn(dot(rotMat(theta)[0, :], W.T).T)
if doFastICA:
# Use FastICA from sklearn
#pdb.set_trace()
from sklearn.decomposition import FastICA
rng = random.RandomState(1)
ica = FastICA(random_state=rng, whiten=False)
ica.fit(W)
Recon = ica.transform(W) # Estimate the sources
#S_fica /= S_fica.std(axis=0) # (should already be done)
Ropt = ica.get_mixing_matrix()
else:
# Manually fit angle using fmin_bfgs
angle0 = 0
xopt = fmin_bfgs(minAngleFn, angle0)
xopt = xopt[0] % pi
Ropt = rotMat(xopt)
Recon = dot(W, Ropt.T)
mnval = array([minAngleFn(aa) for aa in thetas])
pyplot.figure(4)
pyplot.title('objective vs. angle')
#pyplot.plot(thetas, kurt1, 'bo-', thetas, mnval, 'k', xopt, minAngleFn(xopt), 'ko')
pyplot.plot(thetas, mnval, 'b')
if not doFastICA:
pyplot.hold(True)
pyplot.plot(xopt, minAngleFn(xopt), 'ko')
pyplot.figure(5)
pyplot.title('different gaussianness measures vs. angle')
pyplot.subplot(6, 1, 1)
pyplot.title('Kurt')
pyplot.plot(thetas, array([minAngleFnK(aa) for aa in thetas]))
pyplot.subplot(6, 1, 2)
pyplot.title('NegEnt')
pyplot.plot(thetas, array([minAngleFnNEnt(aa) for aa in thetas]))
pyplot.subplot(6, 1, 3)
pyplot.title('LogCosh10')
pyplot.plot(thetas, array([minAngleFnLC10(aa) for aa in thetas]))
pyplot.subplot(6, 1, 4)
pyplot.title('LogCosh15')
pyplot.plot(thetas, array([minAngleFnLC15(aa) for aa in thetas]))
pyplot.subplot(6, 1, 5)
pyplot.title('LogCosh20')
pyplot.plot(thetas, array([minAngleFnLC20(aa) for aa in thetas]))
pyplot.subplot(6, 1, 6)
pyplot.title('NegExp')
pyplot.plot(thetas, array([minAngleFnNExp(aa) for aa in thetas]))
print 'kurt(r1) =', kurt(Recon[:, 0])
print 'kurt(r2) =', kurt(Recon[:, 1])
print
print 'objective(s1) =', minDataFn(s1)
print 'objective(s2) =', minDataFn(s2)
print 'objective(w1) =', minDataFn(w1)
print 'objective(w2) =', minDataFn(w2)
print 'objective(r1) =', minDataFn(Recon[:, 0])
print 'objective(r2) =', minDataFn(Recon[:, 1])
print 'optimal theta:',
if doFastICA:
print '<not computed with FastICA>'
else:
print xopt, '(+pi/2 =', (xopt + pi / 2) % pi, ')'
print 'Optimal rotation matrix:\n', Ropt
pyplot.figure(6)
pyplot.subplot(4, 1, 1)
pyplot.title('original sources')
pyplot.plot(tt, s1, 'bo-')
pyplot.subplot(4, 1, 2)
pyplot.plot(tt, s2, 'bo-')
pyplot.subplot(4, 1, 3)
pyplot.title('reconstructed sources')
pyplot.plot(tt, Recon[:, 0], 'go-')
pyplot.subplot(4, 1, 4)
pyplot.plot(tt, Recon[:, 1], 'go-')
#pyplot.show()
if savedir:
figname = lambda ii: os.path.join(savedir, 'figure_%02d.png' % ii)
for ii in range(6):
pyplot.figure(ii + 1)
pyplot.savefig(figname(ii + 1))
print 'plots saved in', savedir
else:
import ipdb
ipdb.set_trace()