def test_whiteningnode():
line_x = numx.zeros((1000, 2), "d")
line_y = numx.zeros((1000, 2), "d")
line_x[:, 0] = numx.linspace(-1, 1, num=1000, endpoint=1)
line_y[:, 1] = numx.linspace(-0.2, 0.2, num=1000, endpoint=1)
mat = numx.concatenate((line_x, line_y))
utils.rotate(mat, uniform() * 2 * numx.pi)
mat += uniform(2)
mat -= mat.mean(axis=0)
pca = CCIPCAWhiteningNode()
for i in xrange(5):
pca.train(mat)
bpca = WhiteningNode()
bpca.train(mat)
bpca.stop_training()
v = pca.get_projmatrix()
bv = bpca.get_projmatrix()
dcosines = numx.zeros(v.shape[1])
for dim in xrange(v.shape[1]):
dcosines[dim] = numx.fabs(numx.dot(v[:, dim], bv[:, dim].T)) / (
numx.linalg.norm(v[:, dim]) * numx.linalg.norm(bv[:, dim]))
assert_almost_equal(numx.ones(v.shape[1]), dcosines)
def test_mcanode_v2():
iterval = 30
t = numx.linspace(0, 4 * numx.pi, 500)
x = numx.zeros([t.shape[0], 2])
x[:, 0] = numx.real(numx.sin(t) + numx.power(numx.cos(11 * t), 2))
x[:, 1] = numx.cos(11 * t)
expnode = PolynomialExpansionNode(2)
input_data = expnode(x)
input_data = input_data - input_data.mean(axis=0)
wtnnode = WhiteningNode()
input_data = wtnnode(input_data)
input_data = mdp.utils.timediff(input_data)
##Setup node/trainer
output_dim = 4
node = MCANode(output_dim=output_dim, eps=0.05)
bpcanode = PCANode()
bpcanode(input_data)
# bv = bpcanode.v / numx.linalg.norm(bpcanode.v, axis=0)
bv = bpcanode.v / mdp.numx.sum(bpcanode.v**2, axis=0)**0.5
bv = bv[:, ::-1][:, :output_dim]
_tcnt = time.time()
v = []
for i in xrange(iterval * input_data.shape[0]):
node.train(input_data[i % input_data.shape[0]:i % input_data.shape[0] +
1])
if (node.get_current_train_iteration() % 100 == 0):
v.append(node.v)
dcosines = numx.zeros([len(v), output_dim])
for i in xrange(len(v)):
for dim in xrange(output_dim):
dcosines[i,
dim] = numx.fabs(numx.dot(v[i][:, dim], bv[:, dim].T)) / (
numx.linalg.norm(v[i][:, dim]) *
numx.linalg.norm(bv[:, dim]))
print('\nTotal Time for {} iterations: {}'.format(iterval,
time.time() - _tcnt))
assert_almost_equal(numx.ones(output_dim), dcosines[-1], decimal=2)
def __init__(self, lags=1, sfa_ica_coeff=(1., 1.), icaweights=None,
sfaweights=None, whitened=False, white_comp = None,
white_parm = None, eps_contrast=1e-6, max_iter=10000,
RP=None, verbose=False, input_dim=None, output_dim=None,
dtype=None):
"""
Perform Independent Slow Feature Analysis.
The notation is the same used in the paper by Blaschke et al. Please
refer to the paper for more information.
:Parameters:
lags
list of time-lags to generate the time-delayed covariance
matrices (in the paper this is the set of \tau). If
lags is an integer, time-lags 1,2,...,'lags' are used.
Note that time-lag == 0 (instantaneous correlation) is
always implicitly used.
sfa_ica_coeff
a list of float with two entries, which defines the
weights of the SFA and ICA part of the objective
function. They are called b_{SFA} and b_{ICA} in the
paper.
sfaweights
weighting factors for the covariance matrices relative
to the SFA part of the objective function (called
\kappa_{SFA}^{\tau} in the paper). Default is
[1., 0., ..., 0.]
For possible values see the description of icaweights.
icaweights
weighting factors for the cov matrices relative
to the ICA part of the objective function (called
\kappa_{ICA}^{\tau} in the paper). Default is 1.
Possible values are:
- an integer ``n``: all matrices are weighted the same
(note that it does not make sense to have ``n != 1``)
- a list or array of floats of ``len == len(lags)``:
each element of the list is used for weighting the
corresponding matrix
- ``None``: use the default values.
whitened
``True`` if input data is already white, ``False``
otherwise (the data will be whitened internally).
white_comp
If whitened is false, you can set ``white_comp`` to the
number of whitened components to keep during the
calculation (i.e., the input dimensions are reduced to
``white_comp`` by keeping the components of largest variance).
white_parm
a dictionary with additional parameters for whitening.
It is passed directly to the WhiteningNode constructor.
Ex: white_parm = { 'svd' : True }
eps_contrast
Convergence is achieved when the relative
improvement in the contrast is below this threshold.
Values in the range [1E-4, 1E-10] are usually
reasonable.
max_iter
If the algorithms does not achieve convergence within
max_iter iterations raise an Exception. Should be
larger than 100.
RP
Starting rotation-permutation matrix. It is an
input_dim x input_dim matrix used to initially rotate the
input components. If not set, the identity matrix is used.
In the paper this is used to start the algorithm at the
SFA solution (which is often quite near to the optimum).
verbose
print progress information during convergence. This can
slow down the algorithm, but it's the only way to see
the rate of improvement and immediately spot if something
is going wrong.
output_dim
sets the number of independent components that have to
be extracted. Note that if this is not smaller than
input_dim, the problem is solved linearly and SFA
would give the same solution only much faster.
"""
# check that the "lags" argument has some meaningful value
if isinstance(lags, (int, int)):
lags = list(range(1, lags+1))
elif isinstance(lags, (list, tuple)):
lags = numx.array(lags, "i")
elif isinstance(lags, numx.ndarray):
if not (lags.dtype.char in ['i', 'l']):
err_str = "lags must be integer!"
raise NodeException(err_str)
else:
pass
else:
err_str = ("Lags must be int, list or array. Found "
"%s!" % (type(lags).__name__))
raise NodeException(err_str)
self.lags = lags
# sanity checks for weights
if icaweights is None:
self.icaweights = 1.
else:
if (len(icaweights) != len(lags)):
err = ("icaweights vector length is %d, "
"should be %d" % (str(len(icaweights)), str(len(lags))))
raise NodeException(err)
self.icaweights = icaweights
if sfaweights is None:
self.sfaweights = [0]*len(lags)
self.sfaweights[0] = 1.
else:
if (len(sfaweights) != len(lags)):
err = ("sfaweights vector length is %d, "
"should be %d" % (str(len(sfaweights)), str(len(lags))))
raise NodeException(err)
self.sfaweights = sfaweights
# store attributes
self.sfa_ica_coeff = sfa_ica_coeff
self.max_iter = max_iter
self.verbose = verbose
self.eps_contrast = eps_contrast
# if input is not white, insert a WhiteningNode
self.whitened = whitened
if not whitened:
if white_parm is None:
white_parm = {}
if output_dim is not None:
white_comp = output_dim
elif white_comp is not None:
output_dim = white_comp
self.white = WhiteningNode(input_dim=input_dim,
output_dim=white_comp,
dtype=dtype, **white_parm)
# initialize covariance matrices
self.covs = [ DelayCovarianceMatrix(dt, dtype=dtype) for dt in lags ]
# initialize the global rotation-permutation matrix
# if not set that we'll eventually be an identity matrix
self.RP = RP
# initialize verbose structure to print nice and useful progress info
if verbose:
info = { 'sweep' : max(len(str(self.max_iter)), 5),
'perturbe': max(len(str(self.max_iter)), 5),
'float' : 5+8,
'fmt' : "%.5e",
'sep' : " | "}
f1 = "Sweep".center(info['sweep'])
f1_2 = "Pertb". center(info['perturbe'])
f2 = "SFA part".center(info['float'])
f3 = "ICA part".center(info['float'])
f4 = "Contrast".center(info['float'])
header = info['sep'].join([f1, f1_2, f2, f3, f4])
info['header'] = header+'\n'
info['line'] = len(header)*"-"
self._info = info
# finally call base class constructor
super(ISFANode, self).__init__(input_dim, output_dim, dtype)
