import math
import mdp
from isfa_nodes import ISFANode
numx, numx_rand, numx_linalg = mdp.numx, mdp.numx_rand, mdp.numx_linalg
utils = mdp.utils
mult = utils.mult
class ProjectMatrixMixin(object):
"""Mixin class to be inherited by all ICA-like algorithms"""
def get_projmatrix(self, transposed=1):
"""Return the projection matrix."""
self._if_training_stop_training()
Q = self.filters.T
if not self.whitened:
W = self.white.get_projmatrix(transposed=0)
T = mult(Q, W)
else:
T = Q
if transposed:
return T.T
return T
def get_recmatrix(self, transposed=1):
"""Return the back-projection matrix (i.e. the reconstruction matrix).
Note that if the unknown sources are white, this is a good
approximation of the mixing matrix (up to a permutation matrix).
"""
self._if_training_stop_training()
Q = self.filters.T
if not self.whitened:
W = self.white.get_recmatrix(transposed=1)
T = mult(Q, W)
else:
T = Q
if transposed:
return T
return T.T
class ICANode(mdp.Cumulator, mdp.Node, ProjectMatrixMixin):
"""
ICANode is a general class to handle different batch-mode algorithm for
Independent Component Analysis. More information about ICA can be found
among others in
Hyvarinen A., Karhunen J., Oja E. (2001). Independent Component Analysis,
Wiley.
"""
def __init__(self, limit = 0.001, telescope = False, verbose = False,
whitened = False, white_comp = None, white_parm = None,
input_dim = None, dtype = None):
"""
Input arguments:
whitened -- Set whitened is True if input data are already whitened.
Otherwise the node will whiten the data itself.
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 }
limit -- convergence threshold.
telescope -- If telescope == True, use Telescope mode: Instead of
using all input data in a single batch try larger and larger chunks
of the input data until convergence is achieved. This should lead to
significantly faster convergence for stationary statistics. This mode
has not been thoroughly tested and must be considered beta.
"""
self.telescope = telescope
self.verbose = verbose
self.limit = limit
self.whitened = whitened
self.white_comp = white_comp
if white_parm is None:
self.white_parm = {}
else:
self.white_parm = white_parm
super(ICANode, self).__init__(input_dim, None, dtype)
def _set_input_dim(self, n):
self._input_dim = n
if self.whitened:
self.output_dim = n
elif self.white_comp is None:
self.output_dim = n
def _get_supported_dtypes(self):
"""Return the list of dtypes supported by this node."""
return ['float32', 'float64']
def _stop_training(self):
"""Whiten data if needed and call the 'core' routine to perform ICA.
Take care of telescope-mode if needed.
"""
super(ICANode, self)._stop_training()
verbose = self.verbose
core = self.core
limit = self.limit
# ?? rewrite as a 2-phases node
# whiten if needed
if not self.whitened:
self.output_dim = self.white_comp
white = mdp.nodes.WhiteningNode(output_dim = self.white_comp,
dtype=self.dtype,
**self.white_parm)
white.train(self.data)
self.data = white.execute(self.data)
self.white = white
# if output_dim not set, set it now
if self.output_dim is None:
self.output_dim = self.input_dim
data = self.data
# call 'core' in telescope mode if needed
if self.telescope:
minpow = math.frexp(self.input_dim*10)[1]
maxpow = int(numx.log(data.shape[0])/numx.log(2))
for tel in range(minpow, maxpow+1):
index = 2**tel
if verbose:
print "--\nUsing %d inputs" % index
convergence = core(data[:index, :])
if convergence <= limit:
break
else:
convergence = core(data)
if verbose:
print "Convergence criterium: ", convergence
self.convergence = convergence
def core(self, data):
"""This is the core routine of the ICANode. Each subclass must
define this function to return the achieved convergence value.
This function is also responsible for setting the ICA filters
matrix self.filters.
Note that the matrix self.filters is applied to the right of the
matrix containing input data. This is the transposed of the matrix
defining the linear transformation."""
pass
def _execute(self, x):
if not self.whitened:
x = self.white.execute(x)
# self.filters is applied to the right of the
# matrix containing input data. This is the transposed of the matrix
# defining the linear transformation.
return mult(x, self.filters)
def _inverse(self, y):
y = mult(y, self.filters.T)
if not self.whitened:
y = self.white.inverse(y)
return y
class CuBICANode(ICANode):
"""
Perform Independent Component Analysis using the CuBICA algorithm.
Note that CuBICA is a batch-algorithm, which means that it needs
all input data before it can start and compute the ICs. The
algorithm is here given as a Node for convenience, but it actually
accumulates all inputs it receives. Remember that to avoid running
out of memory when you have many components and many time samples.
As an alternative to this batch mode you might consider the telescope
mode (see the docs of the __init__ function).
Reference:
Blaschke, T. and Wiskott, L. (2003).
CuBICA: Independent Component Analysis by Simultaneous Third- and
Fourth-Order Cumulant Diagonalization.
IEEE Transactions on Signal Processing, 52(5), pp. 1250-1256.
Internal variables of interest:
self.white -- the whitening node used for preprocessing.
self.filters -- the ICA filters matrix (this is the transposed of the
projection matrix after whitening).
self.convergence -- the value of the convergence threshold.
"""
def core(self, data):
# keep track of maximum angle of rotation
# angles vary in the range [-pi, +pi]
# put here -2pi < -pi < +pi
self.maxangle = [-2*numx.pi]
verbose = self.verbose
telescope = self.telescope
# we need to copy to avoid overwriting during rotation.
x = data.copy()
# convergence criterium == maxangle
limit = self.limit
comp = x.shape[1]
tlen = x.shape[0]
# some constants
ct_c34 = 0.0625
ct_s34 = 0.25
ct_c44 = 1./384
ct_s44 = 1./96
# initial transposed rotation matrix == identity matrix
Qt = numx.identity(comp, dtype=self.dtype)
# maximum number of sweeps through all possible pairs of signals
num = int(1+round(numx.sqrt(comp)))
count = 0
# start sweeping
for k in range(num):
maxangle = 0
for i in range(comp - 1):
for j in range(i+1, comp):
u1 = x[:, i]
u2 = x[:, j]
sq1 = x[:, i]*x[:, i]
sq2 = x[:, j]*x[:, j]
# calculate the cumulants of 3rd and 4th order.
C111 = mult(sq1, u1)/tlen
C112 = mult(sq1, u2)/tlen
C122 = mult(sq2, u1)/tlen
C222 = mult(sq2, u2)/tlen
C1111 = mult(sq1, sq1)/tlen - 3.
C1112 = mult(sq1*u1, u2)/tlen
C1122 = mult(sq1, sq2)/tlen - 1.
C1222 = mult(sq2*u2, u1)/tlen
C2222 = mult(sq2, sq2)/tlen - 3.
c_34 = ct_c34 * ( (C111*C111+C222*C222)-
3.*(C112*C112+C122*C122)-
2.*(C111*C122+C112*C222) )
s_34 = ct_s34 * ( C111*C112-C122*C222 )
c_44 = ct_c44 *( 7.*(C1111*C1111+C2222*C2222)-
16.*(C1112*C1112+C1222*C1222)-
12.*(C1111*C1122+C1122*C2222)-
36.*(C1122*C1122)-
32.*(C1112*C1222)-
2.*(C1111*C2222) )
s_44 = ct_s44 *( 7.*(C1111*C1112-C1222*C2222)+
6.*(C1112*C1122-C1122*C1222)+
(C1111*C1222-C1112*C2222) )
# rotation angle that maximize the contrast function
phi_max = -0.25 * numx.arctan2(s_34+s_44, c_34+c_44)
# get the new rotation matrix.
# Using the function rotate with angle 'phi' on
# a transformation matrix corresponds to the
# right-multiplication by a rotation matrix
# with angle '-phi'.
utils.rotate(Qt, phi_max, [i, j])
# rotate input data
utils.rotate(x, phi_max, [i, j])
# keep track of maximum angle of rotation
maxangle = max(maxangle, abs(float(phi_max)))
count += 1
self.maxangle.append(maxangle)
if maxangle <= limit:
break
self.iter = k
if verbose:
print "\nSweeps: ", k
self.filters = Qt
# return the convergence criterium
return maxangle
class FastICANode(ICANode):
"""
Perform Independent Component Analysis using the FastICA algorithm.
Note that FastICA is a batch-algorithm. This means that it needs
all input data before it can start and compute the ICs.
The algorithm is here given as a Node for convenience, but it
actually accumulates all inputs it receives. Remember that to avoid
running out of memory when you have many components and many time samples.
FastICA does not support the telescope mode (the convergence
criterium is not robust in telescope mode).
Reference:
Aapo Hyvarinen (1999).
Fast and Robust Fixed-Point Algorithms for Independent Component Analysis
IEEE Transactions on Neural Networks, 10(3):626-634.
Internal variables of interest:
self.white -- the whitening node used for preprocessing.
self.filters -- the ICA filters matrix (this is the transposed of the
projection matrix after whitening).
self.convergence -- the value of the convergence threshold.
History:
- 1.4.1998 created for Matlab by Jarmo Hurri, Hugo Gavert,
Jaakko Sarela, and Aapo Hyvarinen
- 7.3.2003 modified for Python by Thomas Wendler
- 3.6.2004 rewritten and adapted for scipy and MDP by MDP's authors
- 25.5.2005 now independent from scipy. Requires Numeric or numarray
- 26.6.2006 converted to numpy
- 14.9.2007 updated to Matlab version 2.5
"""
def __init__(self, approach = 'defl', g = 'pow3', guess = None,
fine_g = 'pow3', mu = 1, stabilization = False,
sample_size = 1, fine_tanh = 1, fine_gaus = 1,
max_it = 1000, max_it_fine = 100,
failures = 5, limit = 0.001, verbose = False,
whitened = False, white_comp = None, white_parm = None,
input_dim = None, dtype=None):
"""
Input arguments:
General:
whitened -- Set whitened == True if input data are already whitened.
Otherwise the node will whiten the data itself
white_comp -- If whitened == 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 }
limit -- convergence threshold.
Specific for FastICA:
approach -- Approach to use. Possible values are:
'defl' --> deflation
'symm' --> symmetric
g -- Nonlinearity to use. Possible values are:
'pow3' --> x^3
'tanh' --> tanh(fine_tanh*x)
'gaus' --> x*exp(-fine_gaus*x^2/2)
'skew' --> x^2 (for skewed signals)
fine_g -- Nonlinearity for fine tuning. Possible values
are the same as for 'g'. Set it to None to disable fine
tuning.
mu -- Step size
stabilization -- Enable stabilization procedure: the value of mu can
momentarily be halved if the algorithm is stuck between
two points (this is called a stroke). Also if there is no
convergence before half of the maximum number of
iterations has been reached then mu will be halved for
the rest of the rounds.
sample_size -- Percentage of samples used in one iteration. If
sample_size < 1, samples are chosen in random order.
fine_tanh -- parameter for 'tanh' nonlinearity
fine_gaus -- parameter for 'gaus' nonlinearity
guess -- initial guess for the mixing matrix (ignored if None)
max_it -- maximum number of iterations
max_it_fine -- maximum number of iterations for fine tuning
failures -- maximum number of failures to allow in deflation mode
"""
super(FastICANode, self).__init__(limit, False, verbose, whitened,
white_comp, white_parm, input_dim,
dtype)
if approach in ['defl', 'symm']:
self.approach = approach
else:
raise mdp.NodeException('%s approach method not known' % approach)
if g in ['pow3', 'tanh', 'gaus', 'skew']:
self.g = g
else:
raise mdp.NodeException('%s nonlinearity function not known' % g)
if fine_g in ['pow3', 'tanh', 'gaus', 'skew', None]:
self.fine_g = fine_g
else:
errmsg = '%s nonlinearity function not known' % fine_g
raise mdp.NodeException(errmsg)
if sample_size > 0 and sample_size <= 1:
self.sample_size = sample_size
else:
raise mdp.NodeException('0<sample_size<1, %f given' % sample_size)
self.mu = mu
if mu != 1:
self.stabilization = True
else:
self.stabilization = False
self.fine_tanh = fine_tanh
self.fine_gaus = fine_gaus
self.max_it = max_it
self.max_it_fine = max_it_fine
self.failures = failures
self.guess = guess
def _get_rsamples(self, X):
tlen = X.shape[1]
comp = X.shape[0]
mask = numx.where(numx_rand.random(tlen) < self.sample_size)[0]
return X[:, mask]
def core(self, data):
# this is a more or less line per line translation of the original
# matlab code.
# Everything could be done better and more efficiently.
# I just had no time at the moment to do it.
# The logic behind the used_g hell is beyond my understanding :-)))
X = data.T
# casted constants
comp = X.shape[0]
tlen = X.shape[1]
dtype = self.dtype
# Default values and initial definitions
fine_tanh = self.fine_tanh
fine_gaus = self.fine_gaus
approach = self.approach
g = self.g
fine_g = self.fine_g
stabilization = self.stabilization
mu = self.mu
sample_size = self.sample_size
if self.guess is None:
# Take random orthonormal initial vectors.
guess = utils.random_rot(comp, dtype)
else:
# Use user supplied mixing matrix
guess = self._refcast(self.guess)
if not self.whitened:
guess = mult(guess, self.white.get_recmatrix(transposed=1))
limit = self.limit
max_it = self.max_it
max_it_fine = self.max_it_fine
failures = self.failures
verbose = self.verbose
# set non linearities. don't blame me for the awful logic: it comes
# from the matlab program. I didn't dare to understand it and change
# it.
if g == 'pow3':
gOrig = 10
elif g == 'tanh':
gOrig = 20
elif g == 'gaus':
gOrig = 30
else:
gOrig = 40
if sample_size != 1:
gOrig += 2
if mu != 1:
gOrig += 1
fine_tuning = True
if fine_g == 'pow3':
gFine = 11
elif fine_g == 'tanh':
gFine = 21
elif fine_g == 'gaus':
gFine = 31
elif fine_g == 'skew':
gFine = 41
else:
if mu == 1:
gFine = gOrig + 1
else:
stabilization = True
gFine = gOrig
fine_tuning = False
muK = 0.01
used_g = gOrig
stroke = 0
fine_tuned = False
lng = False
# SYMMETRIC APPROACH
if approach == 'symm':
# create list to store convergence
convergence = []
convergence_fine = []
# orthonormal initial vectors.
Q = guess
QOld = numx.zeros(Q.shape, dtype)
QOldF = numx.zeros(Q.shape, dtype)
# This is the actual fixed-point iteration loop.
for round in range(max_it + 1):
if round == max_it:
errstr = 'No convergence after %d steps\n' % max_it
raise mdp.NodeException(errstr)
# Symmetric orthogonalization. Q = Q * real(inv(Q' * Q)^(1/2));
Q = mult(Q, utils.sqrtm(utils.inv(mult(Q.T, Q))))
# Test for termination condition. Note that we consider
# opposite directions here as well.
v1 = 1.-abs((mult(Q.T, QOld)).diagonal()).min(axis=0)
convergence.append(v1)
v2 = 1.-abs((mult(Q.T, QOldF)).diagonal()).min(axis=0)
convergence_fine.append(v2)
if convergence[round] < limit:
if fine_tuning and (not fine_tuned):
if verbose:
print 'Initial convergence, fine-tuning...'
fine_tuned = True
used_g = gFine
mu = muK * self.mu
QOld = numx.zeros(Q.shape, dtype)
QoldF = numx.zeros(Q.shape, dtype)
else:
if verbose:
print 'Convergence after %d steps\n' % round
break
if stabilization:
if (stroke != 0) and (convergence_fine[round] < limit):
if verbose:
print 'Stroke!\n'
stroke = mu
mu = 0.5*mu
if used_g % 2 == 0:
used_g += 1
elif (stroke != 0):
mu = stroke
stroke = 0
if (mu == 1) and (used_g % 2 != 0):
used_g -= 1
elif (not lng) and (round > max_it//2):
if verbose:
print 'Taking long (reducing step size)...'
lng = True
mu = 0.5*mu
if used_g % 2 == 0:
used_g += 1
QOldF = QOld
QOld = Q
# Show the progress...
if verbose:
msg = ('Step no. %d,'
' convergence: %.3f' % (round+1,convergence[round]))
print msg
# First calculate the independent components (u_i's).
# u_i = b_i' x = x' b_i. For all x:s simultaneously this is
# non linearity
if used_g == 10:
u = mult(X.T, Q)
Q = mult(X, u*u*u)/tlen - 3.*Q
elif used_g == 11:
u = mult(X.T, Q)
Gpow3 = u*u*u
Beta = (u*Gpow3).sum(axis=0)
D = numx.diag((1/(Beta - 3*tlen)))
Q = Q + mu * mult(Q, mult((mult(u.T, Gpow3) -
numx.diag(Beta)), D))
elif used_g == 12:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
Q = mult(Xsub, u*u*u)/Xsub.shape[1] - 3.*Q
elif used_g == 13:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
Gpow3 = u*u*u
Beta = (u*Gpow3).sum(axis=0)
D = numx.diag((1/(Beta - 3*Xsub.shape[1])))
Q = Q + mu * mult(Q, mult((mult(u.T, Gpow3) -
numx.diag(Beta)), D))
elif used_g == 20:
u = mult(X.T, Q)
tang = numx.tanh(fine_tanh * u)
temp = (1.-tang*tang).sum(axis=0)/tlen
Q = mult(X, tang)/tlen - temp * Q * fine_tanh
elif used_g == 21:
u = mult(X.T, Q)
tang = numx.tanh(fine_tanh * u)
Beta = (u*tang).sum(axis=0)
D = numx.diag(1/(Beta -
fine_tanh*(1.-tang*tang).sum(axis=0)))
Q = Q + mu * mult(Q,
mult((mult(u.T, tang)-
numx.diag(Beta)), D))
elif used_g == 22:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
tang = numx.tanh(fine_tanh * u)
temp = (1.-tang*tang).sum(axis=0)/Xsub.shape[1]
Q = mult(Xsub, tang)/Xsub.shape[1] - temp * Q * fine_tanh
elif used_g == 23:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
tang = numx.tanh(fine_tanh * u)
Beta = (u*tang).sum(axis=0)
D = numx.diag(1/(Beta -
fine_tanh*(1.-tang*tang).sum(axis=0)))
Q = Q + mu * mult(Q,
mult((mult(u.T, tang)-
numx.diag(Beta)), D))
elif used_g == 30:
u = mult(X.T, Q)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gauss = u*ex
dgauss = (1. - fine_gaus*u2)*ex
Q = (mult(X, gauss)-dgauss.sum(axis=0)*Q)/tlen
elif used_g == 31:
u = mult(X.T, Q)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gaus = u*ex
Beta = (u*gaus).sum(axis=0)
D = numx.diag(1/(Beta -
((1-fine_gaus*u2)*ex).sum(axis=0)))
Q = Q + mu * mult(Q,
mult((mult(u.T, gaus)-
numx.diag(Beta)), D))
elif used_g == 32:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gauss = u*ex
dgauss = (1. - fine_gaus*u2)*ex
Q = (mult(Xsub, gauss)-dgauss.sum(axis=0)*Q)/Xsub.shape[1]
elif used_g == 33:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gaus = u*ex
Beta = (u*gaus).sum(axis=0)
D = numx.diag(1/(Beta -
((1-fine_gaus*u2)*ex).sum(axis=0)))
Q = Q + mu * mult(Q, mult((mult(u.T, gaus)-
numx.diag(Beta)), D))
elif used_g == 40:
u = mult(X.T, Q)
Q = mult(X, u*u)/tlen
elif used_g == 41:
u = mult(X.T, Q)
Gskew = u*u
Beta = (u*Gskew).sum(axis=0)
D = numx.diag(1/Beta)
Q = Q + mu * mult(Q, mult((mult(u.T, Gskew)-
numx.diag(Beta)), D))
elif used_g == 42:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
Q = mult(Xsub, u*u)/Xsub.shape[1]
elif used_g == 43:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, Q)
Gskew = u*u
Beta = (u*Gskew).sum(axis=0)
D = numx.diag(1/Beta)
Q = Q + mu * mult(Q, mult((mult(u.T, Gskew)-
numx.diag(Beta)), D))
else:
errstr = 'Nonlinearity not found: %i' % used_g
raise mdp.NodeException(errstr)
self.convergence = numx.array(convergence)
self.convergence_fine = numx.array(convergence_fine)
ret = convergence[-1]
# DEFLATION APPROACH
elif approach == 'defl':
# adjust limit!
#limit = 1 - limit*limit*0.5
# create array to store convergence
convergence = []
convergence_fine = []
Q = numx.zeros((comp, comp), dtype=dtype)
round = 0
nfail = 0
while round < comp:
mu = self.mu
used_g = gOrig
stroke = 0
fine_tuned = False
lng = False
end_finetuning = 0
# Take a random initial vector of lenght 1 and orthogonalize it
# with respect to the other vectors.
w = guess[:, round]
w -= mult(mult(Q, Q.T), w)
w /= utils.norm2(w)
wOld = numx.zeros(w.shape, dtype)
wOldF = numx.zeros(w.shape, dtype)
# This is the actual fixed-point iteration loop.
i = 1
gabba = 1
#for i in range(max_it + 1):
while i <= max_it + gabba:
# Project the vector into the space orthogonal to the space
# spanned by the earlier found basis vectors. Note that
# we can do the projection with matrix Q, since the zero
# entries do not contribute to the projection.
w -= mult(mult(Q, Q.T), w)
w /= utils.norm2(w)
if not fine_tuned:
if i == max_it + 1:
err_msg = ('Component number %d did not'
'converge in %d iterations.' % (round,
max_it))
if verbose:
print err_msg
if round == 0:
raise mdp.NodeException(err_msg)
nfail += 1
if nfail > failures:
err = ('Too many failures to '
'converge (%d). Giving up.' % nfail)
raise mdp.NodeException(err)
break
else:
if i >= end_finetuning:
wOld = w
# Test for termination condition. Note that the algorithm
# has converged if the direction of w and wOld is the same.
#conv = float(abs((w*wOld).sum()))
conv = min(utils.norm2(w-wOld), utils.norm2(w+wOld))
convergence.append(conv)
if conv < limit:
if fine_tuning and (not fine_tuned):
if verbose:
print 'Initial convergence, fine-tuning...'
fine_tuned = True
gabba = max_it_fine
wOld = numx.zeros(w.shape, dtype)
wOldF = numx.zeros(w.shape, dtype)
used_g = gFine
mu *= self.mu
end_finetuning = max_it_fine + i
else:
nfail = 0
convergence[round] = conv
# Calculate ICA filter.
Q[:, round] = w.copy()
# Show the progress...
if verbose:
print 'IC %d computed ( %d steps )' % (round+1,
i+1)
break
elif stabilization:
conv_fine = min(utils.norm2(w-wOldF),
utils.norm2(w+wOldF))
convergence_fine.append(conv_fine)
if (stroke != 0) and conv_fine < limit:
if verbose:
print 'Stroke!'
stroke = mu
mu = 0.5*mu
if used_g % 2 == 0:
used_g += 1
elif (stroke != 0):
mu = stroke
stroke = 0
if (mu == 1) and (used_g % 2 != 0):
used_g -= 1
elif (not lng) and (round > max_it//2):
if verbose:
print 'Taking long (reducing step size)...'
lng = True
mu = 0.5*mu
if used_g % 2 == 0:
used_g += 1
wOldF = wOld
wOld = w
if used_g == 10:
u = mult(X.T, w)
w = mult(X, u*u*u)/tlen - 3.*w
elif used_g == 11:
u = mult(X.T, w)
EXGpow3 = mult(X, u*u*u)/tlen
Beta = mult(w.T, EXGpow3)
w = w - mu * (EXGpow3 - Beta*w)/(3-Beta)
elif used_g == 12:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
w = mult(Xsub, u*u*u)/Xsub.shape[1] - 3.*w
elif used_g == 13:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
EXGpow3 = mult(Xsub, u*u*u)/Xsub.shape[1]
Beta = mult(w.T, EXGpow3)
w = w - mu * (EXGpow3 - Beta*w)/(3-Beta)
elif used_g == 20:
u = mult(X.T, w)
tang = numx.tanh(fine_tanh * u)
temp = mult((1. - tang*tang).sum(axis=0), w)
w = (mult(X, tang) - fine_tanh*temp)/tlen
elif used_g == 21:
u = mult(X.T, w)
tang = numx.tanh(fine_tanh * u)
Beta = mult(u.T, tang)
temp = (1. - tang*tang).sum(axis=0)
w = w-mu*((mult(X, tang)-Beta*w)/(fine_tanh*temp-Beta))
elif used_g == 22:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
tang = numx.tanh(fine_tanh * u)
temp = mult((1. - tang*tang).sum(axis=0), w)
w = (mult(Xsub, tang) - fine_tanh*temp)/Xsub.shape[1]
elif used_g == 23:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
tang = numx.tanh(fine_tanh * u)
Beta = mult(u.T, tang)
w = w - mu * ((mult(Xsub, tang)-Beta*w) /
(fine_tanh*(1. - tang*tang).sum(axis=0) -
Beta))
elif used_g == 30:
u = mult(X.T, w)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gauss = u*ex
dgauss = (1. - fine_gaus *u2)*ex
w = (mult(X, gauss)-mult(dgauss.sum(axis=0), w))/tlen
elif used_g == 31:
u = mult(X.T, w)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gauss = u*ex
dgauss = (1. - fine_gaus *u2)*ex
Beta = mult(u.T, gauss)
w = w - mu*((mult(X, gauss)-Beta*w)/
(dgauss.sum(axis=0)-Beta))
elif used_g == 32:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gauss = u*ex
dgauss = (1. - fine_gaus *u2)*ex
w = (mult(Xsub, gauss)-
mult(dgauss.sum(axis=0), w))/Xsub.shape[1]
elif used_g == 33:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
u2 = u*u
ex = numx.exp(-fine_gaus*u2*0.5)
gauss = u*ex
dgauss = (1. - fine_gaus *u2)*ex
Beta = mult(u.T, gauss)
w = w - mu*((mult(Xsub, gauss)-Beta*w)/
(dgauss.sum(axis=0)-Beta))
elif used_g == 40:
u = mult(X.T, w)
w = mult(X, u*u)/tlen
elif used_g == 41:
u = mult(X.T, w)
EXGskew = mult(X, u*u) / tlen
Beta = mult(w.T, EXGskew)
w = w - mu * (EXGskew - mult(Beta, w))/(-Beta)
elif used_g == 42:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
w = mult(Xsub, u*u)/Xsub.shape[1]
elif used_g == 43:
Xsub = self._get_rsamples(X)
u = mult(Xsub.T, w)
EXGskew = mult(Xsub, u*u) / Xsub.shape[1]
Beta = mult(w.T, EXGskew)
w = w - mu * (EXGskew - Beta*w)/(-Beta)
else:
errstr = 'Nonlinearity not found: %i' % used_g
raise mdp.NodeException(errstr)
# Normalize the new w.
w /= utils.norm2(w)
i += 1
round += 1
self.convergence = numx.array(convergence)
self.convergence_fine = numx.array(convergence_fine)
ret = convergence[-1]
self.filters = Q
return ret
class TDSEPNode(ISFANode, ProjectMatrixMixin):
"""Perform Independent Component Analysis using the TDSEP algorithm.
Note that TDSEP, as implemented in this Node, is an online algorithm,
i.e. it is suited to be trained on huge data sets, provided that the
training is done sending small chunks of data for each time.
Reference:
Ziehe, Andreas and Muller, Klaus-Robert (1998).
TDSEP an efficient algorithm for blind separation using time structure
in Niklasson, L, Boden, M, and Ziemke, T (Editors), Proc. 8th Int. Conf.
Artificial Neural Networks (ICANN 1998).
Internal variables of interest:
self.white -- the whitening node used for preprocessing.
self.filters -- the ICA filters matrix (this is the transposed of the
projection matrix after whitening).
self.convergence -- the value of the convergence threshold.
"""
def __init__(self, lags=1, limit = 0.00001, max_iter=10000,
verbose = False, whitened = False, white_comp = None,
white_parm = None, input_dim = None, dtype = None):
"""
Input arguments:
lags -- list of time-lags to generate the time-delayed covariance
matrices. If lags is an integer, time-lags 1,2,...,'lags'
are used.
Note that time-lag == 0 (instantaneous correlation) is
always implicitly used.
whitened -- Set whitened is True if input data are already whitened.
Otherwise the node will whiten the data itself.
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 }
limit -- convergence threshold.
max_iter -- If the algorithms does not achieve convergence within
max_iter iterations raise an Exception. Should be
larger than 100.
"""
super(TDSEPNode, self).__init__(lags=lags, sfa_ica_coeff=(0., 1.),
icaweights=None, sfaweights=None,
whitened=whitened,
white_comp=white_comp,
white_parm = None,
eps_contrast=limit,
max_iter=max_iter, RP=None,
verbose=verbose,
input_dim=input_dim,
output_dim=None,
dtype=dtype)
def _stop_training(self, covs=None):
super(TDSEPNode, self)._stop_training(covs)
# set filters
self.filters = self.RP
# set convergence
self.convergence = self.final_contrast
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