def stereo_NMF(SXR,
SXL,
numberOfAccompanimentSpectralShapes,
WM0=None,
HM0=None,
numberOfIterations=50,
updateRulePower=1.0,
verbose=False,
displayEvolution=False):
eps = 10**(-20)
if displayEvolution:
import matplotlib.pyplot as plt
from matplotlib.pyplot import imshow as imageM
plt.ion()
print "Is the display interactive? ", plt.isinteractive()
R = numberOfAccompanimentSpectralShapes
omega = updateRulePower
F, N = SXR.shape
if (F, N) != SXL.shape:
print "The input STFT matrices do not have the same dimension.\n"
print "Please check what happened..."
raise ValueError("Dimension of STFT matrices must be the same.")
if HM0 is None:
HM0 = np.abs(randn(R, N))
else:
if np.array(HM0).shape[0] == R and np.array(HM0).shape[1] == N:
HM0 = np.array(HM0)
else:
print "Wrong dimensions for given HM0, \n"
print "random initialization used instead"
HM0 = np.abs(randn(R, N))
HM = np.copy(HM0)
if WM0 is None:
WM0 = np.abs(randn(F, R))
else:
if np.array(WM0).shape[0] == F and np.array(WM0).shape[1] == R:
WM0 = np.array(WM0)
else:
print "Wrong dimensions for given WM0, \n"
print "random initialization used instead"
WM0 = np.abs(randn(F, R))
WM = np.copy(WM0)
betaR = np.diag(np.random.rand(R))
betaL = np.eye(R) - betaR
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
# temporary matrices
tempNumFbyN = np.zeros([F, N])
tempDenFbyN = np.zeros([F, N])
recoError = np.zeros([numberOfIterations * 3 + 1])
recoError[0] = ISDistortion(SXR, hatSXR) + ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error at beginning: ", recoError[0]
counterError = 1
if displayEvolution:
h1 = plt.figure(1)
for n in np.arange(numberOfIterations):
# order of re-estimation: HF0, HPHI, HM, HGAMMA, WM
if verbose:
print "iteration ", n, " over ", numberOfIterations
if displayEvolution:
h1.clf()
imageM(db(hatSXR))
plt.clim([np.amax(db(hatSXR)) - 100, np.amax(db(hatSXR))])
plt.draw()
# updating HM
HM = HM * \
((np.dot(np.dot((betaR**2), WM.T), SXR /
np.maximum(hatSXR ** 2, eps)) +
np.dot(np.dot((betaL**2), WM.T), SXL /
np.maximum(hatSXL ** 2, eps))
) /
np.maximum(np.dot(np.dot((betaR**2), WM.T), 1 /
np.maximum(hatSXR, eps)) +
np.dot(np.dot((betaL**2), WM.T), 1 /
np.maximum(hatSXL, eps)),
eps)) ** omega
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after HM : ",\
recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating WM
WM = WM * \
((np.dot(SXR / np.maximum(hatSXR ** 2, eps),
np.dot(HM.T, betaR ** 2)) +
np.dot(SXL / np.maximum(hatSXL ** 2, eps),
np.dot(HM.T, betaL ** 2))
) /
(np.dot(1 / np.maximum(hatSXR, eps),
np.dot(HM.T, betaR ** 2)) +
np.dot(1 / np.maximum(hatSXL, eps),
np.dot(HM.T, betaL ** 2))
)) ** omega
sumWM = np.sum(WM, axis=0)
WM[:, sumWM > 0] = (WM[:, sumWM > 0] /
np.outer(np.ones(F), sumWM[sumWM > 0]))
HM = HM * np.outer(sumWM, np.ones(N))
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after WM : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating betaR and betaL
betaR = np.diag(
np.diag(
np.maximum(
betaR *
((np.dot(np.dot(WM.T, SXR / np.maximum(hatSXR**2, eps)),
HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXR, eps)), HM.T)))
**(omega * .1), eps)))
betaL = np.diag(
np.diag(
np.maximum(
betaL *
((np.dot(np.dot(WM.T, SXL / np.maximum(hatSXL**2, eps)),
HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXL, eps)), HM.T)))
**(omega * .1), eps)))
betaR = betaR / np.maximum(betaR + betaL, eps)
betaL = np.copy(np.eye(R) - betaR)
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after BETA : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
return betaR, betaL, HM, WM
def Stereo_SIMM( # the data to be fitted to:
SXR,
SXL,
# the basis matrices for the spectral combs
WF0,
# and for the elementary filters:
WGAMMA,
# number of desired filters, accompaniment spectra:
numberOfFilters=4,
numberOfAccompanimentSpectralShapes=10,
# if any, initial amplitude matrices for
HGAMMA0=None,
HPHI0=None,
HF00=None,
WM0=None,
HM0=None,
# Some more optional arguments, to control the "convergence"
# of the algo
numberOfIterations=1000,
updateRulePower=1.0,
stepNotes=4,
lambdaHF0=0.00,
alphaHF0=0.99,
displayEvolution=False,
verbose=True,
updateHGAMMA=True,
computeError=False):
"""
HGAMMA, HPHI, HF0, HM, WM, recoError =
SIMM(SXR, SXL, WF0, WGAMMA, numberOfFilters=4,
numberOfAccompanimentSpectralShapes=10, HGAMMA0=None, HPHI0=None,
HF00=None, WM0=None, HM0=None, numberOfIterations=1000,
updateRulePower=1.0, stepNotes=4,
lambdaHF0=0.00, alphaHF0=0.99, displayEvolution=False,
verbose=True)
Implementation of the Smooth-filters Instantaneous Mixture Model
(SIMM). This model can be used to estimate the main melody of a
song, and separate the lead voice from the accompaniment, provided
that the basis WF0 is constituted of elements associated to
particular pitches.
Inputs:
SX
the F x N power spectrogram to be approximated.
F is the number of frequency bins, while N is the number of
analysis frames
WF0
the F x NF0 basis matrix containing the NF0 source elements
WGAMMA
the F x P basis matrix of P smooth elementary filters
numberOfFilters
the number of filters K to be considered
numberOfAccompanimentSpectralShapes
the number of spectral shapes R for the accompaniment
HGAMMA0
the P x K decomposition matrix of WPHI on WGAMMA
HPHI0
the K x N amplitude matrix of the filter part of the lead
instrument
HF00
the NF0 x N amplitude matrix for the source part of the lead
instrument
WM0
the F x R the matrix for spectral shapes of the
accompaniment
HM0
the R x N amplitude matrix associated with each of the R
accompaniment spectral shapes
numberOfIterations
the number of iterations for the estimatino algorithm
updateRulePower
the power to which the multiplicative gradient is elevated to
stepNotes
the number of elements in WF0 per semitone. stepNotes=4 means
that there are 48 elements per octave in WF0.
lambdaHF0
Lagrangian multiplier for the octave control
alphaHF0
parameter that controls how much influence a lower octave
can have on the upper octave's amplitude.
Outputs:
HGAMMA
the estimated P x K decomposition matrix of WPHI on WGAMMA
HPHI
the estimated K x N amplitude matrix of the filter part
HF0
the estimated NF0 x N amplitude matrix for the source part
HM
the estimated R x N amplitude matrix for the accompaniment
WM
the estimate F x R spectral shapes for the accompaniment
recoError
the successive values of the Itakura Saito divergence
between the power spectrogram and the spectrogram
computed thanks to the updated estimations of the matrices.
Please also refer to the following article for more details about
the algorithm within this function, as well as the meaning of the
different matrices that are involved:
J.-L. Durrieu, G. Richard, B. David and C. Fevotte
Source/Filter Model for Unsupervised Main Melody
Extraction From Polyphonic Audio Signals
IEEE Transactions on Audio, Speech and Language Processing
Vol. 18, No. 3, March 2010
"""
eps = 10**(-20)
if displayEvolution:
import matplotlib.pyplot as plt
from matplotlib.pyplot import imshow as imageM
plt.ion()
print "Is the display interactive? ", plt.isinteractive()
# renamed for convenience:
K = numberOfFilters
R = numberOfAccompanimentSpectralShapes
omega = updateRulePower
F, N = SXR.shape
if (F, N) != SXL.shape:
print "The input STFT matrices do not have the same dimension.\n"
print "Please check what happened..."
raise ValueError("Dimension of STFT matrices must be the same.")
Fwf0, NF0 = WF0.shape
Fwgamma, P = WGAMMA.shape
# Checking the sizes of the matrices
if Fwf0 != F:
return False # A REVOIR!!!
if HGAMMA0 is None:
HGAMMA0 = np.abs(randn(P, K))
else:
if not (isinstance(HGAMMA0, np.ndarray)): # default behaviour
HGAMMA0 = np.array(HGAMMA0, copy=True, order='C')
Phgamma0, Khgamma0 = HGAMMA0.shape
if Phgamma0 != P or Khgamma0 != K:
print "Wrong dimensions for given HGAMMA0, \n"
print "random initialization used instead"
HGAMMA0 = np.abs(randn(P, K))
HGAMMA = np.array(HGAMMA0, copy=True, order='C')
if HPHI0 is None: # default behaviour
HPHI = np.abs(randn(K, N))
else:
Khphi0, Nhphi0 = np.array(HPHI0).shape
if Khphi0 != K or Nhphi0 != N:
print "Wrong dimensions for given HPHI0, \n"
print "random initialization used instead"
HPHI = np.abs(randn(K, N))
else:
HPHI = np.array(HPHI0, copy=True, order='C')
if HF00 is None:
HF00 = np.abs(randn(NF0, N))
else:
if np.array(HF00).shape[0] == NF0 and np.array(HF00).shape[1] == N:
HF00 = np.array(HF00, copy=True, order='C')
else:
print "Wrong dimensions for given HF00, \n"
print "random initialization used instead"
HF00 = np.abs(randn(NF0, N))
HF0 = np.array(HF00, copy=True, order='C')
if HM0 is None:
HM0 = np.abs(randn(R, N))
else:
if np.array(HM0).shape[0] == R and np.array(HM0).shape[1] == N:
HM0 = np.array(HM0, copy=True, order='C')
else:
print "Wrong dimensions for given HM0, \n"
print "random initialization used instead"
HM0 = np.abs(randn(R, N))
HM = np.array(HM0, copy=True, order='C')
if WM0 is None:
WM0 = np.abs(randn(F, R))
else:
if np.array(WM0).shape[0] == F and np.array(WM0).shape[1] == R:
WM0 = np.array(WM0, copy=True, order='C')
else:
print "Wrong dimensions for given WM0, \n"
print "random initialization used instead"
WM0 = np.abs(randn(F, R))
WM = np.array(WM0, copy=True, order='C')
alphaR = 0.5
alphaL = 0.5
betaR = np.random.rand(R)
betaL = 1 - betaR
# Iterations to estimate the SIMM parameters:
WPHI = np.dot(WGAMMA, HGAMMA)
SF0 = np.dot(WF0, HF0)
SPHI = np.dot(WPHI, HPHI)
hatSXL = SF0 * SPHI
hatSXR = (alphaR**2) * hatSXL
hatSXR += np.dot((WM * (betaR**2)), HM)
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
# temporary matrices
tempNumFbyN = np.zeros([F, N])
tempDenFbyN = np.zeros([F, N])
tempComFbyN = np.zeros([F, N])
# Array containing the reconstruction error after the update of each
# of the parameter matrices:
recoError = np.zeros([numberOfIterations * 5 * 2 + NF0 * 2 + 1])
if computeError:
recoError[0] = ISDistortion(SXR, hatSXR) + ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error at beginning: ", recoError[0]
counterError = 1
if displayEvolution:
h1 = plt.figure(1)
WF0T = np.ascontiguousarray(WF0.T)
# Main loop for multiplicative updating rules:
for n in np.arange(numberOfIterations):
# order of re-estimation: HF0, HPHI, HM, HGAMMA, WM
if verbose:
print "iteration ", n, " over ", numberOfIterations
if displayEvolution:
h1.clf()
imageM(db(HF0))
plt.clim([np.amax(db(HF0)) - 100,
np.amax(db(HF0))])
plt.draw()
# updating HF0:
tempComFbyN = (alphaR**2) * SPHI / np.maximum(hatSXR, eps)
tempDenFbyN = (alphaL**2) * SPHI / np.maximum(hatSXL, eps)
tempNumFbyN = tempComFbyN * SXR / np.maximum(
hatSXR, eps) + tempDenFbyN * SXL / np.maximum(hatSXL, eps)
#tempNumFbyN = ((alphaR**2) * SPHI * SXR) / np.maximum(hatSXR ** 2, eps)\
# + ((alphaL**2) * SPHI * SXL) / np.maximum(hatSXL ** 2, eps)
tempDenFbyN += tempComFbyN
#tempDenFbyN = (alphaR**2) * SPHI / np.maximum(hatSXR, eps)\
# + (alphaL**2) * SPHI / np.maximum(hatSXL, eps)
##if verbose>10: #DEBUG
## print "tempNumFbyN.flags",tempNumFbyN.flags
## print "tempDenFbyN.flags",tempDenFbyN.flags
# This to enable octave control
## HF0[np.arange(12 * stepNotes, NF0), :] \
## = HF0[np.arange(12 * stepNotes, NF0), :] \
## * (np.dot(WF0[:, np.arange(12 * stepNotes,
## NF0)].T, tempNumFbyN) \
## / np.maximum(
## np.dot(WF0[:, np.arange(12 * stepNotes, NF0)].T,
## tempDenFbyN) \
## + lambdaHF0 * (- (alphaHF0 - 1.0) \
## / np.maximum(HF0[
## np.arange(12 * stepNotes, NF0), :], eps) \
## + HF0[
## np.arange(NF0 - 12 * stepNotes), :]),
## eps)) ** omega
##
## HF0[np.arange(12 * stepNotes), :] \
## = HF0[np.arange(12 * stepNotes), :] \
## * (np.dot(WF0[:, np.arange(12 * stepNotes)].T,
## tempNumFbyN) /
## np.maximum(
## np.dot(WF0[:, np.arange(12 * stepNotes)].T,
## tempDenFbyN), eps)) ** omega
# normal update rules:
HF0 *= (np.dot(WF0T, tempNumFbyN) /
np.maximum(np.dot(WF0T, tempDenFbyN), eps))**omega
##if verbose>10: #DEBUG
## print "HF0.flags", HF0.flags
SF0 = np.dot(WF0, HF0, out=SF0)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
if computeError:
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after HF0 : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating HPHI
if updateHGAMMA or True:
tempComFbyN = (alphaR**2) * SF0 / np.maximum(hatSXR, eps)
tempDenFbyN = (alphaL**2) * SF0 / np.maximum(hatSXL, eps)
tempNumFbyN = tempComFbyN * SXR
tempNumFbyN /= np.maximum(hatSXR, eps)
tempNumFbyN += tempDenFbyN * SXL / np.maximum(hatSXL, eps)
tempDenFbyN += tempComFbyN
#tempNumFbyN = ((alphaR**2) * SF0 * SXR) / np.maximum(hatSXR ** 2, eps)\
# + ((alphaL**2) * SF0 * SXL) / np.maximum(hatSXL ** 2, eps)
#tempDenFbyN = (alphaR**2) * SF0 / np.maximum(hatSXR, eps)\
# + (alphaL**2) * SF0 / np.maximum(hatSXL, eps)
HPHI *= (np.dot(WPHI.T, tempNumFbyN) /
np.maximum(np.dot(WPHI.T, tempDenFbyN), eps))**omega
sumHPHI = np.sum(HPHI, axis=0)
HPHI[:, sumHPHI > 0] = HPHI[:, sumHPHI > 0] / np.outer(
np.ones(K), sumHPHI[sumHPHI > 0])
HF0 *= np.outer(np.ones(NF0), sumHPHI)
SF0 = np.dot(WF0, HF0, out=SF0)
SPHI = np.dot(WPHI, HPHI, out=SPHI)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM*(betaR**2),HM),
## eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM*(betaL**2),HM),
## eps)
if computeError:
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after HPHI : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating HM
# tempNumFbyN = SXR / np.maximum(hatSXR ** 2, eps)\
# + SXL / np.maximum(hatSXL ** 2, eps)
# tempDenFbyN = 1 / np.maximum(hatSXR, eps)\
# + 1 / np.maximum(hatSXL, eps)
# HM = np.maximum(HM * (np.dot(WM.T, tempNumFbyN) /
# np.maximum(np.dot(WM.T, tempDenFbyN), eps)) ** omega, eps)
HM *= ((np.dot(
(WM * (betaR**2)).T, SXR / np.maximum(hatSXR**2, eps)) + np.dot(
(WM * (betaL**2)).T, SXL / np.maximum(hatSXL**2, eps))) /
np.maximum(
np.dot(
(WM *
(betaR**2)).T, 1 / np.maximum(hatSXR, eps)) + np.dot(
(WM * (betaL**2)).T, 1 / np.maximum(hatSXL, eps)),
eps))**omega
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM*(betaR**2), HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM*(betaL**2), HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after HM : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating HGAMMA
if updateHGAMMA:
tempComFbyN = (alphaR**2) * SF0 / np.maximum(hatSXR, eps)
tempDenFbyN = (alphaL**2) * SF0 / np.maximum(hatSXL, eps)
tempNumFbyN = tempComFbyN * SXR
tempNumFbyN /= np.maximum(hatSXR, eps)
tempNumFbyN += tempDenFbyN * SXL / np.maximum(hatSXL, eps)
tempDenFbyN += tempComFbyN
##tempNumFbyN = ((alphaR ** 2) * SF0 * SXR) / np.maximum(hatSXR ** 2, eps)\
## + ((alphaL ** 2) * SF0 * SXL) / np.maximum(hatSXL ** 2, eps)
##tempDenFbyN = (alphaR ** 2) * SF0 / np.maximum(hatSXR, eps) \
## + (alphaL ** 2) * SF0 / np.maximum(hatSXL, eps)
HGAMMA *= (
np.dot(WGAMMA.T, np.dot(tempNumFbyN, HPHI.T)) / np.maximum(
np.dot(WGAMMA.T, np.dot(tempDenFbyN, HPHI.T)), eps))**omega
sumHGAMMA = np.sum(HGAMMA, axis=0)
HGAMMA[:, sumHGAMMA > 0] /= sumHGAMMA[sumHGAMMA > 0]
HPHI *= np.outer(sumHGAMMA, np.ones(N))
sumHPHI = np.sum(HPHI, axis=0)
HPHI[:, sumHPHI > 0] /= sumHPHI[sumHPHI > 0]
HF0 *= sumHPHI
WPHI = np.dot(WGAMMA, HGAMMA, out=WPHI)
SF0 = np.dot(WF0, HF0, out=SF0)
SPHI = np.dot(WPHI, HPHI, out=SPHI)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM*(betaR**2),HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM*(betaL**2),HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after HGAMMA: ",
## print recoError[counterError] - recoError[counterError - 1]
##
counterError += 1
# updating WM, after a certain number of iterations (here, after 1 iteration)
if n > -1: # this test can be used such that WM is updated only
# after a certain number of iterations
## tempNumFbyN = SX / np.maximum(hatSX ** 2, eps)
## tempDenFbyN = 1 / np.maximum(hatSX, eps)
## WM = np.maximum(WM * (np.dot(tempNumFbyN, HM.T) /
## np.maximum(np.dot(tempDenFbyN, HM.T),
## eps)) ** omega, eps)
WM = WM * \
((np.dot(SXR / np.maximum(hatSXR ** 2, eps),
HM.T * (betaR ** 2)) +
np.dot(SXL / np.maximum(hatSXL ** 2, eps),
HM.T * (betaL ** 2))
) /
(np.dot(1 / np.maximum(hatSXR, eps),
HM.T * (betaR ** 2)) +
np.dot(1 / np.maximum(hatSXL, eps),
HM.T * (betaL ** 2))
)) ** omega
sumWM = np.sum(WM, axis=0)
WM[:, sumWM > 0] /= sumWM[sumWM > 0]
HM *= np.vstack(sumWM)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM * (betaR**2), HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM * (betaL**2), HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after WM : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating alphaR and alphaL:
tempDenFbyN = SF0 * SPHI / np.maximum(hatSXR, eps)
tempNumFbyN = tempDenFbyN * SXR / np.maximum(hatSXR, eps)
## tempDenFbyN = SF0 * SPHI / np.maximum(hatSXR, eps)
alphaR = np.maximum(
alphaR * (np.sum(tempNumFbyN) / np.sum(tempDenFbyN))**(omega * .1),
eps)
tempDenFbyN = SF0 * SPHI / np.maximum(hatSXL, eps)
tempNumFbyN = tempDenFbyN * SXL / np.maximum(hatSXL, eps)
alphaL = np.maximum(
alphaL * (np.sum(tempNumFbyN) / np.sum(tempDenFbyN))**(omega * .1),
eps)
alphaR = alphaR / np.maximum(alphaR + alphaL, .001)
alphaL = np.copy(1 - alphaR)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM * (betaR**2), HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM * (betaL**2), HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after ALPHA : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating betaR and betaL
betaR *= np.diag(
((np.dot(np.dot(WM.T, SXR / np.maximum(hatSXR**2, eps)), HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXR, eps)), HM.T)))**(
omega * .1))
betaL *= np.diag(
((np.dot(np.dot(WM.T, SXL / np.maximum(hatSXL**2, eps)), HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXL, eps)), HM.T)))**(
omega * .1))
betaR = betaR / np.maximum(betaR + betaL, eps)
# betaL = np.copy(np.eye(R) - betaR)
betaL = 1 - betaR
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM * (betaR**2),HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM * (betaL**2),HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after BETA : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
return alphaR, alphaL, HGAMMA, HPHI, HF0, np.diag(betaR), np.diag(
betaL), HM, WM, recoError
def stereo_NMF(SXR, SXL,
numberOfAccompanimentSpectralShapes,
WM0=None, HM0=None,
numberOfIterations=50, updateRulePower=1.0,
verbose=False, displayEvolution=False):
eps = 10 ** (-20)
if displayEvolution:
import matplotlib.pyplot as plt
from matplotlib.pyplot import imshow as imageM
plt.ion()
print "Is the display interactive? ", plt.isinteractive()
R = numberOfAccompanimentSpectralShapes
omega = updateRulePower
F, N = SXR.shape
if (F, N) != SXL.shape:
print "The input STFT matrices do not have the same dimension.\n"
print "Please check what happened..."
raise ValueError("Dimension of STFT matrices must be the same.")
if HM0 is None:
HM0 = np.abs(randn(R, N))
else:
if np.array(HM0).shape[0] == R and np.array(HM0).shape[1] == N:
HM0 = np.array(HM0)
else:
print "Wrong dimensions for given HM0, \n"
print "random initialization used instead"
HM0 = np.abs(randn(R, N))
HM = np.copy(HM0)
if WM0 is None:
WM0 = np.abs(randn(F, R))
else:
if np.array(WM0).shape[0] == F and np.array(WM0).shape[1] == R:
WM0 = np.array(WM0)
else:
print "Wrong dimensions for given WM0, \n"
print "random initialization used instead"
WM0 = np.abs(randn(F, R))
WM = np.copy(WM0)
betaR = np.diag(np.random.rand(R))
betaL = np.eye(R) - betaR
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
# temporary matrices
tempNumFbyN = np.zeros([F, N])
tempDenFbyN = np.zeros([F, N])
recoError = np.zeros([numberOfIterations * 3 + 1])
recoError[0] = ISDistortion(SXR, hatSXR) + ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error at beginning: ", recoError[0]
counterError = 1
if displayEvolution:
h1 = plt.figure(1)
for n in np.arange(numberOfIterations):
# order of re-estimation: HF0, HPHI, HM, HGAMMA, WM
if verbose:
print "iteration ", n, " over ", numberOfIterations
if displayEvolution:
h1.clf()
imageM(db(hatSXR))
plt.clim([np.amax(db(hatSXR))-100, np.amax(db(hatSXR))])
plt.draw()
# updating HM
HM = HM * \
((np.dot(np.dot((betaR**2), WM.T), SXR /
np.maximum(hatSXR ** 2, eps)) +
np.dot(np.dot((betaL**2), WM.T), SXL /
np.maximum(hatSXL ** 2, eps))
) /
np.maximum(np.dot(np.dot((betaR**2), WM.T), 1 /
np.maximum(hatSXR, eps)) +
np.dot(np.dot((betaL**2), WM.T), 1 /
np.maximum(hatSXL, eps)),
eps)) ** omega
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2),HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2),HM), eps)
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after HM : ",\
recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating WM
WM = WM * \
((np.dot(SXR / np.maximum(hatSXR ** 2, eps),
np.dot(HM.T, betaR ** 2)) +
np.dot(SXL / np.maximum(hatSXL ** 2, eps),
np.dot(HM.T, betaL ** 2))
) /
(np.dot(1 / np.maximum(hatSXR, eps),
np.dot(HM.T, betaR ** 2)) +
np.dot(1 / np.maximum(hatSXL, eps),
np.dot(HM.T, betaL ** 2))
)) ** omega
sumWM = np.sum(WM, axis=0)
WM[:, sumWM>0] = (WM[:, sumWM>0] /
np.outer(np.ones(F),sumWM[sumWM>0]))
HM = HM * np.outer(sumWM, np.ones(N))
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after WM : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating betaR and betaL
betaR = np.diag(np.diag(np.maximum(betaR *
((np.dot(np.dot(WM.T, SXR / np.maximum(hatSXR ** 2,
eps)),
HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXR,
eps)),
HM.T))) ** (omega*.1), eps)))
betaL = np.diag(np.diag(np.maximum(betaL *
((np.dot(np.dot(WM.T, SXL / np.maximum(hatSXL ** 2,
eps)),
HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXL,
eps)),
HM.T))) ** (omega*.1), eps)))
betaR = betaR / np.maximum(betaR + betaL, eps)
betaL = np.copy(np.eye(R) - betaR)
hatSXR = np.maximum(np.dot(np.dot(WM, betaR**2), HM), eps)
hatSXL = np.maximum(np.dot(np.dot(WM, betaL**2), HM), eps)
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after BETA : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
return betaR, betaL, HM, WM
# draw figure plus formant annotated
FHzmax = 4000.0
nFmax = np.int32(np.ceil(FHzmax/Fs*NFT))
ytickslab = np.array([1000, 2000, 3000, 4000])
ytickspos = np.int32(np.ceil(ytickslab/Fs*NFT))
fontsize = 16
figheight=4.5
figwidth=9.0
displayEvolution = False #True
if displayEvolution:
plt.figure(1)#, figsize=[figwidth, figheight])
plt.clf()
imageM(db(specFromLpc))
plt.hold(True)
trueFormant = {}
for n in range(3):
trueFormant[n] = bigdat[filenb,5+n+3*np.arange(8)]
if displayEvolution:
plt.plot(timeStampsInFrame,
trueFormant[n]/np.double(fs)*NFT,
'ok')
if displayEvolution:
plt.plot(freqLpc.T/np.double(fs)*NFT, )
plt.axis('tight')
plt.draw()
def Stereo_SIMM(# the data to be fitted to:
SXR, SXL,
# the basis matrices for the spectral combs
WF0,
# and for the elementary filters:
WGAMMA,
# number of desired filters, accompaniment spectra:
numberOfFilters=4, numberOfAccompanimentSpectralShapes=10,
# if any, initial amplitude matrices for
HGAMMA0=None, HPHI0=None,
HF00=None,
WM0=None, HM0=None,
# Some more optional arguments, to control the "convergence"
# of the algo
numberOfIterations=1000, updateRulePower=1.0,
stepNotes=4,
lambdaHF0=0.00,alphaHF0=0.99,
displayEvolution=False, verbose=True,
updateHGAMMA=True,
computeError=False):
"""
HGAMMA, HPHI, HF0, HM, WM, recoError =
SIMM(SXR, SXL, WF0, WGAMMA, numberOfFilters=4,
numberOfAccompanimentSpectralShapes=10, HGAMMA0=None, HPHI0=None,
HF00=None, WM0=None, HM0=None, numberOfIterations=1000,
updateRulePower=1.0, stepNotes=4,
lambdaHF0=0.00, alphaHF0=0.99, displayEvolution=False,
verbose=True)
Implementation of the Smooth-filters Instantaneous Mixture Model
(SIMM). This model can be used to estimate the main melody of a
song, and separate the lead voice from the accompaniment, provided
that the basis WF0 is constituted of elements associated to
particular pitches.
Inputs:
SX
the F x N power spectrogram to be approximated.
F is the number of frequency bins, while N is the number of
analysis frames
WF0
the F x NF0 basis matrix containing the NF0 source elements
WGAMMA
the F x P basis matrix of P smooth elementary filters
numberOfFilters
the number of filters K to be considered
numberOfAccompanimentSpectralShapes
the number of spectral shapes R for the accompaniment
HGAMMA0
the P x K decomposition matrix of WPHI on WGAMMA
HPHI0
the K x N amplitude matrix of the filter part of the lead
instrument
HF00
the NF0 x N amplitude matrix for the source part of the lead
instrument
WM0
the F x R the matrix for spectral shapes of the
accompaniment
HM0
the R x N amplitude matrix associated with each of the R
accompaniment spectral shapes
numberOfIterations
the number of iterations for the estimatino algorithm
updateRulePower
the power to which the multiplicative gradient is elevated to
stepNotes
the number of elements in WF0 per semitone. stepNotes=4 means
that there are 48 elements per octave in WF0.
lambdaHF0
Lagrangian multiplier for the octave control
alphaHF0
parameter that controls how much influence a lower octave
can have on the upper octave's amplitude.
Outputs:
HGAMMA
the estimated P x K decomposition matrix of WPHI on WGAMMA
HPHI
the estimated K x N amplitude matrix of the filter part
HF0
the estimated NF0 x N amplitude matrix for the source part
HM
the estimated R x N amplitude matrix for the accompaniment
WM
the estimate F x R spectral shapes for the accompaniment
recoError
the successive values of the Itakura Saito divergence
between the power spectrogram and the spectrogram
computed thanks to the updated estimations of the matrices.
Please also refer to the following article for more details about
the algorithm within this function, as well as the meaning of the
different matrices that are involved:
J.-L. Durrieu, G. Richard, B. David and C. Fevotte
Source/Filter Model for Unsupervised Main Melody
Extraction From Polyphonic Audio Signals
IEEE Transactions on Audio, Speech and Language Processing
Vol. 18, No. 3, March 2010
"""
eps = 10 ** (-20)
if displayEvolution:
import matplotlib.pyplot as plt
from matplotlib.pyplot import imshow as imageM
plt.ion()
print "Is the display interactive? ", plt.isinteractive()
# renamed for convenience:
K = numberOfFilters
R = numberOfAccompanimentSpectralShapes
omega = updateRulePower
F, N = SXR.shape
if (F, N) != SXL.shape:
print "The input STFT matrices do not have the same dimension.\n"
print "Please check what happened..."
raise ValueError("Dimension of STFT matrices must be the same.")
Fwf0, NF0 = WF0.shape
Fwgamma, P = WGAMMA.shape
# Checking the sizes of the matrices
if Fwf0 != F:
return False # A REVOIR!!!
if HGAMMA0 is None:
HGAMMA0 = np.abs(randn(P, K))
else:
if not(isinstance(HGAMMA0,np.ndarray)): # default behaviour
HGAMMA0 = np.array(HGAMMA0, copy=True, order='C')
Phgamma0, Khgamma0 = HGAMMA0.shape
if Phgamma0 != P or Khgamma0 != K:
print "Wrong dimensions for given HGAMMA0, \n"
print "random initialization used instead"
HGAMMA0 = np.abs(randn(P, K))
HGAMMA = np.array(HGAMMA0, copy=True, order='C')
if HPHI0 is None: # default behaviour
HPHI = np.abs(randn(K, N))
else:
Khphi0, Nhphi0 = np.array(HPHI0).shape
if Khphi0 != K or Nhphi0 != N:
print "Wrong dimensions for given HPHI0, \n"
print "random initialization used instead"
HPHI = np.abs(randn(K, N))
else:
HPHI = np.array(HPHI0, copy=True, order='C')
if HF00 is None:
HF00 = np.abs(randn(NF0, N))
else:
if np.array(HF00).shape[0] == NF0 and np.array(HF00).shape[1] == N:
HF00 = np.array(HF00, copy=True, order='C')
else:
print "Wrong dimensions for given HF00, \n"
print "random initialization used instead"
HF00 = np.abs(randn(NF0, N))
HF0 = np.array(HF00, copy=True, order='C')
if HM0 is None:
HM0 = np.abs(randn(R, N))
else:
if np.array(HM0).shape[0] == R and np.array(HM0).shape[1] == N:
HM0 = np.array(HM0, copy=True, order='C')
else:
print "Wrong dimensions for given HM0, \n"
print "random initialization used instead"
HM0 = np.abs(randn(R, N))
HM = np.array(HM0, copy=True, order='C')
if WM0 is None:
WM0 = np.abs(randn(F, R))
else:
if np.array(WM0).shape[0] == F and np.array(WM0).shape[1] == R:
WM0 = np.array(WM0, copy=True, order='C')
else:
print "Wrong dimensions for given WM0, \n"
print "random initialization used instead"
WM0 = np.abs(randn(F, R))
WM = np.array(WM0, copy=True, order='C')
alphaR = 0.5
alphaL = 0.5
betaR = np.random.rand(R)
betaL = 1 - betaR
# Iterations to estimate the SIMM parameters:
WPHI = np.dot(WGAMMA, HGAMMA)
SF0 = np.dot(WF0, HF0)
SPHI = np.dot(WPHI, HPHI)
hatSXL = SF0 * SPHI
hatSXR = (alphaR**2) * hatSXL
hatSXR += np.dot((WM * (betaR**2)), HM)
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
# temporary matrices
tempNumFbyN = np.zeros([F, N])
tempDenFbyN = np.zeros([F, N])
tempComFbyN = np.zeros([F, N])
# Array containing the reconstruction error after the update of each
# of the parameter matrices:
recoError = np.zeros([numberOfIterations * 5 * 2 + NF0 * 2 + 1])
if computeError:
recoError[0] = ISDistortion(SXR, hatSXR) + ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error at beginning: ", recoError[0]
counterError = 1
if displayEvolution:
h1 = plt.figure(1)
WF0T = np.ascontiguousarray(WF0.T)
# Main loop for multiplicative updating rules:
for n in np.arange(numberOfIterations):
# order of re-estimation: HF0, HPHI, HM, HGAMMA, WM
if verbose:
print "iteration ", n, " over ", numberOfIterations
if displayEvolution:
h1.clf()
imageM(db(HF0))
plt.clim([np.amax(db(HF0))-100, np.amax(db(HF0))]);plt.draw()
# updating HF0:
tempComFbyN = (alphaR**2) * SPHI / np.maximum(hatSXR, eps)
tempDenFbyN = (alphaL**2) * SPHI / np.maximum(hatSXL, eps)
tempNumFbyN = tempComFbyN * SXR / np.maximum(hatSXR, eps) + tempDenFbyN * SXL / np.maximum(hatSXL, eps)
#tempNumFbyN = ((alphaR**2) * SPHI * SXR) / np.maximum(hatSXR ** 2, eps)\
# + ((alphaL**2) * SPHI * SXL) / np.maximum(hatSXL ** 2, eps)
tempDenFbyN += tempComFbyN
#tempDenFbyN = (alphaR**2) * SPHI / np.maximum(hatSXR, eps)\
# + (alphaL**2) * SPHI / np.maximum(hatSXL, eps)
##if verbose>10: #DEBUG
## print "tempNumFbyN.flags",tempNumFbyN.flags
## print "tempDenFbyN.flags",tempDenFbyN.flags
# This to enable octave control
## HF0[np.arange(12 * stepNotes, NF0), :] \
## = HF0[np.arange(12 * stepNotes, NF0), :] \
## * (np.dot(WF0[:, np.arange(12 * stepNotes,
## NF0)].T, tempNumFbyN) \
## / np.maximum(
## np.dot(WF0[:, np.arange(12 * stepNotes, NF0)].T,
## tempDenFbyN) \
## + lambdaHF0 * (- (alphaHF0 - 1.0) \
## / np.maximum(HF0[
## np.arange(12 * stepNotes, NF0), :], eps) \
## + HF0[
## np.arange(NF0 - 12 * stepNotes), :]),
## eps)) ** omega
##
## HF0[np.arange(12 * stepNotes), :] \
## = HF0[np.arange(12 * stepNotes), :] \
## * (np.dot(WF0[:, np.arange(12 * stepNotes)].T,
## tempNumFbyN) /
## np.maximum(
## np.dot(WF0[:, np.arange(12 * stepNotes)].T,
## tempDenFbyN), eps)) ** omega
# normal update rules:
HF0 *= (np.dot(WF0T, tempNumFbyN) /
np.maximum(np.dot(WF0T, tempDenFbyN), eps)) ** omega
##if verbose>10: #DEBUG
## print "HF0.flags", HF0.flags
SF0 = np.dot(WF0, HF0, out=SF0)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
if computeError:
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after HF0 : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating HPHI
if updateHGAMMA or True:
tempComFbyN = (alphaR**2) * SF0 / np.maximum(hatSXR, eps)
tempDenFbyN = (alphaL**2) * SF0 / np.maximum(hatSXL, eps)
tempNumFbyN = tempComFbyN * SXR
tempNumFbyN /= np.maximum(hatSXR, eps)
tempNumFbyN += tempDenFbyN * SXL / np.maximum(hatSXL, eps)
tempDenFbyN += tempComFbyN
#tempNumFbyN = ((alphaR**2) * SF0 * SXR) / np.maximum(hatSXR ** 2, eps)\
# + ((alphaL**2) * SF0 * SXL) / np.maximum(hatSXL ** 2, eps)
#tempDenFbyN = (alphaR**2) * SF0 / np.maximum(hatSXR, eps)\
# + (alphaL**2) * SF0 / np.maximum(hatSXL, eps)
HPHI *= (np.dot(WPHI.T, tempNumFbyN) / np.maximum(np.dot(WPHI.T, tempDenFbyN), eps)) ** omega
sumHPHI = np.sum(HPHI, axis=0)
HPHI[:, sumHPHI>0] = HPHI[:, sumHPHI>0] / np.outer(np.ones(K), sumHPHI[sumHPHI>0])
HF0 *= np.outer(np.ones(NF0), sumHPHI)
SF0 = np.dot(WF0, HF0, out=SF0)
SPHI = np.dot(WPHI, HPHI, out=SPHI)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM*(betaR**2),HM),
## eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM*(betaL**2),HM),
## eps)
if computeError:
recoError[counterError] = ISDistortion(SXR, hatSXR) \
+ ISDistortion(SXL, hatSXL)
if verbose:
print "Reconstruction error difference after HPHI : ",
print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating HM
# tempNumFbyN = SXR / np.maximum(hatSXR ** 2, eps)\
# + SXL / np.maximum(hatSXL ** 2, eps)
# tempDenFbyN = 1 / np.maximum(hatSXR, eps)\
# + 1 / np.maximum(hatSXL, eps)
# HM = np.maximum(HM * (np.dot(WM.T, tempNumFbyN) /
# np.maximum(np.dot(WM.T, tempDenFbyN), eps)) ** omega, eps)
HM *= (
(
np.dot((WM * (betaR**2)).T,
SXR /np.maximum(hatSXR ** 2, eps))
+ np.dot((WM*(betaL**2)).T,
SXL /np.maximum(hatSXL ** 2, eps))
) /
np.maximum(np.dot((WM*(betaR**2)).T,
1 / np.maximum(hatSXR, eps))
+ np.dot((WM*(betaL**2)).T,
1 /np.maximum(hatSXL, eps)), eps)
) ** omega
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM*(betaR**2), HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM*(betaL**2), HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after HM : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating HGAMMA
if updateHGAMMA:
tempComFbyN = (alphaR**2) * SF0 / np.maximum(hatSXR, eps)
tempDenFbyN = (alphaL**2) * SF0 / np.maximum(hatSXL, eps)
tempNumFbyN = tempComFbyN * SXR
tempNumFbyN /= np.maximum(hatSXR, eps)
tempNumFbyN += tempDenFbyN * SXL / np.maximum(hatSXL, eps)
tempDenFbyN += tempComFbyN
##tempNumFbyN = ((alphaR ** 2) * SF0 * SXR) / np.maximum(hatSXR ** 2, eps)\
## + ((alphaL ** 2) * SF0 * SXL) / np.maximum(hatSXL ** 2, eps)
##tempDenFbyN = (alphaR ** 2) * SF0 / np.maximum(hatSXR, eps) \
## + (alphaL ** 2) * SF0 / np.maximum(hatSXL, eps)
HGAMMA *= (np.dot(WGAMMA.T, np.dot(tempNumFbyN, HPHI.T)) / np.maximum(np.dot(WGAMMA.T, np.dot(tempDenFbyN, HPHI.T)), eps)) ** omega
sumHGAMMA = np.sum(HGAMMA, axis=0)
HGAMMA[:, sumHGAMMA>0] /= sumHGAMMA[sumHGAMMA>0]
HPHI *= np.outer(sumHGAMMA, np.ones(N))
sumHPHI = np.sum(HPHI, axis=0)
HPHI[:, sumHPHI>0] /= sumHPHI[sumHPHI>0]
HF0 *= sumHPHI
WPHI = np.dot(WGAMMA, HGAMMA, out=WPHI)
SF0 = np.dot(WF0, HF0, out=SF0)
SPHI = np.dot(WPHI, HPHI, out=SPHI)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM*(betaR**2),HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM*(betaL**2),HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after HGAMMA: ",
## print recoError[counterError] - recoError[counterError - 1]
##
counterError += 1
# updating WM, after a certain number of iterations (here, after 1 iteration)
if n > -1: # this test can be used such that WM is updated only
# after a certain number of iterations
## tempNumFbyN = SX / np.maximum(hatSX ** 2, eps)
## tempDenFbyN = 1 / np.maximum(hatSX, eps)
## WM = np.maximum(WM * (np.dot(tempNumFbyN, HM.T) /
## np.maximum(np.dot(tempDenFbyN, HM.T),
## eps)) ** omega, eps)
WM = WM * \
((np.dot(SXR / np.maximum(hatSXR ** 2, eps),
HM.T * (betaR ** 2)) +
np.dot(SXL / np.maximum(hatSXL ** 2, eps),
HM.T * (betaL ** 2))
) /
(np.dot(1 / np.maximum(hatSXR, eps),
HM.T * (betaR ** 2)) +
np.dot(1 / np.maximum(hatSXL, eps),
HM.T * (betaL ** 2))
)) ** omega
sumWM = np.sum(WM, axis=0)
WM[:, sumWM>0] /= sumWM[sumWM>0]
HM *= np.vstack(sumWM)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM * (betaR**2), HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM * (betaL**2), HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after WM : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating alphaR and alphaL:
tempDenFbyN = SF0 * SPHI / np.maximum(hatSXR, eps)
tempNumFbyN = tempDenFbyN * SXR / np.maximum(hatSXR, eps)
## tempDenFbyN = SF0 * SPHI / np.maximum(hatSXR, eps)
alphaR = np.maximum(alphaR *
(np.sum(tempNumFbyN) /
np.sum(tempDenFbyN)) ** (omega*.1), eps)
tempDenFbyN = SF0 * SPHI / np.maximum(hatSXL, eps)
tempNumFbyN = tempDenFbyN * SXL / np.maximum(hatSXL, eps)
alphaL = np.maximum(alphaL *
(np.sum(tempNumFbyN) /
np.sum(tempDenFbyN)) ** (omega*.1), eps)
alphaR = alphaR / np.maximum(alphaR + alphaL, .001)
alphaL = np.copy(1 - alphaR)
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM * (betaR**2), HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM * (betaL**2), HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after ALPHA : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
# updating betaR and betaL
betaR *= np.diag(
((np.dot(np.dot(WM.T, SXR / np.maximum(hatSXR ** 2, eps)), HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXR, eps)), HM.T)))
** (omega*.1))
betaL *= np.diag(
((np.dot(np.dot(WM.T, SXL / np.maximum(hatSXL ** 2, eps)), HM.T)) /
(np.dot(np.dot(WM.T, 1 / np.maximum(hatSXL, eps)), HM.T)))
** (omega*.1))
betaR = betaR / np.maximum(betaR + betaL, eps)
# betaL = np.copy(np.eye(R) - betaR)
betaL = 1 - betaR
hatSXL = SF0 * SPHI
hatSXR = np.dot((WM * (betaR**2)), HM, out=hatSXR)
hatSXR += (alphaR**2) * hatSXL
hatSXL *= (alphaL**2)
hatSXL += np.dot((WM * (betaL**2)), HM)
hatSXR = np.maximum(hatSXR, eps)
hatSXL = np.maximum(hatSXL, eps)
##hatSXR = np.maximum((alphaR**2) * SF0 * SPHI + \
## np.dot(WM * (betaR**2),HM), eps)
##hatSXL = np.maximum((alphaL**2) * SF0 * SPHI + \
## np.dot(WM * (betaL**2),HM), eps)
## recoError[counterError] = ISDistortion(SXR, hatSXR) \
## + ISDistortion(SXL, hatSXL)
##
## if verbose:
## print "Reconstruction error difference after BETA : ",
## print recoError[counterError] - recoError[counterError - 1]
counterError += 1
return alphaR, alphaL, HGAMMA, HPHI, HF0, np.diag(betaR), np.diag(betaL), HM, WM, recoError