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blinkiva_gauss.py
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blinkiva_gauss.py
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# Copyright (c) 2019 Robin Scheibler
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
'''
Blind Source Separation using Independent Vector Analysis with Microphones and Blinkies
2019 (c) Robin Scheibler, MIT License
'''
import numpy as np
from pyroomacoustics.bss import projection_back
def blinkiva_gauss(X, U, n_src=None,
n_iter=20, n_nmf_sub_iter=20, proj_back=True, W0=None, R0=None,
seed=None, epsilon=0.5, sparse_reg=0., print_cost=False,
return_filters=False, callback=None):
'''
Implementation of BlinkIVA algorithm for blind source separation using jointly
microphones and sound power sensors "blinkies". The algorithm was presented in
R. Scheibler and N. Ono, *Multi-modal Blind Source Separation with Microphones and Blinkies,*
Proc. IEEE ICASSP, Brighton, UK, May, 2019. DOI: 10.1109/ICASSP.2019.8682594
https://arxiv.org/abs/1904.02334
Parameters
----------
X: ndarray (nframes, nfrequencies, nchannels)
STFT representation of the signal
U: ndarray (nframes, nblinkies)
The matrix containing the blinky signals
n_src: int, optional
The number of sources or independent components
n_iter: int, optional
The number of iterations (default 20)
n_nmf_sub_iter: int, optional
The number of NMF iteration to run between two updates of the demixing
matrices (default 20)
proj_back: bool, optional
Scaling on first mic by back projection (default True)
W0: ndarray (nfrequencies, nchannels, nchannels), optional
Initial value for demixing matrix
R0: ndarray (nframes, nsrc), optional
Initial value of the activations
seed: int, optional
A seed to make deterministic the random initialization of NMF parts,
when None (default), the random number generator is used in its current state
epsilon: float, optional
A regularization value to prevent too large values after the division
sparse_reg: float
A regularization term to make the activation matrix sparse
print_cost: bool, optional
Print the value of the cost function at each iteration
return_filters: bool, optional
If true, the function will return the demixing matrix, gains, and activations too
callback: func
A callback function called every 10 iterations, allows to monitor convergence
Returns
-------
Returns an (nframes, nfrequencies, nsources) array. Also returns
the demixing matrix (nfrequencies, nchannels, nsources), gains (nsrc, nblinkies),
and activations (nframes, nchannels) if ``return_filters`` keyword is True.
'''
n_frames, n_freq, n_chan = X.shape
_, n_blink = U.shape
if _ != n_frames:
raise ValueError('The microphones and blinky signals should have the same number of frames')
# default to determined case
if n_src is None:
n_src = X.shape[2]
# initialize the demixing matrices
if W0 is None:
W = np.array([np.eye(n_chan, n_chan) for f in range(n_freq)], dtype=X.dtype)
else:
W = W0.copy()
# we will threshold entries of R and G that get to small
machine_epsilon = np.finfo(float).eps
# we will only work with the blinky signal normalized by frequency
U_mean = U / n_freq / 2.
I = np.eye(n_chan,n_chan)
Y = np.zeros((n_frames, n_freq, n_chan), dtype=X.dtype)
V = np.zeros((n_freq, n_chan, n_chan, n_chan), dtype=X.dtype)
P = np.zeros((n_frames, n_chan))
# initialize the parts of NMF
R_all = np.ones((n_frames, n_chan))
R = R_all[:,:n_src] # subset tied to NMF of blinkies
if seed is not None:
rng_state = np.random.get_state()
np.random.seed(seed)
if R0 is None:
R[:,:] = 0.1 + 0.9 * np.random.rand(n_frames, n_src)
R /= np.mean(R, axis=0, keepdims=True)
else:
R[:,:] = R0
G = 0.1 + 0.9 * np.random.rand(n_src, n_blink)
U_hat = np.dot(R, G)
G *= np.sum(U_mean, axis=0, keepdims=True) / np.sum(U_hat, axis=0, keepdims=True)
if seed is not None:
np.random.set_state(rng_state)
def cost(Y, W, R, G):
pwr = np.linalg.norm(Y, axis=1) ** 2
cf1 = -2 * Y.shape[0] * np.sum(np.linalg.slogdet(W)[1])
cf2 = np.sum(Y.shape[1] * np.log(R) + pwr / R)
U_hat = np.dot(R[:,:n_src], G)
cf3 = np.sum(np.log(U_hat) + U / U_hat / 2)
return { 'iva' : cf1 + cf2, 'nmf' : cf2 + cf3, 'blinkiva' : cf1 + cf2 + cf3 }
def rescale(W, P, R, G):
# Fix the scale of all variables
lmb = 1. / np.mean(R, axis=0)
R *= lmb[None,:]
P *= lmb[None,:]
W *= np.sqrt(lmb[None,None,:])
G /= lmb[:G.shape[0],None]
# Compute the demixed output
def demix(Y, X, W, P, R_all):
for f in range(n_freq):
Y[:,f,:] = np.dot(X[:,f,:], np.conj(W[f,:,:]))
# The sources magnitudes averaged over frequencies
# shape: (n_frames, n_src)
P[:,:] = np.linalg.norm(Y, axis=1) ** 2 / n_freq
# copy activations for sources not tied to NMF
R_all[:,n_src:] = P[:,n_src:]
# initial demixing
demix(Y, X, W, P, R_all)
cost_joint_list = []
# NMF + IVA joint updates
for epoch in range(n_iter):
if callback is not None and epoch % 10 == 0:
if proj_back:
z = projection_back(Y, X[:,:,0])
callback(Y * np.conj(z[None,:,:]))
else:
callback(Y, extra=[W,G,R,X,U])
if print_cost and epoch % 10 == 0:
print('Cost function: iva={iva:13.0f} nmf={nmf:13.0f} iva+nmf={blinkiva:13.0f}'.format(
**cost(Y, W, R_all, G)))
for sub_epoch in range(n_nmf_sub_iter):
# Update the activations
U_hat = np.dot(R, G)
U_hat_I = 1. / U_hat
R_I = 1. / R
R *= np.sqrt(
(P[:,:n_src] * R_I ** 2 + np.dot(U_mean * U_hat_I ** 2, G.T))
/ (R_I + np.dot(U_hat_I, G.T) + sparse_reg)
)
R[R < machine_epsilon] = machine_epsilon
# Update the gains
U_hat = np.dot(R, G)
U_hat_I = 1. / U_hat
G *= np.sqrt( np.dot(R.T, U_mean * U_hat_I ** 2) / np.dot(R.T, U_hat_I) )
G[G < machine_epsilon] = machine_epsilon
# normalize
#rescale(W, P, R_all, G)
# Compute Auxiliary Variable
# shape: (n_freq, n_src, n_mic, n_mic)
denom = 2 * R_all
denom[denom < epsilon] = epsilon # regularize this part
# 1) promote all arrays to (n_frames, n_freq, n_chan, n_chan, n_chan)
# 2) take the outer product (complex) of the last two dimensions
# to get the covariance matrix over the microphones
# 3) average over the time frames (index 0)
V = np.mean(
(X[:,:,None,:,None] / denom[:,None,:,None,None])
* np.conj(X[:,:,None,None,:]),
axis=0,
)
# Update now the demixing matrix
#for s in range(n_src):
for s in range(n_chan):
W_H = np.conj(np.swapaxes(W, 1, 2))
WV = np.matmul(W_H, V[:,s,:,:])
rhs = I[None,:,s][[0] * WV.shape[0],:]
W[:,:,s] = np.linalg.solve(WV, rhs)
P1 = np.conj(W[:,:,s])
P2 = np.sum(V[:,s,:,:] * W[:,None,:,s], axis=-1)
W[:,:,s] /= np.sqrt(np.sum(P1 * P2, axis=1))[:,None]
demix(Y, X, W, P, R_all)
# Rescale all variables before continuing
rescale(W, P, R_all, G)
if proj_back:
z = projection_back(Y, X[:,:,0])
Y *= np.conj(z[None,:,:])
if return_filters:
return Y, W, G, R_all
else:
return Y