This repository contains the code for the paper "MM Algorithms for Joint Independent Subspace Analysis with Application to Blind Single and Multi-Source Extraction" by Robin Scheibler and Nobutaka Ono.
In this work, we propose efficient algorithms for joint independent subspace analysis (JISA), an extension of independent component analysis that deals with parallel mixtures, where not all the components are independent. We derive an algorithmic framework for JISA based on the majorization-minimization (MM) optimization technique (JISA-MM). We use a well-known inequality for super-Gaussian sources to derive a surrogate function of the negative log-likelihood of the observed data. The minimization of this surrogate function leads to a variant of the hybrid exact-approximate diagonalization problem, but where multiple demixing vectors are grouped together. In the spirit of auxiliary function based independent vector analysis (AuxIVA), we propose several updates that can be applied alternately to one, or jointly to two, groups of demixing vectors.
Recently, blind extraction of one or more sources has gained interest as a reasonable way of exploiting larger microphone arrays to achieve better separation. In particular, several MM algorithms have been proposed for overdetermined IVA (OverIVA). By applying JISA-MM, we are not only able to rederive these in a general manner, but also find several new algorithms. We run extensive numerical experiments to evaluate their performance, and compare it to that of full separation with AuxIVA. We find that algorithms using pairwise updates of two sources, or of one source and the background have the fastest convergence, and are able to separate target sources quickly and precisely from the background. In addition, we characterize the performance of all algorithms under a large number of noise, reverberation, and background mismatch conditions.
Separation performance for different numbers of sources and microphones. Similar to experiment in overiva paper, but with more algorithms and SINR points. This time, we can plot histograms (instead of boxplots).
Plot runtime of algorithm vs SDR (or SIR).
We vary three parameters
- The signal-to-interference-and-noise ratio
- The number of interferers (background Gaussianity)
- The distance from microphones to sources (reverberation time)
The example.py programe allows to test the different algorithms on simulated scenarios.
For example, try running
python ./example.py -a overiva-ip2 -s 2 -m 4
to extract two sources with four microphones using the algorithm overiva-ip2.
The full usage instructions is provided below.
> python ./example.py --help
usage: example.py [-h] [--no_cb] [-b BLOCK]
[-a {auxiva,auxiva2,overiva,overiva-ip,overiva-ip2,overiva-ip-block,overiva-ip2-block,overiva-demix-bg,five,ogive,ogive-mix,ogive-demix,ogive-switch,auxiva-pca,pca}]
[-d {laplace,gauss}] [-i {pca}] [-m MICS] [-s SRCS]
[-z INTERF] [--sinr SINR] [-n N_ITER] [--gui] [--save]
[--seed SEED]
Demonstration of blind source extraction using FIVE.
optional arguments:
-h, --help show this help message and exit
--no_cb Removes callback function
-b BLOCK, --block BLOCK
STFT block size
-a {auxiva,auxiva2,overiva,overiva-ip,overiva-ip2,overiva-ip-block,overiva-ip2-block,overiva-demix-bg,five,ogive,ogive-mix,ogive-demix,ogive-switch,auxiva-pca,pca}, --algo {auxiva,auxiva2,overiva,overiva-ip,overiva-ip2,overiva-ip-block,overiva-ip2-block,overiva-demix-bg,five,ogive,ogive-mix,ogive-demix,ogive-switch,auxiva-pca,pca}
Chooses BSS method to run
-d {laplace,gauss}, --dist {laplace,gauss}
IVA model distribution
-i {pca}, --init {pca}
Initialization, eye: identity, eig: principal
eigenvectors
-m MICS, --mics MICS Number of mics
-s SRCS, --srcs SRCS Number of sources
-z INTERF, --interf INTERF
Number of interferers
--sinr SINR Signal-to-interference-and-noise ratio
-n N_ITER, --n_iter N_ITER
Number of iterations
--gui Creates a small GUI for easy playback of the sound
samples
--save Saves the output of the separation to wav files
--seed SEED Random number generator seed
The code can be run serially, or using multiple parallel workers via ipyparallel. Moreover, it is possible to only run a few loops to test whether the code is running or not.
-
Run test loops serially
python ./paper_simulation.py ./experiment1_config.json.json -t -s python ./paper_simulation.py ./experiment2_config.json.json -t -s -
Run test loops in parallel
# start workers in the background # N is the number of parallel process, often "# threads - 1" ipcluster start --daemonize -n N # run the simulation python ./paper_simulation.py ./experiment1_config.json -t python ./paper_simulation.py ./experiment2_config.json -t # stop the workers ipcluster stop -
Run the whole simulation
# start workers in the background # N is the number of parallel process, often "# threads - 1" ipcluster start --daemonize -n N # run the simulation python ./paper_simulation.py ./experiment1_config.json python ./paper_simulation.py ./experiment2_config.json # stop the workers ipcluster stop
The results are saved in a new folder data/<data>-<time>_five_sim_<flag_or_hash>
containing the following files
parameters.json # the list of global parameters of the simulation
arguments.json # the list of all combinations of arguments simulated
data.json # the results of the simulation
Figure 1., 2., 3., and 4. from the paper are produced then by running
./prepare_figures.sh
The code is provided under MIT license.