__ ______ __ __ __ __
\ \ / / ___| \/ | \/ |
\ \ /\ / / | _| |\/| | |\/| |
\ V V /| |_| | | | | | | |
\_/\_/ \____|_| |_|_| |_|
An implementation of the WGMM
in thesis Speech Enhancement using Fiber Acoustic Sensor
at Concordia University and article Bayesian modelling of the temporal aspects of smart home activity with circular statistics
.
@mastersthesis{wang2020speech,
title={Speech Enhancement using Fiber Acoustic Sensor},
author={Wang, Miao},
year={2020},
school={Concordia University},
url={https://spectrum.library.concordia.ca/id/eprint/986722/1/Miao_MASc_S2020.pdf}
}
@inproceedings{diethe2015bayesian,
title={Bayesian modelling of the temporal aspects of smart home activity with circular statistics},
author={Diethe, Tom and Twomey, Niall and Flach, Peter},
booktitle={Joint European Conference on Machine Learning and Knowledge Discovery in Databases},
pages={279--294},
year={2015},
organization={Springer}
}
The WGMM
here is designed to solve the phase ambiguity between 0
and T
, which could be any positive value like and
.
install this code using pip:
pip install https://github.com/ludlows/wgmm/archive/refs/heads/main.zip
install this code using setup.py
python setup.py install
distribution of synthesized angular (circular) values | probability density function (PDF) obtained by WGMM |
---|---|
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Python code to fit
these synthesized values is shown below:
# import modules
import numpy as np
from wgmm import WGMixModel
# set initial values
weights_init = np.array([0.5,0.5])
means_init = np.array([[270.0],[180.0]]) / 180.0 * np.pi
covars_init = np.zeros((2,1,1))
covars_init[0,0,0] = 0.8
covars_init[1,0,0] = 0.8
periods = np.array([2*np.pi])
# build model
model = WGMixModel(n_components=2, weights_init=weights_init,
means_init=means_init, covars_init=covars_init,
periods=periods,
tol=1e-4, reg_covar=1e-6, max_iter=1000)
# fit samples
model.fit(samples)
# print parameters estimated by WGMM
print(model.means_ / np.pi * 180) # 355.13560655, 99.36977191
print(model.weights_)
print(model.covars_)
details about this example could be found in this notebook.
Here we show an example to cluster heterogeneous samples (angles are circular and radius not).
polar plot of synthesized dataset | clusters obtained by WGMM |
---|---|
![]() |
![]() |
# import modules
import numpy as np
from wgmm import WGMixModel
# set initial values
weights_init = np.array([0.9,0.1])
means_init = np.array([[270.0, 0.5],[180.0, 0.7]]) #/ 180.0 * np.pi
means_init[:,0] = means_init[:,0] / 180.0 * np.pi
covars_init = np.zeros((2,2,2))
covars_init[0,:,:] = np.array([[0.1,0],[0,0.1]])
covars_init[1,:,:] = np.array([[0.1,0],[0,0.1]])
periods = np.array([2*np.pi, 3]) # 3 is big enough here since radius is not a circular variable, and it ranges from 0 to 1
#build model
model = WGMixModel(n_components=2,
weights_init=weights_init,
means_init=means_init,
covars_init=covars_init,
periods=periods,
tol=1e-4, reg_covar=1e-6, max_iter=100)
# fit samples
model.fit(samples_wgmm)
# print parameters estimated by WGMM
means_estimated = model.means_.copy()
means_estimated[:,0] = means_estimated[:,0] / np.pi * 180
means_estimated
# array([[355.11574106, 0.39957169],
# [100.05972748, 0.70743917]])
# classify samples
labels = model.predict(samples_wgmm)
details about this example could be found in this notebook.
Please cite this code if you are using it in a project.
@mastersthesis{wang2020speech,
title={Speech Enhancement using Fiber Acoustic Sensor},
author={Wang, Miao},
year={2020},
school={Concordia University},
url={https://spectrum.library.concordia.ca/id/eprint/986722/1/Miao_MASc_S2020.pdf}}