__        ______ __  __ __  __  
\ \      / / ___|  \/  |  \/  | 
 \ \ /\ / / |  _| |\/| | |\/| | 
  \ V  V /| |_| | |  | | |  | | 
   \_/\_/  \____|_|  |_|_|  |_| 

WGMM (Wrapped Gaussian Mixture Model) for angular (circular) clustering

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

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

Example-1: angular clustering in a polar coordinate

distribution of synthesized angular (circular) values	probability density function (PDF) obtained by WGMM

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.

Example-2: clustering samples in a polar coordinate

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.

Cite this code

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}}

The Derivation