Python implementation of a complex-valued version of the expectation-maximization (EM) algorithm for fitting Mixture of Factor Analyzers (MFA). Some parts of the implementation are based on the PYPI implementation from https://pypi.org/project/mofa/ with substantial speed-ups, new functionalities, and a complex-valued extension. The EM algorithm maximizes the likelihood of a circularly symmetric Gaussian distribution.
The main implementation is contained in MFA_cplx.py with the class MFA_cplx.
The file MFA_cplx_example.py provides useful examples of how to use the code.
This code is written in Python. It uses the numpy, scipy, sklearn, and time packages. The code was tested with Python 3.7.
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fit(data): Fitting the MFA parameters to the provided complex-valued dataset of shape(n_samples, n_dim). -
predict_proba_max(data): Predict the labels for the data samples using trained model. -
predict_proba(X): Predict posterior probability of each component given the data. -
sample(n_samples): Generate random samples from the fitted MFA.
The results of the following work are based (in parts) on the complex-valued MFA implementation:
- B. Fesl, N. Turan, and W. Utschick, “Low-Rank Structured MMSE Channel Estimation with Mixtures of Factor Analyzers,” in 57th Asilomar Conf. Signals, Syst., Comput., 2023. https://arxiv.org/abs/2304.14809
The original code from https://pypi.org/project/mofa/ is covered by the following license:
Copyright 2012 Ross Fadely, Daniel Foreman-Mackey, David W. Hogg, and contributors.
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.
The contributions and extensions are covered by the BSD 3-Clause License:
BSD 3-Clause License
Copyright (c) 2023 Benedikt Fesl. All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
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