Created
October 18, 2012 22:35
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Rectify a 1d binary signal with an HMM
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import numpy as np | |
from sklearn.hmm import MultinomialHMM | |
import matplotlib.pyplot as pp | |
# sample run lengths from exponential distribution | |
run_lengths = np.array(np.random.exponential(100, size=10), dtype=np.int) | |
# make the signal from the run lengths | |
signal = [] | |
for i, l in enumerate(run_lengths): | |
signal.extend([i % 2] * l) | |
signal = np.array(signal) | |
# flip a one tenth of the bits randomly | |
fraction_to_flip = 0.1 | |
r = np.random.randint(len(signal), size=fraction_to_flip*len(signal)) | |
fuzzy_signal = np.array(signal, copy=True) | |
fuzzy_signal[r] = np.logical_not(signal[r]) | |
# parameterize a hidden markov model | |
metastability = 0.9 | |
pcorrectemission = 0.9 | |
transmat = np.array([[metastability, 1-metastability], [1-metastability, metastability]]) | |
emission = np.array([[pcorrectemission, 1-pcorrectemission], [1-pcorrectemission, pcorrectemission]]) | |
hmm = MultinomialHMM(n_components=2, startprob=[0.5, 0.5], transmat=transmat) | |
hmm.emissionprob_ = emission | |
# find the most likely sequence to have generated the signal | |
corrected = hmm.predict(fuzzy_signal) | |
# plot the original signal, the fuzzy signal and the rectified signal | |
pp.subplot(311) | |
pp.plot(signal, label='signal') | |
pp.xlabel('original') | |
pp.subplot(312) | |
pp.plot(fuzzy_signal, label='fuzzy') | |
pp.xlabel('fuzzy') | |
pp.subplot(313) | |
pp.plot(corrected, label='corrected') | |
pp.xlabel('corrected') | |
pp.show() |
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