Note

Go to the end to download the full example code.

Run AMICA on EEG Data

And compare results to Fortran AMICA.

import amica
from amica import AMICA
import matplotlib.pyplot as plt
import mne

import numpy as np

Download sample data

data_path = amica.datasets.data_path()

Load Fortran AMICA initial weights and results

This is not necessary to run AMICA in Python, but we are going to compare amica-python results to those obtained from the original Fortran implementation.

initial_weights, initial_scales, initial_locations = amica.utils.load_initial_weights(
    data_path / "eeglab_sample_data" / "amicaout_test", n_components=32, n_mixtures=3
    )

Load EEG data

amica_outdir = data_path / "eeglab_sample_data" / "amicaout_test"
fortran_results = amica.utils.load_fortran_results(
    amica_outdir, n_components=32, n_mixtures=3
    )

raw = mne.io.read_raw_eeglab(
    data_path / "eeglab_sample_data"/ "eeglab_data.set", preload=True
    )
data = raw.get_data().T  # Shape (n_samples, n_channels)
data *= 1e6  # Convert from Volts to microVolts

Reading /home/circleci/amica_test_data/eeglab_sample_data/eeglab_data.fdt
Reading 0 ... 30503  =      0.000 ...   238.305 secs...

Run AMICA-Python

transformer = AMICA(
        max_iter=200,
        w_init=initial_weights,
        sbeta_init=initial_scales,
        mu_init=initial_locations,
)
transformer.fit(data)

INFO     | getting the mean ... - amica.linalg:pre_whiten
INFO     |  Getting the covariance matrix ... - amica.linalg:pre_whiten
INFO     | doing eigenvalue decomposition for 32 features ... - amica.linalg:pre_whiten
INFO     | minimum eigenvalues: [4.87990051 6.92011971 7.65621479] - amica.linalg:pre_whiten
INFO     | maximum eigenvalues: [9711.14308385 3039.68504351 1244.41294471] - amica.linalg:pre_whiten
INFO     | num eigvals kept: 32 - amica.linalg:pre_whiten
INFO     | Sphering the data... - amica.linalg:pre_whiten
INFO     | numeigs = 32, nw = 32 - amica.linalg:pre_whiten
INFO     | 1: block size = 30504 - amica.core:solve
INFO     | Solving. (please be patient, this may take a while)... - amica.core:solve
INFO     | Iteration 1, lrate = 0.05000, LL = -3.5136812, nd = 0.0578126, D = 0.00446 0.00446 took 0.61 seconds - amica.core:optimize
INFO     | Iteration 2, lrate = 0.05000, LL = -3.4687938, nd = 0.0254382, D = 0.00391 0.00391 took 0.50 seconds - amica.core:optimize
INFO     | Iteration 3, lrate = 0.05000, LL = -3.4616091, nd = 0.0243398, D = 0.00376 0.00376 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 4, lrate = 0.05000, LL = -3.4589193, nd = 0.0270364, D = 0.00554 0.00554 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 5, lrate = 0.05000, LL = -3.4569812, nd = 0.0277558, D = 0.00994 0.00994 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 6, lrate = 0.05000, LL = -3.4553322, nd = 0.0273357, D = 0.01680 0.01680 took 0.41 seconds - amica.core:optimize
INFO     | Iteration 7, lrate = 0.05000, LL = -3.4538623, nd = 0.0264404, D = 0.02561 0.02561 took 0.38 seconds - amica.core:optimize
INFO     | Iteration 8, lrate = 0.05000, LL = -3.4525343, nd = 0.0253345, D = 0.03580 0.03580 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 9, lrate = 0.05000, LL = -3.4513419, nd = 0.0240417, D = 0.04681 0.04681 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 10, lrate = 0.05000, LL = -3.4502908, nd = 0.0225440, D = 0.05812 0.05812 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 11, lrate = 0.05000, LL = -3.4493812, nd = 0.0208842, D = 0.06919 0.06919 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 12, lrate = 0.05000, LL = -3.4486110, nd = 0.0191358, D = 0.07957 0.07957 took 0.50 seconds - amica.core:optimize
INFO     | Iteration 13, lrate = 0.05000, LL = -3.4479766, nd = 0.0173017, D = 0.08886 0.08886 took 0.41 seconds - amica.core:optimize
INFO     | Iteration 14, lrate = 0.05000, LL = -3.4474541, nd = 0.0157049, D = 0.09674 0.09674 took 0.48 seconds - amica.core:optimize
INFO     | Iteration 15, lrate = 0.05000, LL = -3.4470230, nd = 0.0143406, D = 0.10318 0.10318 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 16, lrate = 0.05000, LL = -3.4466620, nd = 0.0132093, D = 0.10822 0.10822 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 17, lrate = 0.05000, LL = -3.4463566, nd = 0.0123128, D = 0.11195 0.11195 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 18, lrate = 0.05000, LL = -3.4460886, nd = 0.0116321, D = 0.11453 0.11453 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 19, lrate = 0.05000, LL = -3.4458483, nd = 0.0111260, D = 0.11613 0.11613 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 20, lrate = 0.05000, LL = -3.4456281, nd = 0.0107474, D = 0.11691 0.11691 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 21, lrate = 0.05000, LL = -3.4454248, nd = 0.0104621, D = 0.11705 0.11705 took 0.49 seconds - amica.core:optimize
INFO     | Iteration 22, lrate = 0.05000, LL = -3.4452315, nd = 0.0102427, D = 0.11668 0.11668 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 23, lrate = 0.05000, LL = -3.4450469, nd = 0.0100642, D = 0.11591 0.11591 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 24, lrate = 0.05000, LL = -3.4448684, nd = 0.0099194, D = 0.11485 0.11485 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 25, lrate = 0.05000, LL = -3.4446946, nd = 0.0097942, D = 0.11356 0.11356 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 26, lrate = 0.05000, LL = -3.4445274, nd = 0.0096848, D = 0.11212 0.11212 took 0.32 seconds - amica.core:optimize
INFO     | Iteration 27, lrate = 0.05000, LL = -3.4443640, nd = 0.0095878, D = 0.11055 0.11055 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 28, lrate = 0.05000, LL = -3.4442042, nd = 0.0094994, D = 0.10891 0.10891 took 0.88 seconds - amica.core:optimize
INFO     | Iteration 29, lrate = 0.05000, LL = -3.4440468, nd = 0.0094174, D = 0.10722 0.10722 took 1.72 seconds - amica.core:optimize
INFO     | Iteration 30, lrate = 0.05000, LL = -3.4438931, nd = 0.0093397, D = 0.10550 0.10550 took 1.20 seconds - amica.core:optimize
INFO     | Iteration 31, lrate = 0.05000, LL = -3.4437427, nd = 0.0092648, D = 0.10377 0.10377 took 1.30 seconds - amica.core:optimize
INFO     | Iteration 32, lrate = 0.05000, LL = -3.4435953, nd = 0.0091963, D = 0.10203 0.10203 took 0.69 seconds - amica.core:optimize
INFO     | Iteration 33, lrate = 0.05000, LL = -3.4434508, nd = 0.0091354, D = 0.10031 0.10031 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 34, lrate = 0.05000, LL = -3.4433075, nd = 0.0090772, D = 0.09860 0.09860 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 35, lrate = 0.05000, LL = -3.4431664, nd = 0.0090246, D = 0.09690 0.09690 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 36, lrate = 0.05000, LL = -3.4430270, nd = 0.0089755, D = 0.09524 0.09524 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 37, lrate = 0.05000, LL = -3.4428892, nd = 0.0089301, D = 0.09360 0.09360 took 0.30 seconds - amica.core:optimize
INFO     | Iteration 38, lrate = 0.05000, LL = -3.4427538, nd = 0.0088823, D = 0.09199 0.09199 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 39, lrate = 0.05000, LL = -3.4426197, nd = 0.0088381, D = 0.09042 0.09042 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 40, lrate = 0.05000, LL = -3.4424862, nd = 0.0087970, D = 0.08887 0.08887 took 0.30 seconds - amica.core:optimize
INFO     | Iteration 41, lrate = 0.05000, LL = -3.4423540, nd = 0.0087556, D = 0.08736 0.08736 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 42, lrate = 0.05000, LL = -3.4422232, nd = 0.0087197, D = 0.08588 0.08588 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 43, lrate = 0.05000, LL = -3.4420933, nd = 0.0086862, D = 0.08444 0.08444 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 44, lrate = 0.05000, LL = -3.4419646, nd = 0.0086524, D = 0.08303 0.08303 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 45, lrate = 0.05000, LL = -3.4418373, nd = 0.0086199, D = 0.08166 0.08166 took 0.31 seconds - amica.core:optimize
INFO     | Iteration 46, lrate = 0.05000, LL = -3.4417108, nd = 0.0085875, D = 0.08031 0.08031 took 0.39 seconds - amica.core:optimize
INFO     | Iteration 47, lrate = 0.05000, LL = -3.4415852, nd = 0.0085546, D = 0.07900 0.07900 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 48, lrate = 0.05000, LL = -3.4414605, nd = 0.0085204, D = 0.07772 0.07772 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 49, lrate = 0.05000, LL = -3.4413368, nd = 0.0084880, D = 0.07648 0.07648 took 0.40 seconds - amica.core:optimize
INFO     | Iteration 50, lrate = 0.05000, LL = -3.4412141, nd = 0.0073543, D = 0.07526 0.07526 took 0.50 seconds - amica.core:optimize
INFO     | Starting Newton ... setting numdecs to 0 - amica.core:optimize
INFO     | Iteration 51, lrate = 0.10000, LL = -3.4410153, nd = 0.0073382, D = 0.07393 0.07393 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 52, lrate = 0.20000, LL = -3.4406297, nd = 0.0072815, D = 0.07138 0.07138 took 0.49 seconds - amica.core:optimize
INFO     | Iteration 53, lrate = 0.30000, LL = -3.4400645, nd = 0.0072103, D = 0.06776 0.06776 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 54, lrate = 0.40000, LL = -3.4393286, nd = 0.0071177, D = 0.06335 0.06335 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 55, lrate = 0.50000, LL = -3.4384318, nd = 0.0070106, D = 0.05841 0.05841 took 0.90 seconds - amica.core:optimize
INFO     | Iteration 56, lrate = 0.60000, LL = -3.4373848, nd = 0.0068971, D = 0.05329 0.05329 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 57, lrate = 0.70000, LL = -3.4361987, nd = 0.0067655, D = 0.04824 0.04824 took 0.58 seconds - amica.core:optimize
INFO     | Iteration 58, lrate = 0.80000, LL = -3.4348913, nd = 0.0065746, D = 0.04351 0.04351 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 59, lrate = 0.90000, LL = -3.4334897, nd = 0.0063575, D = 0.03915 0.03915 took 0.50 seconds - amica.core:optimize
INFO     | Iteration 60, lrate = 1.00000, LL = -3.4320188, nd = 0.0061067, D = 0.03526 0.03526 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 61, lrate = 1.00000, LL = -3.4306358, nd = 0.0058437, D = 0.03208 0.03208 took 0.50 seconds - amica.core:optimize
INFO     | Iteration 62, lrate = 1.00000, LL = -3.4293480, nd = 0.0055608, D = 0.02950 0.02950 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 63, lrate = 1.00000, LL = -3.4281674, nd = 0.0052852, D = 0.02744 0.02744 took 0.79 seconds - amica.core:optimize
INFO     | Iteration 64, lrate = 1.00000, LL = -3.4270908, nd = 0.0050457, D = 0.02596 0.02596 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 65, lrate = 1.00000, LL = -3.4261086, nd = 0.0048192, D = 0.02501 0.02501 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 66, lrate = 1.00000, LL = -3.4252134, nd = 0.0046352, D = 0.02453 0.02453 took 1.11 seconds - amica.core:optimize
INFO     | Iteration 67, lrate = 1.00000, LL = -3.4243906, nd = 0.0044602, D = 0.02436 0.02436 took 0.58 seconds - amica.core:optimize
INFO     | Iteration 68, lrate = 1.00000, LL = -3.4236320, nd = 0.0042983, D = 0.02438 0.02438 took 0.42 seconds - amica.core:optimize
INFO     | Iteration 69, lrate = 1.00000, LL = -3.4229292, nd = 0.0041607, D = 0.02452 0.02452 took 0.68 seconds - amica.core:optimize
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INFO     | Iteration 71, lrate = 1.00000, LL = -3.4216493, nd = 0.0039241, D = 0.02491 0.02491 took 0.59 seconds - amica.core:optimize
INFO     | Iteration 72, lrate = 1.00000, LL = -3.4210611, nd = 0.0038298, D = 0.02513 0.02513 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 73, lrate = 1.00000, LL = -3.4205009, nd = 0.0037453, D = 0.02540 0.02540 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 74, lrate = 1.00000, LL = -3.4199619, nd = 0.0036837, D = 0.02570 0.02570 took 0.79 seconds - amica.core:optimize
INFO     | Iteration 75, lrate = 1.00000, LL = -3.4194385, nd = 0.0036249, D = 0.02600 0.02600 took 0.61 seconds - amica.core:optimize
INFO     | Iteration 76, lrate = 1.00000, LL = -3.4189275, nd = 0.0035612, D = 0.02632 0.02632 took 0.70 seconds - amica.core:optimize
INFO     | Iteration 77, lrate = 1.00000, LL = -3.4184312, nd = 0.0035074, D = 0.02664 0.02664 took 0.60 seconds - amica.core:optimize
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INFO     | Iteration 86, lrate = 1.00000, LL = -3.4147410, nd = 0.0028211, D = 0.03037 0.03037 took 0.49 seconds - amica.core:optimize
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INFO     | Iteration 88, lrate = 1.00000, LL = -3.4141223, nd = 0.0026898, D = 0.03132 0.03132 took 0.59 seconds - amica.core:optimize
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INFO     | Iteration 90, lrate = 1.00000, LL = -3.4135576, nd = 0.0025806, D = 0.03223 0.03223 took 0.59 seconds - amica.core:optimize
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INFO     | Iteration 92, lrate = 1.00000, LL = -3.4130358, nd = 0.0024917, D = 0.03309 0.03309 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 93, lrate = 1.00000, LL = -3.4127897, nd = 0.0024397, D = 0.03351 0.03351 took 1.72 seconds - amica.core:optimize
INFO     | Iteration 94, lrate = 1.00000, LL = -3.4125521, nd = 0.0023930, D = 0.03393 0.03393 took 1.59 seconds - amica.core:optimize
INFO     | Iteration 95, lrate = 1.00000, LL = -3.4123238, nd = 0.0023509, D = 0.03434 0.03434 took 0.61 seconds - amica.core:optimize
INFO     | Iteration 96, lrate = 1.00000, LL = -3.4121040, nd = 0.0023114, D = 0.03475 0.03475 took 0.58 seconds - amica.core:optimize
INFO     | Iteration 97, lrate = 1.00000, LL = -3.4118909, nd = 0.0022850, D = 0.03514 0.03514 took 0.60 seconds - amica.core:optimize
INFO     | Iteration 98, lrate = 1.00000, LL = -3.4116837, nd = 0.0022638, D = 0.03552 0.03552 took 0.59 seconds - amica.core:optimize
INFO     | Iteration 99, lrate = 1.00000, LL = -3.4114808, nd = 0.0022458, D = 0.03588 0.03588 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 100, lrate = 1.00000, LL = -3.4112805, nd = 0.0022392, D = 0.03622 0.03622 took 0.51 seconds - amica.core:optimize
INFO     | Iteration 101, lrate = 1.00000, LL = -3.4112473, nd = 0.0022956, D = 0.03622 0.03622 took 0.58 seconds - amica.core:optimize
INFO     | Iteration 102, lrate = 1.00000, LL = -3.4112207, nd = 0.0023272, D = 0.03622 0.03622 took 0.51 seconds - amica.core:optimize
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INFO     | Iteration 126, lrate = 1.00000, LL = -3.4074624, nd = 0.0018728, D = 0.04090 0.04090 took 0.91 seconds - amica.core:optimize
INFO     | Iteration 127, lrate = 1.00000, LL = -3.4073182, nd = 0.0018270, D = 0.04111 0.04111 took 0.90 seconds - amica.core:optimize
INFO     | Iteration 128, lrate = 1.00000, LL = -3.4071802, nd = 0.0017890, D = 0.04130 0.04130 took 0.69 seconds - amica.core:optimize
INFO     | Iteration 129, lrate = 1.00000, LL = -3.4070460, nd = 0.0017514, D = 0.04150 0.04150 took 0.81 seconds - amica.core:optimize
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INFO     | Iteration 196, lrate = 1.00000, LL = -3.4019946, nd = 0.0007490, D = 0.05059 0.05059 took 0.90 seconds - amica.core:optimize
INFO     | Iteration 197, lrate = 1.00000, LL = -3.4019579, nd = 0.0007465, D = 0.05073 0.05073 took 0.90 seconds - amica.core:optimize
INFO     | Iteration 198, lrate = 1.00000, LL = -3.4019210, nd = 0.0007458, D = 0.05088 0.05088 took 0.79 seconds - amica.core:optimize
INFO     | Iteration 199, lrate = 1.00000, LL = -3.4018832, nd = 0.0007426, D = 0.05102 0.05102 took 0.80 seconds - amica.core:optimize
INFO     | Iteration 200, lrate = 1.00000, LL = -3.4018445, nd = 0.0007407, D = 0.05115 0.05115 took 0.70 seconds - amica.core:optimize
WARNING  | Maximum number of iterations reached before convergence. Consider increasing max_iter or relaxing tol. - amica.core:optimize
INFO     | Finished in 121.91 seconds - amica.core:optimize

AMICA(max_iter=200,
      mu_init=array([[0.50965947, 0.04527889, 0.35247896],
       [0.8762351 , 0.26628711, 0.99480272],
       [0.40212523, 0.27389552, 0.20770561],
       [0.65411987, 0.34182142, 0.09300251],
       [0.80444938, 0.44339815, 0.8126825 ],
       [0.97930402, 0.74877807, 0.04348142],
       [0.78631199, 0.60419269, 0.85805117],
       [0.02165665, 0.84801097, 0.85489792],
       [0.27966586, 0.56910808, 0.53418476],
       [0....
       [0.76343641, 0.05840647, 0.34338642, ..., 0.97308572, 0.76182668,
        0.83096944],
       [0.58233765, 0.04081942, 0.43449808, ..., 0.33150471, 0.73984712,
        0.66007229],
       ...,
       [0.63443108, 0.33966091, 0.97756094, ..., 0.92677176, 0.24606719,
        0.54599154],
       [0.85448053, 0.88756462, 0.86326901, ..., 0.93752582, 0.87834654,
        0.02637342],
       [0.93852255, 0.64263167, 0.14632447, ..., 0.74057343, 0.5679117 ,
        0.47788761]], shape=(32, 32)))
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Compare results

def plot_topomaps(A, output="python"):
    fig, ax = plt.subplots(
        nrows=8,
        ncols=4,
        figsize=(8, 12),
        constrained_layout=True
        )
    for i, this_ax in zip(range(32), ax.flat):
        mne.viz.plot_topomap(
            A[:, i],
            pos=raw.info,
            axes=this_ax,
            show=False,
        )
        this_ax.set_title(f"Component {i}")
    fig.suptitle(f"AMICA Component Topomaps ({output})", fontsize=16)
    return fig, ax

fig1, ax1 = plot_topomaps(transformer.mixing_, output="python")
AMICA Component Topomaps (python), Component 0, Component 1, Component 2, Component 3, Component 4, Component 5, Component 6, Component 7, Component 8, Component 9, Component 10, Component 11, Component 12, Component 13, Component 14, Component 15, Component 16, Component 17, Component 18, Component 19, Component 20, Component 21, Component 22, Component 23, Component 24, Component 25, Component 26, Component 27, Component 28, Component 29, Component 30, Component 31

The Fortran mixing matrix is in sphered space. We need to unwhiten it first.

A_fortran = np.linalg.pinv(fortran_results['S']) @ fortran_results['A']
fig2, ax2 = plot_topomaps(A_fortran, output="fortran")
AMICA Component Topomaps (fortran), Component 0, Component 1, Component 2, Component 3, Component 4, Component 5, Component 6, Component 7, Component 8, Component 9, Component 10, Component 11, Component 12, Component 13, Component 14, Component 15, Component 16, Component 17, Component 18, Component 19, Component 20, Component 21, Component 22, Component 23, Component 24, Component 25, Component 26, Component 27, Component 28, Component 29, Component 30, Component 31

Total running time of the script: (2 minutes 7.955 seconds)

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