Note

Go to the end to download the full example code.

Run ICA On Toy Data

import matplotlib.pyplot as plt
import numpy as np

from sklearn.decomposition import FastICA

import amica
from amica import AMICA

Generate Data and Load AMICA Results for Comparison

%%

data_dir = amica.datasets.data_path() / "toy_2" / "amicaout_toy_2"

Downloading data from 'https://github.com/scott-huberty/amica/releases/download/v0.5.0/test_output.tar.gz' to file '/home/circleci/amica_test_data/0610669c678872814029216a7b152c02-test_output.tar.gz'.

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Downloading data from 'https://github.com/marcromani/cocktail/raw/refs/heads/master/examples/data/example2_baboon' to file '/home/circleci/amica_test_data/photos/example2_baboon'.

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x = amica.utils.generate_toy_data(n_samples=10_000, noise_factor=.05, seed=42)

Run AMICA and FastICA for comparison

fi = FastICA()
z = fi.fit_transform(x)

transformer = AMICA(mean_center=False, whiten="variance", random_state=42,)
transformer.fit(x.copy())

INFO     |  Getting the covariance matrix ... - amica.linalg:pre_whiten
INFO     | doing eigenvalue decomposition for 2 features ... - amica.linalg:pre_whiten
INFO     | minimum eigenvalues: [0.37647124] - amica.linalg:pre_whiten
INFO     | maximum eigenvalues: [0.8583412  0.37647124] - amica.linalg:pre_whiten
INFO     | num eigvals kept: 2 - amica.linalg:pre_whiten
INFO     | numeigs = 2, nw = 2 - amica.linalg:pre_whiten
INFO     | 1: block size = 10000 - amica.core:solve
INFO     | Solving. (please be patient, this may take a while)... - amica.core:solve
INFO     | Iteration 1, lrate = 0.05000, LL = -1.2404086, nd = 0.3271082, D = 0.00000 0.00000 took 0.18 seconds - amica.core:optimize
INFO     | Iteration 2, lrate = 0.05000, LL = -0.9388079, nd = 0.4452878, D = 0.00028 0.00028 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 3, lrate = 0.05000, LL = -0.3732032, nd = 1.4492905, D = 0.00283 0.00283 took 0.28 seconds - amica.core:optimize
INFO     | Iteration 4, lrate = 0.05000, LL = -0.7599340, nd = 9.0485077, D = 0.02049 0.02049 took 0.10 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 5, lrate = 0.05000, LL = -4.3733390, nd = 7.4506971, D = 0.09379 0.09379 took 0.01 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 6, lrate = 0.05000, LL = -1.3599251, nd = 1.0459140, D = 0.00300 0.00300 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 7, lrate = 0.05000, LL = -0.8593365, nd = 1.2508692, D = 0.00338 0.00338 took 0.20 seconds - amica.core:optimize
INFO     | Iteration 8, lrate = 0.05000, LL = -0.3891906, nd = 0.7114393, D = 0.02153 0.02153 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 9, lrate = 0.05000, LL = -0.2046074, nd = 4.1126799, D = 0.01819 0.01819 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 10, lrate = 0.05000, LL = -4.0326292, nd = 6.1754284, D = 0.04891 0.04891 took 0.01 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 11, lrate = 0.02500, LL = -1.1276689, nd = 0.7439036, D = 0.12458 0.12458 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 12, lrate = 0.02500, LL = -1.0260615, nd = 0.9633519, D = 0.10518 0.10518 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 13, lrate = 0.02500, LL = -0.9109509, nd = 1.2744462, D = 0.08356 0.08356 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 14, lrate = 0.02500, LL = -0.7315015, nd = 1.7270097, D = 0.05955 0.05955 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 15, lrate = 0.02500, LL = -0.4263898, nd = 2.0082044, D = 0.03453 0.03453 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 16, lrate = 0.02500, LL = -0.2171495, nd = 3.3470332, D = 0.01634 0.01634 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 17, lrate = 0.02500, LL = -0.5501854, nd = 6.0195004, D = 0.04675 0.04675 took 0.10 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 18, lrate = 0.02500, LL = -1.0080710, nd = 5.5384510, D = 0.00411 0.00411 took 0.01 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 19, lrate = 0.02500, LL = -0.4563570, nd = 2.7422435, D = 0.02381 0.02381 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 20, lrate = 0.02500, LL = -0.4066058, nd = 4.7236690, D = 0.02573 0.02573 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 21, lrate = 0.02500, LL = -0.6955061, nd = 5.1571653, D = 0.02670 0.02670 took 0.09 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 22, lrate = 0.01250, LL = -0.4699946, nd = 3.5127570, D = 0.02670 0.02670 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 23, lrate = 0.01250, LL = -0.2256437, nd = 1.9579720, D = 0.02675 0.02675 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 24, lrate = 0.01250, LL = -0.0741462, nd = 3.0094490, D = 0.02652 0.02652 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 25, lrate = 0.01250, LL = -0.2005211, nd = 7.0580107, D = 0.02725 0.02725 took 0.01 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 26, lrate = 0.01250, LL = -1.2528611, nd = 12.5408472, D = 0.02606 0.02606 took 0.09 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 27, lrate = 0.01250, LL = -1.0761606, nd = 3.4892089, D = 0.02678 0.02678 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 28, lrate = 0.01250, LL = -0.5022428, nd = 1.7313613, D = 0.02680 0.02680 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 29, lrate = 0.01250, LL = -0.2475714, nd = 1.3936721, D = 0.02684 0.02684 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 30, lrate = 0.01250, LL = -0.0596082, nd = 1.1056724, D = 0.02705 0.02705 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 31, lrate = 0.01250, LL = -0.0209911, nd = 3.2504222, D = 0.02683 0.02683 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 32, lrate = 0.01250, LL = -0.2988120, nd = 9.0796415, D = 0.02777 0.02777 took 0.09 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 33, lrate = 0.00625, LL = -0.3873452, nd = 7.4532201, D = 0.02684 0.02684 took 0.01 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 34, lrate = 0.00625, LL = -0.1712784, nd = 3.6463878, D = 0.02692 0.02692 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 35, lrate = 0.00625, LL = -0.0306190, nd = 1.7708229, D = 0.02699 0.02699 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 36, lrate = 0.00625, LL = 0.0057096, nd = 1.8354946, D = 0.02712 0.02712 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 37, lrate = 0.00625, LL = -0.0017881, nd = 3.0292594, D = 0.02692 0.02692 took 0.01 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 38, lrate = 0.00625, LL = -0.0461398, nd = 4.8991281, D = 0.02732 0.02732 took 0.09 seconds - amica.core:optimize
INFO     | Likelihood decreasing! - amica.core:optimize
INFO     | Iteration 39, lrate = 0.00313, LL = 0.0054423, nd = 2.2609983, D = 0.02703 0.02703 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 40, lrate = 0.00313, LL = 0.0203280, nd = 1.0488128, D = 0.02708 0.02708 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 41, lrate = 0.00313, LL = 0.0235723, nd = 0.6412568, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 42, lrate = 0.00313, LL = 0.0246634, nd = 0.4099266, D = 0.02707 0.02707 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 43, lrate = 0.00313, LL = 0.0253594, nd = 0.2874689, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 44, lrate = 0.00313, LL = 0.0259008, nd = 0.2012207, D = 0.02707 0.02707 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 45, lrate = 0.00313, LL = 0.0263752, nd = 0.1532054, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 46, lrate = 0.00313, LL = 0.0268068, nd = 0.1110954, D = 0.02707 0.02707 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 47, lrate = 0.00313, LL = 0.0272101, nd = 0.0904491, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 48, lrate = 0.00313, LL = 0.0275888, nd = 0.0660557, D = 0.02708 0.02708 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 49, lrate = 0.00313, LL = 0.0279465, nd = 0.0589878, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 50, lrate = 0.00313, LL = 0.0282845, nd = 0.0001178, D = 0.02708 0.02708 took 0.09 seconds - amica.core:optimize
INFO     | Starting Newton ... setting numdecs to 0 - amica.core:optimize
INFO     | Iteration 51, lrate = 0.00625, LL = 0.0286074, nd = 0.0000768, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 52, lrate = 0.01250, LL = 0.0289080, nd = 0.0000687, D = 0.02708 0.02708 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 53, lrate = 0.02500, LL = 0.0291901, nd = 0.0000660, D = 0.02708 0.02708 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 54, lrate = 0.05000, LL = 0.0294545, nd = 0.0000621, D = 0.02708 0.02708 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 55, lrate = 0.10000, LL = 0.0297017, nd = 0.0000563, D = 0.02708 0.02708 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 56, lrate = 0.20000, LL = 0.0299319, nd = 0.0000481, D = 0.02708 0.02708 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 57, lrate = 0.30000, LL = 0.0301453, nd = 0.0000400, D = 0.02709 0.02709 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 58, lrate = 0.40000, LL = 0.0303423, nd = 0.0000325, D = 0.02709 0.02709 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 59, lrate = 0.50000, LL = 0.0305234, nd = 0.0000260, D = 0.02709 0.02709 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 60, lrate = 0.60000, LL = 0.0306888, nd = 0.0000209, D = 0.02709 0.02709 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 61, lrate = 0.70000, LL = 0.0308391, nd = 0.0000171, D = 0.02710 0.02710 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 62, lrate = 0.80000, LL = 0.0309749, nd = 0.0000143, D = 0.02710 0.02710 took 0.09 seconds - amica.core:optimize
INFO     | Iteration 63, lrate = 0.90000, LL = 0.0310968, nd = 0.0000122, D = 0.02710 0.02710 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 64, lrate = 1.00000, LL = 0.0312055, nd = 0.0000106, D = 0.02710 0.02710 took 0.20 seconds - amica.core:optimize
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INFO     | Iteration 67, lrate = 1.00000, LL = 0.0314592, nd = 0.0000085, D = 0.02710 0.02710 took 0.09 seconds - amica.core:optimize
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INFO     | Iteration 81, lrate = 1.00000, LL = 0.0317771, nd = 0.0000016, D = 0.02709 0.02709 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 82, lrate = 1.00000, LL = 0.0317772, nd = 0.0000015, D = 0.02709 0.02709 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 83, lrate = 1.00000, LL = 0.0317772, nd = 0.0000015, D = 0.02709 0.02709 took 0.01 seconds - amica.core:optimize
INFO     | Iteration 84, lrate = 1.00000, LL = 0.0317773, nd = 0.0000014, D = 0.02709 0.02709 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 85, lrate = 1.00000, LL = 0.0317773, nd = 0.0000013, D = 0.02709 0.02709 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 86, lrate = 1.00000, LL = 0.0317773, nd = 0.0000012, D = 0.02709 0.02709 took 0.10 seconds - amica.core:optimize
INFO     | Iteration 87, lrate = 1.00000, LL = 0.0317774, nd = 0.0000012, D = 0.02709 0.02709 took 0.09 seconds - amica.core:optimize
INFO     | Exiting because likelihood increasing by less than 1e-07 for more than 5 iterations ... - amica.core:optimize
INFO     | Finished in 5.98 seconds - amica.core:optimize

AMICA(mean_center=False, random_state=42, whiten='variance')
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apply the learned unmixing matrix to the data

y = transformer.transform(x)

fortran_results = amica.utils.load_fortran_results(
    data_dir, n_components=2, n_mixtures=3
    )
W_f = fortran_results["W"][:, :, 0]
y2 = x @ (W_f @ fortran_results["S"]).T

Plot Results

fig, ax = plt.subplots(4, 1, sharex=True)
for i, l, v in zip([1, 2, 3, 4], ['Sources', 'AMICA', 'AMICA-Python', 'FastICA'], [x, y2, y, z]):
    ax = plt.subplot(4, 1, i)
    ax.plot(v[:1000])
    ax.set_xticks([])
    ax.set_yticks([])
    ax.set_ylabel(l)
    ax.set_ylim([-1.1 * np.max(v), 1.1 * np.max(v)])
plot toy

Total running time of the script: (0 minutes 15.644 seconds)

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