infomax

The infomax package is an R implementation of the Infomax and Extended Infomax algorithms (Bell & Sejnowski, 1995; Makeig, Bell, Jung, & Sejnowski, 1996) for Independent Component Analysis.

Installation

The package is not currently released on CRAN.

You can install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("eegverse/infomax")

Example

library(infomax)
## basic example code

ICA can be used to separate linear mixtures of different, independent signal sources.

In the example below, we generate two independent signals and then mix them together.

time_x <- seq(0, 1, by = 1/256)
source_a <- sin(2 * pi * 5 * time_x)
source_b <- sin(2 * pi * 10 * time_x)
plot(time_x, source_a, type = "l")

plot(time_x, source_b, type = "l")

plot(time_x, source_a + 2 * source_b, type = "l")

plot(time_x, source_a * 3.4 + 1.5 * source_b, type = "l")

The function returns the estimated mixing matrix, unmixing matrix, and unmixed source timecourses.

mixed_data <- matrix(NA,
                     nrow = length(time_x),
                     ncol = 2)
mixed_data[, 1] <- source_a + 2 * source_b
mixed_data[, 2] <- source_a * 3.4 + 1.5 * source_b
dat_out <- run_infomax(mixed_data, whiten = "PCA")
#> Step: 1, lrate: 0.007213, wchange: 0.28490205, angledelta:  0.0
#> Step: 2, lrate: 0.007213, wchange: 0.19372638, angledelta:  0.0
#> Step: 3, lrate: 0.007213, wchange: 0.06888960, angledelta: 57.2
#> Step: 4, lrate: 0.007213, wchange: 0.01313297, angledelta: 110.8
#> Step: 5, lrate: 0.007069, wchange: 0.00574232, angledelta: 77.0
#> Step: 6, lrate: 0.006928, wchange: 0.00548345, angledelta: 123.5
#> Step: 7, lrate: 0.006789, wchange: 0.00702279, angledelta: 49.7
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#> Step: 9, lrate: 0.006653, wchange: 0.00209702, angledelta: 153.3
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#> Step: 11, lrate: 0.006520, wchange: 0.00798864, angledelta: 98.5
#> Step: 12, lrate: 0.006390, wchange: 0.01428885, angledelta: 108.8
#> Step: 13, lrate: 0.006262, wchange: 0.01934073, angledelta: 139.2
#> Step: 14, lrate: 0.006137, wchange: 0.00502298, angledelta: 19.1
#> Step: 15, lrate: 0.006137, wchange: 0.00600605, angledelta: 142.0
#> Step: 16, lrate: 0.006014, wchange: 0.00174998, angledelta: 104.8
#> Step: 17, lrate: 0.005894, wchange: 0.00060647, angledelta: 158.0
#> Step: 18, lrate: 0.005776, wchange: 0.01723064, angledelta: 91.6
#> Step: 19, lrate: 0.005661, wchange: 0.00226964, angledelta: 141.5
#> Step: 20, lrate: 0.005547, wchange: 0.00759579, angledelta: 69.5
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#> Step: 22, lrate: 0.005328, wchange: 0.00246479, angledelta: 136.2
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#> Step: 27, lrate: 0.004914, wchange: 0.02261153, angledelta: 132.0
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#> Step: 29, lrate: 0.004719, wchange: 0.00863023, angledelta: 66.3
#> Step: 30, lrate: 0.004625, wchange: 0.00616765, angledelta: 155.2
#> Step: 31, lrate: 0.004533, wchange: 0.00872553, angledelta: 10.6
#> Step: 32, lrate: 0.004533, wchange: 0.00936136, angledelta: 162.8
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#> Step: 38, lrate: 0.004015, wchange: 0.00671098, angledelta: 163.2
#> Step: 39, lrate: 0.003935, wchange: 0.00336665, angledelta: 138.5
#> Step: 40, lrate: 0.003856, wchange: 0.00502550, angledelta: 103.8
#> Step: 41, lrate: 0.003779, wchange: 0.00220277, angledelta: 137.1
#> Step: 42, lrate: 0.003703, wchange: 0.00158227, angledelta: 131.9
#> Step: 43, lrate: 0.003629, wchange: 0.00279609, angledelta: 145.9
#> Step: 44, lrate: 0.003557, wchange: 0.00688606, angledelta: 131.3
#> Step: 45, lrate: 0.003486, wchange: 0.00680703, angledelta: 173.0
#> Step: 46, lrate: 0.003416, wchange: 0.00250783, angledelta: 168.6
#> Step: 47, lrate: 0.003348, wchange: 0.00039759, angledelta: 168.2
#> Step: 48, lrate: 0.003281, wchange: 0.00013156, angledelta: 58.4
#> Step: 49, lrate: 0.003281, wchange: 0.00042586, angledelta: 121.1
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#> Step: 55, lrate: 0.002965, wchange: 0.00678104, angledelta: 156.3
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#> Step: 57, lrate: 0.002848, wchange: 0.00068130, angledelta: 77.9
#> Step: 58, lrate: 0.002791, wchange: 0.00112608, angledelta: 50.1
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#> Step: 60, lrate: 0.002791, wchange: 0.00174587, angledelta: 153.1
#> Step: 61, lrate: 0.002735, wchange: 0.00090990, angledelta: 56.7
#> Step: 62, lrate: 0.002735, wchange: 0.00108477, angledelta: 77.0
#> Step: 63, lrate: 0.002681, wchange: 0.00004078, angledelta: 81.2
#> Step: 64, lrate: 0.002627, wchange: 0.00272043, angledelta: 101.1
#> Step: 65, lrate: 0.002574, wchange: 0.00125290, angledelta: 128.3
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#> Step: 80, lrate: 0.001980, wchange: 0.00013104, angledelta: 65.6
#> Step: 81, lrate: 0.001940, wchange: 0.00000327, angledelta: 75.0
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#> Step: 84, lrate: 0.001863, wchange: 0.00305039, angledelta: 121.8
#> Step: 85, lrate: 0.001826, wchange: 0.00077491, angledelta: 121.1
#> Step: 86, lrate: 0.001790, wchange: 0.00093906, angledelta: 125.5
#> Step: 87, lrate: 0.001754, wchange: 0.00018180, angledelta: 93.3
#> Step: 88, lrate: 0.001719, wchange: 0.00015410, angledelta: 42.5
#> Step: 89, lrate: 0.001719, wchange: 0.00009494, angledelta: 99.1
#> Step: 90, lrate: 0.001684, wchange: 0.00041558, angledelta: 25.6
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#> Step: 97, lrate: 0.001492, wchange: 0.00009162, angledelta: 158.5
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#> Step: 113, lrate: 0.001102, wchange: 0.00010144, angledelta: 87.5
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#> Step: 115, lrate: 0.001058, wchange: 0.00017447, angledelta: 143.9
#> Step: 116, lrate: 0.001037, wchange: 0.00012742, angledelta: 126.1
#> Step: 117, lrate: 0.001016, wchange: 0.00005223, angledelta: 128.7
#> Step: 118, lrate: 0.000996, wchange: 0.00023688, angledelta: 106.6
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#> Step: 120, lrate: 0.000957, wchange: 0.00018728, angledelta: 170.5
#> Step: 121, lrate: 0.000938, wchange: 0.00005520, angledelta: 158.4
#> Step: 122, lrate: 0.000919, wchange: 0.00000947, angledelta: 126.7
#> Step: 123, lrate: 0.000900, wchange: 0.00003605, angledelta: 80.6
#> Step: 124, lrate: 0.000882, wchange: 0.00002980, angledelta: 120.0
#> Step: 125, lrate: 0.000865, wchange: 0.00001249, angledelta: 89.1
#> Step: 126, lrate: 0.000847, wchange: 0.00001080, angledelta: 155.9
#> Step: 127, lrate: 0.000830, wchange: 0.00006515, angledelta: 97.0
#> Step: 128, lrate: 0.000814, wchange: 0.00006241, angledelta: 101.0
#> Step: 129, lrate: 0.000798, wchange: 0.00004524, angledelta: 53.8
#> Step: 130, lrate: 0.000798, wchange: 0.00002732, angledelta: 132.1
#> Step: 131, lrate: 0.000782, wchange: 0.00004272, angledelta: 141.7
#> Step: 132, lrate: 0.000766, wchange: 0.00004027, angledelta: 142.4
#> Step: 133, lrate: 0.000751, wchange: 0.00001677, angledelta: 105.1
#> Step: 134, lrate: 0.000736, wchange: 0.00007619, angledelta: 69.0
#> Step: 135, lrate: 0.000721, wchange: 0.00002384, angledelta: 116.2
#> Step: 136, lrate: 0.000707, wchange: 0.00005678, angledelta: 16.6
#> ICA running time: 0.07 s
plot(time_x,
     dat_out$S[,1],
     type = "l")

plot(time_x,
     dat_out$S[,2],
     type = "l")

References

• Bell, A.J., & Sejnowski, T.J. (1995). An information-maximization approach to blind separation and blind deconvolution. Neural Computation, 7, 1129-159
• Makeig, S., Bell, A.J., Jung, T-P and Sejnowski, T.J., “Independent component analysis of electroencephalographic data,” In: D. Touretzky, M. Mozer and M. Hasselmo (Eds). Advances in Neural Information Processing Systems 8:145-151, MIT Press, Cambridge, MA (1996).