Expand description

Independent Component Analysis (ICA)

linfa-ica aims to provide pure Rust implementations of ICA algorithms.

ICA separates mutivariate signals into their additive, independent subcomponents. ICA is primarily used for separating superimposed signals and not for dimensionality reduction.

Input data is whitened (remove underlying correlation) before modeling.

The Big Picture

linfa-ica is a crate in the linfa ecosystem, an effort to create a toolkit for classical Machine Learning implemented in pure Rust, akin to Python’s scikit-learn.

Current state

linfa-ica currently provides an implementation of the following methods:

  • Fast Independent Component Analysis (Fast ICA)


Here’s an example of ICA unmixing the mixture of two signals

use linfa::{
    traits::{Fit, Predict},
use linfa_ica::fast_ica::{FastIca, GFunc};
use ndarray::{array, concatenate};
use ndarray::{Array, Array2, Axis};
use ndarray_npy::write_npy;
use ndarray_rand::{rand::SeedableRng, rand_distr::Uniform, RandomExt};
use rand_xoshiro::Xoshiro256Plus;

let nsamples = 2000;
// Creating a sine wave signal
let source1 = Array::linspace(0., 8., nsamples).mapv(|x| (2f64 * x).sin());
// Creating a sawtooth signal
let source2 = Array::linspace(0., 8., nsamples).mapv(|x| {
    let tmp = (4f64 * x).sin();
    if tmp > 0. {
        return 1.;

// Column concatenating both the signals
let mut sources_original = concatenate![

// Adding random noise to the signals
let mut rng = Xoshiro256Plus::seed_from_u64(42);
sources_original +=
    &Array::random_using((2000, 2), Uniform::new(0.0, 1.0), &mut rng).mapv(|x| x * 0.2);

// Mixing the two signals
let mixing = array![[1., 1.], [0.5, 2.]];
// Shape of the data is (2000 x 2)
// This data will be unmixed by ICA to recover back the original signals
let sources_mixed = sources_original.dot(&mixing.t());

// Fitting the model
// We set the G function used in the approximation of neg-entropy as logcosh
// with its alpha value as 1
// `ncomponents` is not set, it will be automatically be assigned 2 from
// the input
let ica = FastIca::params().gfunc(GFunc::Logcosh(1.0));
let ica = ica.fit(&DatasetBase::from(sources_mixed.view())).unwrap();

// Here we unmix the data to recover back the original signals
let sources_ica = ica.predict(&sources_mixed);


Fast algorithm for Independent Component Analysis (ICA)