Independent component analysis (ICA) is a feature extraction technique in signal processing which can be considered a generalization of principal component analysis (PCA). ICA is most commonly used on the problem of blind signal separation (BSS).
The purpose of ICA is to separate a set of source signals from a set of mixed signals without requiring information about the source signals or the mixing process.
This concept can be more simply understood with the so-called cocktail-party problem, which deals with the difficult task of distinguishing between two original speech signals (i.e. two people talking independently of each other) when the signals are mixed together. Imagine that you are in a room where these two people are speaking simultaneously and being recorded by two microphones in different locations, with the microphones able to record time signals consisting of the amplitudes of the sound recordings and the time index. The goal of ICA, then, is to determine the original speech signals (see Figure 1 below) of the two people using only the mixed speech signals (see Figure 2 below) recorded by the two microphones.
ICA works by assuming that the mixed signals are made up of additive subcomponents which are non-Gaussian signals and statistically independent from each other. In other words, each subcomponent is treated as a random variable rather than a proper time signal.
While ICA was originally developed to solve problems like the cocktail-party problem, it has since been found that the technique has many more applications than first anticipated. Some of these include:
- Automatic removal of motion artifacts: identifying and removing motion related artifacts from functional MRI (fMRI) scans. (See ICA-AROMA)
- Separation of artifacts in magnetoencephalography (MEG) data: extracting the essential features of neuromagnetic signals in the presence of disruptive artifacts that may have higher amplitudes than the original brain signals and may resemble pathological signals in shape.
- Finding hidden factors in financial data: trying to reveal common underlying factors in data about currency exchange rates or daily returns of stocks that would otherwise remain hidden.
- Reducing noise in natural images: finding ICA filters for natural images and using the ICA decomposition to improve the clarity and sharpness of images that have been corrupted with additive Gaussiane noise.
Face recognition by Independent Component Analysis
M S Bartlett, J R Movellan, T J Sejnowski
Independent Component Analysis -- A Gentle Introduction
Independent Component Analysis: Algorithms and Applications
Aapo Hyvärinen, Erkki Oja
Introduction to Machine Learning 10701 Independent Component Analysis
Barnabás Póczos, Aarti Singh
Documentaries, videos and podcasts
Independent Components Analysis - Georgia Tech - Machine Learning
February 23, 2015
Independent Components Analysis Two - Georgia Tech - Machine Learning
February 23, 2015
Lecture 15 | Machine Learning (Stanford)
- Principal component analysis (PCA)Technique used to find the most valuable parts of all of the variables in a dataset and to then transform the original variables into a smaller set of linear combinations.
- Factor analysisA method for modeling observed variables and their variance/covariance structures in terms of a smaller number of underlying, unobservable factors.
- Projection pursuit
- Non-negative matrix factorization (NMF)A matrix factorization method where all of the values in matrices are constrained to be non-negative so that they are easier to inspect. It is useful in data mining because it has the effect of clustering the input data.
- Singular value decomposition (SVD)A popular method of matrix decomposition that reduces a complex matrix into its constituent parts so that subsequent matrix calculations are simpler.
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