Independent Component Analysis

Independent component analysis separates observed multivariate signals into statistically independent, non-Gaussian source components by maximizing non-Gaussianity of linear projections.

독립성분분석은 선형 투영의 비정규성을 최대화해 관측된 다변량 신호를 통계적으로 독립인 비정규 원천 성분으로 분리하는 기법입니다.

My sensor readings look like mixtures of several underlying signals; how can I separate the original sources?

센서 측정값이 여러 신호가 섞인 것 같은데, 원래 신호들을 어떻게 분리할 수 있나요?

Independent component analysis assumes the observed variables are linear mixtures of independent non-Gaussian sources and estimates an unmixing matrix that makes the recovered components as non-Gaussian as possible. FastICA on standardized inputs returns the components and a mixing matrix, although the sign, scale and order of the components are not identified.

When to use Independent Component Analysis

• Observed variables are plausibly linear mixtures of independent source signals.
• The sources are expected to be non-Gaussian, for example skewed or heavy-tailed.
• You want to remove artifacts or isolate distinct signals in multichannel data.

When to use something else

• You only want to summarize variance with uncorrelated components; use principal component analysis instead.
• You want latent variables that explain correlations among items; use exploratory factor analysis instead.

Assumptions and requirements

• Sources are statistically independent.
• At most one source is Gaussian.
• Mixing is linear and instantaneous.
• The number of components does not exceed the number of observed variables.

What the analysis reports

• Mixing matrix
• Reconstruction error (RMSE) of the standardized inputs
• Excess kurtosis of each component
• Convergence information

How to report it

Independent component analysis (FastICA, standardized inputs; N = [n]) extracted [k] components from [p] variables; the algorithm converged after [value] iterations.

Related methods

• Principal Component Analysis (PCA)
• Exploratory Factor Analysis (EFA)
• Non Negative Matrix Factorization (NMF)

Run Independent Component Analysis on Quorant