Tabular comparison of the limitations of different ICA algorithms

 

A tabular comparison of the limitations of different ICA algorithms:

ICA Algorithm

Key Limitations

When to Avoid

FastICA

- Assumes linear mixing
- Sensitive to outliers
- Requires non-Gaussian sources

Noisy data, Gaussian-like signals

Infomax ICA

- Slow convergence
- May get stuck in local optima
- Needs tuning of learning rate

Large datasets, real-time applications

JADE (Joint Approx. Diagonalization)

- Computationally expensive (O(n³))
- Struggles with high-dimensional data

Big data (e.g., 4D fMRI), low-resource systems

Robust ICA (R-FastICA)

- Still assumes near-linear mixing
- Complex parameter tuning

Strongly nonlinear mixtures

DeepICA (Neural ICA)

- Requires large datasets
- Black-box nature (less interpretable)
- High computational cost

Small datasets, when interpretability is critical

Online ICA

- Less accurate than batch ICA
- Sensitive to initialization
- Drift over time

Offline analysis, precision-critical tasks

Sparse ICA

- Dependency on sparsity level
- May lose weak but important components

Non-sparse sources (e.g., smooth signals)

t-ICA (Student’s t-ICA)

- Assumes heavy-tailed noise
- Slower than FastICA

Light-tailed noise distributions

Topographic ICA (TICA)

- Complex implementation
- Requires predefined topology

Unstructured data (no clear component hierarchy)

Kernel ICA

- Very high computational cost
- Hard to scale beyond small datasets

High-dimensional data (e.g., images)

Key Takeaways:

1.    Classic ICA (FastICA/JADE) struggles with noise, nonlinearity, and scalability.

2.    Deep/Neural ICA improves flexibility but sacrifices interpretability and speed.

3.    Robust/Online ICA trades accuracy for stability in real-world conditions.

4.    Domain-specific variants (e.g., Sparse/t-ICA) make assumptions that may not hold universally.

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