2nd/10_Wiki/Topics/AI_and_ML/Independent Component Analysis (ICA).md

---
id: wiki-2026-0508-independent-component-analysis-i
title: Independent Component Analysis (ICA)
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [ICA, FastICA, blind source separation, cocktail party, sklearn ICA]
duplicate_of: none
source_trust_level: A
confidence_score: 0.94
verification_status: applied
tags: [statistics, ica, source-separation, signal-processing, dimensionality]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: scikit-learn / MNE-Python
---

# Independent Component Analysis (ICA)

## 매 한 줄
> **"매 mixed signal 의 의 의 statistically independent source 의 separate"**. 매 cocktail party problem. 매 vs PCA: 매 ICA 의 non-Gaussian / independence, 매 PCA 의 variance-max. 매 famous: FastICA. 매 응용: 매 EEG 의 artifact remove, 매 audio source separate.

## 매 핵심

### 매 model
- 매 X = AS — 매 X (observed mix), A (mixing matrix), S (independent sources).
- 매 estimate W ≈ A⁻¹ → 매 S = WX.

### 매 vs PCA
- **PCA**: 매 uncorrelated + variance max.
- **ICA**: 매 statistically independent (stronger).

### 매 응용
1. **EEG**: 매 eye blink / muscle artifact remove.
2. **Audio**: 매 source separation (legacy — modern uses DL).
3. **fMRI**: 매 default mode network identify.
4. **Finance**: 매 factor extraction.

## 💻 패턴

### scikit-learn FastICA
```python
from sklearn.decomposition import FastICA
ica = FastICA(n_components=3, random_state=0)
S = ica.fit_transform(X)  # 매 X: [n_samples, n_features]
A = ica.mixing_  # 매 mixing matrix
# 매 X ≈ S @ A.T
```

### Cocktail party (3 mics, 3 speakers)
```python
import numpy as np
from sklearn.decomposition import FastICA

# 매 3 sources
t = np.linspace(0, 8, 2000)
s1 = np.sin(2 * t)
s2 = np.sign(np.sin(3 * t))
s3 = np.random.normal(size=2000)

S = np.c_[s1, s2, s3]
A = np.array([[1, 1, 1], [0.5, 2, 1], [1.5, 1, 2]])
X = S @ A.T  # 매 3 mics

ica = FastICA(n_components=3)
S_estimated = ica.fit_transform(X)
```

### EEG artifact removal (MNE)
```python
import mne
raw = mne.io.read_raw_edf('eeg.edf', preload=True)
ica = mne.preprocessing.ICA(n_components=20, random_state=0).fit(raw)

# 매 detect eye blink (using EOG)
eog_idx, scores = ica.find_bads_eog(raw, ch_name='EOG')
ica.exclude = eog_idx
ica.apply(raw)  # 매 modify raw in-place
```

### Whitening (preprocess)
```python
def whiten(X):
    X_centered = X - X.mean(axis=0)
    cov = np.cov(X_centered.T)
    U, S, _ = np.linalg.svd(cov)
    W = U @ np.diag(1 / np.sqrt(S + 1e-9)) @ U.T
    return X_centered @ W
```

### FastICA (manual)
```python
def fast_ica(X, n_components, max_iter=200, tol=1e-4):
    """매 simplified FastICA via deflation."""
    X_white = whiten(X)
    W = np.zeros((n_components, X.shape[1]))
    for i in range(n_components):
        w = np.random.randn(X.shape[1])
        w /= np.linalg.norm(w)
        for _ in range(max_iter):
            wx = X_white @ w
            g = np.tanh(wx)  # 매 nonlinearity
            g_prime = 1 - g ** 2
            w_new = (X_white.T @ g) / X.shape[0] - g_prime.mean() * w
            
            # 매 deflate (orthogonalize against found components)
            for j in range(i):
                w_new -= (w_new @ W[j]) * W[j]
            w_new /= np.linalg.norm(w_new)
            
            if abs(abs(w @ w_new) - 1) < tol: break
            w = w_new
        W[i] = w
    return W
```

### Validate (correlation with known sources)
```python
def correlate_with_sources(estimated, true_sources):
    # 매 each estimated → best-matching true
    n = estimated.shape[1]
    matches = []
    for i in range(n):
        best_corr = max(abs(np.corrcoef(estimated[:, i], true_sources[:, j])[0, 1]) for j in range(n))
        matches.append(best_corr)
    return matches  # 매 ideally close to 1
```

### Audio source separation (legacy)
```python
import scipy.io.wavfile as wav
sr, mix = wav.read('mix.wav')  # 매 stereo
ica = FastICA(n_components=2)
S = ica.fit_transform(mix)
wav.write('source1.wav', sr, S[:, 0])
wav.write('source2.wav', sr, S[:, 1])
```

### Component selection (EEG)
```python
def detect_artifact_components(ica, raw):
    bad = []
    eog_idx, _ = ica.find_bads_eog(raw)
    ecg_idx, _ = ica.find_bads_ecg(raw)
    return eog_idx + ecg_idx
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Source separation | ICA (small N) |
| Audio modern | DL (Demucs) — not ICA |
| EEG artifact | MNE-Python ICA |
| fMRI | spatial ICA |
| Variance reduction | PCA (not ICA) |

**기본값**: 매 EEG / fMRI = ICA. 매 modern audio = DL. 매 always whitening preprocess.

## 🔗 Graph
- 부모: [[Statistics]]
- 변형: [[FastICA]]
- Adjacent: [[PCA]] · [[Factor-Analysis]]

## 🤖 LLM 활용
**언제**: 매 EEG / fMRI. 매 small-source separation.
**언제 X**: 매 modern audio (use Demucs).

## ❌ 안티패턴
- **No whitening**: 매 convergence X.
- **N components > N sources**: 매 noise component.
- **Gaussian sources**: 매 ICA fail (need non-Gaussian).
- **Order assumption**: 매 ICA 매 component order arbitrary.

## 🧪 검증 / 중복
- Verified (Hyvärinen FastICA 2000, MNE docs).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — ICA + 매 sklearn / MNE / manual / cocktail code |