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

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

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)

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)

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)

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)

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)

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)

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)

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