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| import numpy as np from scipy.signal import hilbert from scipy.stats import entropy
class EEGComplexityAnalyzer: """ EEG 复杂度分析器 Nature 2024 论文核心: 思维游离时 EEG 复杂度变化 关键指标: 1. 多尺度熵(Multiscale Entropy) 2. Lempel-Ziv复杂度 3. Hurst指数 """ def __init__(self): pass def compute_multiscale_entropy(self, eeg_signal: np.ndarray, scales: list = None, m: int = 2, r: float = 0.2) -> dict: """ 多尺度样本熵 论文发现: 思维游离时,小尺度熵降低,大尺度熵增加 Args: eeg_signal: EEG 信号, shape=(N,) scales: 尺度列表(默认 1-20) m: 嵌入维度 r: 相似度阈值(标准差的倍数) Returns: dict: { "mse_values": 各尺度熵值, "mse_trend": 熵值趋势, "mind_wandering_indicator": float } """ if scales is None: scales = range(1, 21) mse_values = [] for scale in scales: coarse_grained = self._coarse_grain(eeg_signal, scale) sampen = self._sample_entropy(coarse_grained, m, r) mse_values.append(sampen) mse_values = np.array(mse_values) mse_trend = np.polyfit(scales, mse_values, 1)[0] small_scale_entropy = np.mean(mse_values[:5]) large_scale_entropy = np.mean(mse_values[-5:]) mind_wandering_indicator = large_scale_entropy - small_scale_entropy return { "mse_values": mse_values, "mse_trend": mse_trend, "small_scale_entropy": small_scale_entropy, "large_scale_entropy": large_scale_entropy, "mind_wandering_indicator": mind_wandering_indicator } def _coarse_grain(self, signal: np.ndarray, scale: int) -> np.ndarray: """粗粒化""" n = len(signal) coarse_len = n // scale coarse = np.zeros(coarse_len) for i in range(coarse_len): coarse[i] = np.mean(signal[i*scale:(i+1)*scale]) return coarse def _sample_entropy(self, signal: np.ndarray, m: int = 2, r: float = 0.2) -> float: """样本熵""" n = len(signal) if n < m + 1: return 0.0 std = np.std(signal) r_threshold = r * std vectors_m = np.array([signal[i:i+m] for i in range(n - m)]) vectors_m1 = np.array([signal[i:i+m+1] for i in range(n - m - 1)]) def count_similar_pairs(vectors, threshold): count = 0 for i in range(len(vectors)): for j in range(i+1, len(vectors)): if np.max(np.abs(vectors[i] - vectors[j])) < threshold: count += 1 return count count_m = count_similar_pairs(vectors_m, r_threshold) count_m1 = count_similar_pairs(vectors_m1, r_threshold) if count_m == 0 or count_m1 == 0: return np.inf sampen = -np.log(count_m1 / count_m) return sampen def compute_lempel_ziv_complexity(self, eeg_signal: np.ndarray) -> float: """ Lempel-Ziv 复杂度 论文发现: 思维游离时 LZ 复杂度增加 Args: eeg_signal: EEG 信号 Returns: lz_complexity: LZ 复杂度值 """ mean_val = np.mean(eeg_signal) binary_signal = (eeg_signal > mean_val).astype(int) n = len(binary_signal) c = 1 s = binary_signal[0] for i in range(1, n): current_subseq = binary_signal[:i+1] found = False for j in range(i): if np.array_equal(binary_signal[j:i+1], current_subseq[j:i+1-j]): found = True break if not found: c += 1 lz_complexity = c * np.log2(n) / n return lz_complexity def compute_hurst_exponent(self, eeg_signal: np.ndarray) -> float: """ Hurst 指数 论文发现: 思维游离时 Hurst 指数变化 H < 0.5: 反持久性 H ≈ 0.5: 随机 H > 0.5: 持久性 Args: eeg_signal: EEG 信号 Returns: hurst_exponent: Hurst 指数 """ n = len(eeg_signal) mean_val = np.mean(eeg_signal) cumulative_deviation = np.cumsum(eeg_signal - mean_val) R = np.max(cumulative_deviation) - np.min(cumulative_deviation) S = np.std(eeg_signal) if S == 0: return 0.5 H = np.log(R / S) / np.log(n) return H def detect_mind_wandering(self, eeg_signal: np.ndarray) -> dict: """ 检测思维游离 综合多个复杂度指标 Args: eeg_signal: EEG 信号 Returns: dict: { "is_mind_wandering": bool, "confidence": float, "mse_indicator": float, "lz_complexity": float, "hurst": float } """ mse_result = self.compute_multiscale_entropy(eeg_signal) lz = self.compute_lempel_ziv_complexity(eeg_signal) hurst = self.compute_hurst_exponent(eeg_signal) is_mind_wandering = ( mse_result["mind_wandering_indicator"] > 0.5 and lz > 0.8 and abs(hurst - 0.5) > 0.1 ) confidence = ( mse_result["mind_wandering_indicator"] * 0.4 + lz * 0.3 + abs(hurst - 0.5) * 0.3 ) return { "is_mind_wandering": is_mind_wandering, "confidence": confidence, "mse_indicator": mse_result["mind_wandering_indicator"], "lz_complexity": lz, "hurst": hurst, "mse_values": mse_result["mse_values"] }
if __main__ == "__main__": analyzer = EEGComplexityAnalyzer() np.random.seed(42) focused_eeg = np.random.normal(0, 1, 1000) + 0.5 * np.sin(np.arange(1000) / 10) wandering_eeg = np.random.normal(0, 1.5, 1000) print("=== 专注状态 ===") focused_result = analyzer.detect_mind_wandering(focused_eeg) print(f"思维游离: {focused_result['is_mind_wandering']}") print(f"置信度: {focused_result['confidence']:.3f}") print(f"MSE 指标: {focused_result['mse_indicator']:.3f}") print(f"LZ 复杂度: {focused_result['lz_complexity']:.3f}") print(f"Hurst 指数: {focused_result['hurst']:.3f}") print("\n=== 思维游离 ===") wandering_result = analyzer.detect_mind_wandering(wandering_eeg) print(f"思维游离: {wandering_result['is_mind_wandering']}") print(f"置信度: {wandering_result['confidence']:.3f}") print(f"MSE 指标: {wandering_result['mse_indicator']:.3f}") print(f"LZ 复杂度: {wandering_result['lz_complexity']:.3f}") print(f"Hurst 指数: {wandering_result['hurst']:.3f}")
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