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json
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English
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Tags:
time-series
time-series-decomposition
benchmark
component-recovery
symbolic-regression
icml-2026
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17b7ba4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 | import numpy as np
from typing import Dict, Any, List, Optional
from ..core import DecompResult
from ..registry import MethodRegistry
from .utils import dominant_frequency
try:
from vmdpy import VMD
_HAS_VMD = True
except ImportError:
_HAS_VMD = False
def select_seasonal_modes(
freqs: np.ndarray,
primary_freq: Optional[float],
num_modes: int,
) -> List[int]:
if primary_freq and primary_freq > 0:
order = np.argsort(np.abs(freqs - primary_freq))
else:
order = np.argsort(-freqs) # choose higher-frequency modes if no hint
selected = []
for idx in order:
idx_val = int(np.asarray(idx).ravel()[0])
if idx_val not in selected:
selected.append(idx_val)
if len(selected) >= max(1, num_modes):
break
return selected
@MethodRegistry.register("VMD")
def vmd_decompose(
y: np.ndarray,
params: Dict[str, Any],
) -> DecompResult:
if not _HAS_VMD:
raise ImportError("vmdpy is required for VMD decomposition.")
cfg = params.copy()
# v1.1.0: Auto-calculate K based on periods if not specified
periods = cfg.get("periods", [])
primary_period = cfg.get("primary_period")
if not periods and primary_period:
periods = [primary_period]
n_periods = max(1, len(periods)) if periods else 1
default_K = max(5, 2 * n_periods + 2) # At least trend + seasonal modes + buffer
K = int(cfg.get("K", default_K))
alpha = float(cfg.get("alpha", 300.0)) # v1.1.0: reduced from 2000 to 300
tau = float(cfg.get("tau", 0.0))
DC = int(cfg.get("DC", 0))
init = int(cfg.get("init", 1))
tol = float(cfg.get("tol", 1e-7))
modes, _, omega = VMD(y, alpha, tau, K, DC, init, tol)
modes = np.asarray(modes, dtype=float)
if modes.ndim == 1:
modes = modes[np.newaxis, :]
omega = np.asarray(omega, dtype=float)
if omega.ndim == 2:
omega = omega[-1]
fs = float(cfg.get("fs", 1.0))
scale = fs / (2 * np.pi) if fs > 0 else 1.0
freqs = np.abs(omega) * scale
dom_freqs = np.array([dominant_frequency(mode, fs) for mode in modes])
primary_period = cfg.get("primary_period")
primary_freq = 1.0 / float(primary_period) if primary_period else None
freq_basis = dom_freqs if np.all(np.isfinite(dom_freqs)) and dom_freqs.any() else freqs
trend_cutoff = cfg.get(
"trend_freq_max",
primary_freq / 5.0 if primary_freq else max(float(np.min(freq_basis)) * 1.5, 0.01),
)
trend_mask = freq_basis <= max(trend_cutoff, 1e-6)
if not trend_mask.any():
trend_mask[np.argmin(freq_basis)] = True
trend_indices = np.where(trend_mask)[0].tolist()
seasonal_num = int(cfg.get("seasonal_num_modes", 1))
seasonal_indices = select_seasonal_modes(freq_basis, primary_freq, num_modes=seasonal_num)
seasonal_indices = [idx for idx in seasonal_indices if idx not in trend_indices]
if not seasonal_indices:
alt = np.argsort(freqs)[::-1]
for idx in alt:
if idx not in trend_indices:
seasonal_indices.append(int(idx))
if len(seasonal_indices) >= seasonal_num:
break
season_mask = np.zeros(len(freqs), dtype=bool)
for idx in seasonal_indices:
season_mask[idx] = True
season = modes[season_mask].sum(axis=0) if seasonal_indices else np.zeros_like(modes[0])
noise_mask = ~(trend_mask | season_mask)
residual = modes[noise_mask].sum(axis=0) if noise_mask.any() else np.zeros_like(season)
# v1.1.0: Direct trend extraction from low-freq modes (not subtraction)
trend = modes[trend_mask].sum(axis=0) if trend_mask.any() else np.zeros_like(season)
return DecompResult(
trend=trend,
season=season,
residual=residual,
meta={
"method": "VMD",
"center_frequencies": freqs.tolist(),
"dominant_frequencies": dom_freqs.tolist(),
"trend_index": trend_indices,
"season_indices": seasonal_indices,
}
)
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