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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 | from __future__ import annotations
from time import perf_counter
from typing import Any, Dict, List
import numpy as np
from ..backends import finalize_result, split_runtime_params
from ..core import DecompResult
from ..registry import MethodRegistry
from .utils import dominant_frequency
try:
from sklearn.utils.extmath import randomized_svd
_HAS_RANDOMIZED_SVD = True
_RANDOMIZED_SVD_IMPORT_ERROR = None
except Exception as exc: # pragma: no cover - optional import path
randomized_svd = None
_HAS_RANDOMIZED_SVD = False
_RANDOMIZED_SVD_IMPORT_ERROR = exc
def _diagonal_averaging(matrix: np.ndarray) -> np.ndarray:
rows, cols = matrix.shape
length = rows + cols - 1
recon = np.zeros(length, dtype=float)
counts = np.zeros(length, dtype=float)
for i in range(rows):
for j in range(cols):
recon[i + j] += matrix[i, j]
counts[i + j] += 1.0
counts[counts == 0.0] = 1.0
return recon / counts
def _build_mssa_trajectory(y: np.ndarray, window: int) -> np.ndarray:
length, n_channels = y.shape
k = length - window + 1
trajectory = np.empty((window * n_channels, k), dtype=float)
for channel_idx in range(n_channels):
offset = channel_idx * window
channel = y[:, channel_idx]
for col in range(k):
trajectory[offset : offset + window, col] = channel[col : col + window]
return trajectory
def _reconstruct_mode(mode_matrix: np.ndarray, window: int, n_channels: int, length: int) -> np.ndarray:
mode = np.empty((length, n_channels), dtype=float)
for channel_idx in range(n_channels):
start = channel_idx * window
stop = start + window
mode[:, channel_idx] = _diagonal_averaging(mode_matrix[start:stop, :])[:length]
return mode
def _fit_svd(
trajectory: np.ndarray,
rank: int,
speed_mode: str,
seed: int | None,
) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
max_rank = min(rank, trajectory.shape[0], trajectory.shape[1])
if max_rank <= 0:
raise ValueError("MSSA rank must be positive.")
if speed_mode == "fast":
if not _HAS_RANDOMIZED_SVD:
raise ImportError(
"MSSA speed_mode='fast' requires scikit-learn randomized_svd."
) from _RANDOMIZED_SVD_IMPORT_ERROR
n_iter = 5 if max_rank <= 8 else 7
U, s, Vt = randomized_svd(
trajectory,
n_components=max_rank,
n_iter=n_iter,
random_state=seed,
)
return U, s, Vt
U, s, Vt = np.linalg.svd(trajectory, full_matrices=False)
return U[:, :max_rank], s[:max_rank], Vt[:max_rank, :]
def _dominant_frequency_2d(mode: np.ndarray, fs: float) -> float:
aggregate = np.mean(np.asarray(mode, dtype=float), axis=1)
return dominant_frequency(aggregate, fs=fs)
def _sum_modes(modes: np.ndarray, indices: List[int], shape: tuple[int, int]) -> np.ndarray:
if not indices:
return np.zeros(shape, dtype=float)
valid = [idx for idx in indices if 0 <= idx < modes.shape[0]]
if not valid:
return np.zeros(shape, dtype=float)
return np.sum(modes[valid, :, :], axis=0)
def _auto_group_modes(
modes: np.ndarray,
*,
fs: float,
primary_period: float | None,
trend_components: List[int],
season_components: List[int],
cfg: Dict[str, Any],
) -> tuple[List[int], List[int], List[float]]:
dom_freqs = [_dominant_frequency_2d(mode, fs=fs) for mode in modes]
if trend_components or season_components:
return trend_components, season_components, dom_freqs
num_modes = modes.shape[0]
if primary_period is not None and primary_period > 0:
f0 = 1.0 / primary_period
tol = float(cfg.get("season_freq_tol_ratio", 0.25)) * f0
low_freq_threshold = float(cfg.get("trend_freq_threshold", f0 / 4.0 if f0 else 0.05))
for idx, f_dom in enumerate(dom_freqs):
if f_dom <= max(low_freq_threshold, 1e-8):
trend_components.append(idx)
elif f0 > 0 and abs(f_dom - f0) <= max(tol, 1e-8):
season_components.append(idx)
if not trend_components and num_modes >= 1:
trend_components.append(0)
if not season_components:
for idx in range(num_modes):
if idx not in trend_components:
season_components.append(idx)
break
else:
if num_modes >= 1:
trend_components.append(0)
if num_modes >= 2:
trend_components.append(1)
if num_modes >= 4:
season_components.extend([2, 3])
elif num_modes >= 3:
season_components.append(2)
return trend_components, season_components, dom_freqs
@MethodRegistry.register("MSSA", input_mode="multivariate")
def mssa_decompose(
y: np.ndarray,
params: Dict[str, Any],
) -> DecompResult:
started_at = perf_counter()
cfg, runtime = split_runtime_params(params)
if runtime.backend == "native":
raise RuntimeError("MSSA does not provide a native backend.")
if runtime.backend == "gpu":
raise ValueError("MSSA does not provide a GPU backend.")
y_arr = np.asarray(y, dtype=float)
if y_arr.ndim != 2:
raise ValueError("MSSA requires a 2D input array with shape (T, C).")
length, n_channels = y_arr.shape
if length < 4:
raise ValueError("MSSA requires length >= 4.")
if n_channels < 2:
raise ValueError("MSSA requires at least two channels.")
window = int(cfg.get("window", max(4, length // 4)))
window = min(max(2, window), length - 1)
rank = int(cfg.get("rank", min(10, window * n_channels, length - window + 1)))
rank = max(1, min(rank, window * n_channels, length - window + 1))
fs = float(cfg.get("fs", 1.0))
primary_period = cfg.get("primary_period")
primary_period = float(primary_period) if primary_period not in (None, 0) else None
trajectory = _build_mssa_trajectory(y_arr, window=window)
U, s, Vt = _fit_svd(trajectory, rank=rank, speed_mode=runtime.speed_mode, seed=runtime.seed)
modes = []
for idx in range(len(s)):
mode_matrix = np.outer(U[:, idx], s[idx] * Vt[idx, :])
modes.append(_reconstruct_mode(mode_matrix, window=window, n_channels=n_channels, length=length))
if modes:
mode_array = np.stack(modes, axis=0)
else:
mode_array = np.zeros((0, length, n_channels), dtype=float)
trend_components = list(cfg.get("trend_components", []))
season_components = list(cfg.get("season_components", []))
trend_components, season_components, dom_freqs = _auto_group_modes(
mode_array,
fs=fs,
primary_period=primary_period,
trend_components=trend_components,
season_components=season_components,
cfg=cfg,
)
trend = _sum_modes(mode_array, trend_components, y_arr.shape)
season = _sum_modes(mode_array, season_components, y_arr.shape)
residual = y_arr - trend - season
result = DecompResult(
trend=trend,
season=season,
residual=residual,
components={"modes": mode_array},
meta={
"method": "MSSA",
"window": window,
"rank": rank,
"n_channels": n_channels,
"singular_values": [float(val) for val in s.tolist()],
"trend_components": trend_components,
"season_components": season_components,
"dominant_frequencies": dom_freqs,
},
)
return finalize_result(
result,
method="MSSA",
runtime=runtime,
backend_used="python",
started_at=started_at,
)
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