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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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File size: 7,352 Bytes
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 | import numpy as np
from time import perf_counter
from typing import Dict, Any, List, Optional
from .._native import invoke_native
from ..backends import finalize_result, resolve_backend, result_from_native_payload, split_runtime_params
from ..core import DecompResult
from ..registry import MethodRegistry
from .utils import dominant_frequency
def _dominant_frequency(x: np.ndarray, fs: float = 1.0) -> float:
return dominant_frequency(x, fs)
def _diagonal_averaging(matrix: np.ndarray) -> np.ndarray:
L, K = matrix.shape
T = L + K - 1
recon = np.zeros(T)
counts = np.zeros(T)
for i in range(L):
for j in range(K):
recon[i + j] += matrix[i, j]
counts[i + j] += 1.0
counts[counts == 0.0] = 1.0
return recon / counts
def _basic_ssa(y: np.ndarray, window: int, rank: int) -> List[np.ndarray]:
y_arr = np.asarray(y, dtype=float)
T = y_arr.shape[0]
L = int(window)
if L < 2 or L > T - 1:
raise ValueError(f"Invalid SSA window length L={L} for T={T}")
K = T - L + 1
X = np.empty((L, K), dtype=float)
for i in range(K):
X[:, i] = y_arr[i : i + L]
U, s, Vt = np.linalg.svd(X, full_matrices=False)
d = min(rank, U.shape[1])
rc_list: List[np.ndarray] = []
for idx in range(d):
Xi = np.outer(U[:, idx], s[idx] * Vt[idx, :])
rc = _diagonal_averaging(Xi)[:T]
rc_list.append(rc)
return rc_list
def _diagonal_averaging_fast(matrix: np.ndarray) -> np.ndarray:
L, K = matrix.shape
T = L + K - 1
anti_diag_ids = np.add.outer(np.arange(L), np.arange(K)).ravel()
flat = np.asarray(matrix, dtype=float).ravel()
sums = np.bincount(anti_diag_ids, weights=flat, minlength=T)
counts = np.bincount(anti_diag_ids, minlength=T).astype(float)
counts[counts == 0.0] = 1.0
return sums / counts
def _basic_ssa_fast(y: np.ndarray, window: int, rank: int) -> List[np.ndarray]:
y_arr = np.asarray(y, dtype=float).reshape(-1)
T = y_arr.shape[0]
L = int(window)
if L < 2 or L > T - 1:
raise ValueError(f"Invalid SSA window length L={L} for T={T}")
X = np.lib.stride_tricks.sliding_window_view(y_arr, L).T.copy()
U, s, Vt = np.linalg.svd(X, full_matrices=False)
d = min(rank, U.shape[1])
rc_list: List[np.ndarray] = []
for idx in range(d):
Xi = np.outer(U[:, idx], s[idx] * Vt[idx, :])
rc = _diagonal_averaging_fast(Xi)[:T]
rc_list.append(rc)
return rc_list
def _sum_components(components: List[np.ndarray], indices: List[int], length: int) -> np.ndarray:
if not indices:
return np.zeros(length)
out = np.zeros(length)
for idx in indices:
if 0 <= idx < len(components):
out += components[idx]
return out
@MethodRegistry.register("SSA")
def ssa_decompose(
y: np.ndarray,
params: Dict[str, Any],
) -> DecompResult:
started_at = perf_counter()
cfg, runtime = split_runtime_params(params)
y_arr = np.asarray(y, dtype=float)
T = y_arr.shape[0]
window = int(cfg.get("window", max(4, T // 4)))
window = min(max(2, window), T - 1)
rank = int(cfg.get("rank", 10))
rank = max(1, min(rank, window, T - 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
backend = resolve_backend("SSA", runtime, native_methods=("ssa_decompose",))
if backend == "native":
payload = invoke_native(
"ssa_decompose",
y_arr,
window=window,
rank=rank,
fs=fs,
primary_period=primary_period,
trend_components=list(cfg.get("trend_components", [])),
season_components=list(cfg.get("season_components", [])),
season_freq_tol_ratio=float(cfg.get("season_freq_tol_ratio", 0.25)),
trend_freq_threshold=cfg.get("trend_freq_threshold"),
)
return finalize_result(
result_from_native_payload(payload, method="SSA"),
method="SSA",
runtime=runtime,
backend_used="native",
started_at=started_at,
)
if runtime.speed_mode == "fast":
rc_list = _basic_ssa_fast(y_arr, window=window, rank=rank)
else:
rc_list = _basic_ssa(y_arr, window=window, rank=rank)
num_rc = len(rc_list)
if num_rc == 0:
zeros = np.zeros_like(y_arr)
return finalize_result(
DecompResult(
trend=zeros,
season=zeros,
residual=y_arr.copy(),
components={"rc_list": np.zeros((0, T), dtype=float)},
meta={"method": "SSA", "window": window, "rank": rank, "rc_list_shape": [0, T]}
),
method="SSA",
runtime=runtime,
backend_used="python",
started_at=started_at,
)
trend_components = list(cfg.get("trend_components", []))
season_components = list(cfg.get("season_components", []))
# Auto-grouping logic
if not trend_components and not season_components:
if primary_period is not None and primary_period > 0:
dom_freqs = [_dominant_frequency(rc, fs=fs) for rc in rc_list]
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)
# Fallback if empty
if not trend_components and num_rc >= 1:
trend_components.append(0)
if not season_components:
for idx in range(num_rc):
if idx not in trend_components:
season_components.append(idx)
break
else:
# Default heuristic
if num_rc >= 1: trend_components.append(0)
if num_rc >= 2: trend_components.append(1)
if num_rc >= 4: season_components.extend([2, 3])
elif num_rc >= 3: season_components.append(2)
trend = _sum_components(rc_list, trend_components, T)
season = _sum_components(rc_list, season_components, T)
residual = y_arr - trend - season
return finalize_result(
DecompResult(
trend=trend,
season=season,
residual=residual,
components={"rc_list": np.stack(rc_list, axis=0)},
meta={
"method": "SSA",
"window": window,
"rank": rank,
"trend_components": trend_components,
"season_components": season_components,
"rc_list_shape": [len(rc_list), T],
}
),
method="SSA",
runtime=runtime,
backend_used="python",
started_at=started_at,
)
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