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from __future__ import annotations
from dataclasses import dataclass, field
from typing import Any, Iterable, Sequence
import numpy as np
from numpy.typing import NDArray
from scipy.stats import kurtosis, skew
from sklearn.base import BaseEstimator, TransformerMixin
def _as_3d(X: Any) -> NDArray[np.float64]:
arr = np.asarray(X, dtype=np.float64)
if arr.ndim == 2:
arr = arr[:, :, None]
if arr.ndim != 3:
raise ValueError(f'Expected X shape (n,T,C) or (n,T); got {arr.shape}')
return arr
def _safe_zscore_per_window(X: NDArray[np.float64], eps: float=1e-06) -> NDArray[np.float64]:
mu = np.nanmean(X, axis=1, keepdims=True)
sd = np.nanstd(X, axis=1, keepdims=True)
sd = np.where(sd < eps, 1.0, sd)
return np.nan_to_num((X - mu) / sd, nan=0.0, posinf=0.0, neginf=0.0)
def _slope(y: NDArray[np.float64]) -> NDArray[np.float64]:
T = y.shape[1]
t = np.arange(T, dtype=np.float64)
tc = t - t.mean()
denom = float(np.dot(tc, tc)) or 1.0
yc = y - np.mean(y, axis=1, keepdims=True)
return np.einsum('t,ntc->nc', tc, yc) / denom
def _zero_crossing_rate(X: NDArray[np.float64]) -> NDArray[np.float64]:
s = np.signbit(X)
return np.mean(s[:, 1:, :] != s[:, :-1, :], axis=1)
def _segment_view(X: NDArray[np.float64], w: int) -> NDArray[np.float64]:
n, T, C = X.shape
if w <= 0:
raise ValueError('w must be positive')
seg_len = int(np.ceil(T / w))
T2 = seg_len * w
if T2 != T:
pad = np.repeat(X[:, -1:, :], T2 - T, axis=1)
X = np.concatenate([X, pad], axis=1)
return X.reshape(n, w, seg_len, C)
def _spectral_features(X: NDArray[np.float64], bands: Sequence[tuple[float, float]]) -> NDArray[np.float64]:
n, T, C = X.shape
x = X - np.mean(X, axis=1, keepdims=True)
fft = np.fft.rfft(x, axis=1)
power = np.abs(fft) ** 2 / max(T, 1)
freqs = np.fft.rfftfreq(T, d=1.0)
total = np.sum(power[:, 1:, :], axis=1) + 1e-12 if power.shape[1] > 1 else np.ones((n, C))
feats: list[NDArray[np.float64]] = []
for lo, hi in bands:
mask = (freqs >= lo) & (freqs < hi)
if not np.any(mask):
feats.append(np.zeros((n, C), dtype=np.float64))
else:
feats.append(np.sum(power[:, mask, :], axis=1) / total)
p = power[:, 1:, :] / (total[:, None, :] if power.shape[1] > 1 else 1.0)
entropy = -np.sum(np.where(p > 0, p * np.log(p + 1e-12), 0.0), axis=1) / np.log(max(p.shape[1], 2)) if power.shape[1] > 1 else np.zeros((n, C))
centroid = np.sum(freqs[1:, None] * power[:, 1:, :], axis=1) / total if power.shape[1] > 1 else np.zeros((n, C))
peak = freqs[1:][np.argmax(power[:, 1:, :], axis=1)] if power.shape[1] > 1 else np.zeros((n, C))
feats.extend([entropy, centroid, peak])
return np.concatenate([f.reshape(n, -1) for f in feats], axis=1)
def _autocorr_features(X: NDArray[np.float64], lags: Sequence[int]) -> NDArray[np.float64]:
n, T, C = X.shape
x = X - np.mean(X, axis=1, keepdims=True)
denom = np.sum(x * x, axis=1) + 1e-12
feats = []
for lag in lags:
if lag <= 0 or lag >= T:
feats.append(np.zeros((n, C), dtype=np.float64))
else:
feats.append(np.sum(x[:, :-lag, :] * x[:, lag:, :], axis=1) / denom)
return np.concatenate([f.reshape(n, -1) for f in feats], axis=1) if feats else np.empty((n, 0))
def _transition_features(x: NDArray[np.float64], n_bins: int=6) -> NDArray[np.float64]:
n, T, C = x.shape
outs: list[NDArray[np.float64]] = []
for c in range(C):
xc = x[:, :, c]
q = np.quantile(xc, np.linspace(0, 1, n_bins + 1)[1:-1], axis=1).T
states = np.sum(xc[:, :, None] > q[:, None, :], axis=2).astype(np.int64)
mat = np.zeros((n, n_bins, n_bins), dtype=np.float64)
for i in range(n):
np.add.at(mat[i], (states[i, :-1], states[i, 1:]), 1.0)
row = mat.sum(axis=2, keepdims=True)
mat = np.where(row > 0, mat / np.maximum(row, 1.0), 0.0)
hist = np.mean(np.eye(n_bins)[states], axis=1)
flat = mat.reshape(n, -1)
ent = -np.sum(np.where(flat > 0, flat * np.log(flat + 1e-12), 0.0), axis=1, keepdims=True)
outs.extend([hist, flat, ent])
return np.concatenate(outs, axis=1) if outs else np.empty((n, 0))
@dataclass
class WearableFeatureExtractor(BaseEstimator, TransformerMixin):
zscore: bool = True
include_raw_stats: bool = True
include_magnitude: bool = True
include_jerk: bool = True
include_multiscale: bool = True
segment_sizes: tuple[int, ...] = (4, 8, 16)
include_spectral: bool = True
spectral_bands: tuple[tuple[float, float], ...] = ((0.0, 0.05), (0.05, 0.15), (0.15, 0.3), (0.3, 0.51))
include_autocorr: bool = True
autocorr_lags: tuple[int, ...] = (1, 2, 4, 8, 16, 32)
include_cross_channel: bool = True
include_symbolic: bool = True
symbolic_bins: int = 6
feature_names_: list[str] = field(default_factory=list, init=False)
def fit(self, X: Any, y: Any | None=None) -> 'WearableFeatureExtractor':
self.transform(X[:min(len(X), 3)] if hasattr(X, '__len__') else X)
return self
def transform(self, X: Any) -> NDArray[np.float64]:
X3 = _as_3d(X)
if self.zscore:
Xn = _safe_zscore_per_window(X3)
else:
Xn = np.nan_to_num(X3, nan=0.0, posinf=0.0, neginf=0.0)
variants = [Xn]
names_prefix = ['ch']
if self.include_magnitude and Xn.shape[2] >= 2:
mag = np.linalg.norm(Xn[:, :, :min(3, Xn.shape[2])], axis=2, keepdims=True)
variants.append(mag)
names_prefix.append('mag')
if self.include_jerk:
jerk = np.diff(Xn, axis=1, prepend=Xn[:, :1, :])
variants.append(jerk)
names_prefix.append('jerk')
if Xn.shape[2] >= 2:
variants.append(np.linalg.norm(jerk[:, :, :min(3, Xn.shape[2])], axis=2, keepdims=True))
names_prefix.append('jerk_mag')
feat_blocks: list[NDArray[np.float64]] = []
feature_names: list[str] = []
for V, prefix in zip(variants, names_prefix):
n, T, C = V.shape
if self.include_raw_stats:
stats = [np.mean(V, axis=1), np.std(V, axis=1), np.min(V, axis=1), np.max(V, axis=1), np.median(V, axis=1), np.quantile(V, 0.25, axis=1), np.quantile(V, 0.75, axis=1), np.mean(V * V, axis=1), np.mean(np.diff(V, axis=1, prepend=V[:, :1, :]), axis=1), np.std(np.diff(V, axis=1, prepend=V[:, :1, :]), axis=1), _zero_crossing_rate(V), _slope(V), skew(V, axis=1, nan_policy='omit'), kurtosis(V, axis=1, nan_policy='omit')]
block = np.concatenate([np.nan_to_num(s).reshape(n, -1) for s in stats], axis=1)
feat_blocks.append(block)
feature_names.extend([f'{prefix}_stat_{i}' for i in range(block.shape[1])])
if self.include_multiscale:
for w in self.segment_sizes:
if w > T:
continue
seg = _segment_view(V, int(w))
means = np.mean(seg, axis=2).reshape(n, -1)
stds = np.std(seg, axis=2).reshape(n, -1)
rng = (np.max(seg, axis=2) - np.min(seg, axis=2)).reshape(n, -1)
slopes = []
for j in range(int(w)):
slopes.append(_slope(seg[:, j, :, :]))
slopes_arr = np.stack(slopes, axis=1).reshape(n, -1)
block = np.concatenate([means, stds, rng, slopes_arr], axis=1)
feat_blocks.append(block)
feature_names.extend([f'{prefix}_seg{w}_{i}' for i in range(block.shape[1])])
if self.include_spectral:
block = _spectral_features(V, self.spectral_bands)
feat_blocks.append(block)
feature_names.extend([f'{prefix}_fft_{i}' for i in range(block.shape[1])])
if self.include_autocorr:
lags = tuple((l for l in self.autocorr_lags if l < T))
block = _autocorr_features(V, lags)
feat_blocks.append(block)
feature_names.extend([f'{prefix}_acf_{i}' for i in range(block.shape[1])])
if self.include_symbolic and V.shape[1] >= 8:
Vsym = V if V.shape[2] <= 3 else V[:, :, :3]
block = _transition_features(Vsym, n_bins=int(self.symbolic_bins))
feat_blocks.append(block)
feature_names.extend([f'{prefix}_sym_{i}' for i in range(block.shape[1])])
if self.include_cross_channel and Xn.shape[2] > 1:
n, _, C = Xn.shape
corr_feats = []
for i in range(C):
for j in range(i + 1, C):
xi = Xn[:, :, i] - Xn[:, :, i].mean(axis=1, keepdims=True)
xj = Xn[:, :, j] - Xn[:, :, j].mean(axis=1, keepdims=True)
corr = np.sum(xi * xj, axis=1) / (np.sqrt(np.sum(xi * xi, axis=1) * np.sum(xj * xj, axis=1)) + 1e-12)
corr_feats.append(corr[:, None])
if corr_feats:
block = np.concatenate(corr_feats, axis=1)
feat_blocks.append(block)
feature_names.extend([f'corr_{i}' for i in range(block.shape[1])])
if not feat_blocks:
raise ValueError('No feature blocks enabled')
F = np.concatenate(feat_blocks, axis=1)
F = np.nan_to_num(F, nan=0.0, posinf=0.0, neginf=0.0).astype(np.float64, copy=False)
self.feature_names_ = feature_names
return F
@dataclass
class RandomConvSketch(BaseEstimator, TransformerMixin):
n_kernels: int = 256
kernel_lengths: tuple[int, ...] = (7, 9, 11, 15)
dilations: tuple[int, ...] = (1, 2, 4)
random_state: int = 42
zscore: bool = True
kernels_: list[dict[str, Any]] = field(default_factory=list, init=False)
def fit(self, X: Any, y: Any | None=None) -> 'RandomConvSketch':
X3 = _as_3d(X)
_, T, C = X3.shape
rng = np.random.default_rng(self.random_state)
kernels: list[dict[str, Any]] = []
for _ in range(int(self.n_kernels)):
length = int(rng.choice(self.kernel_lengths))
dilation = int(rng.choice(self.dilations))
max_span = (length - 1) * dilation + 1
if max_span > T:
dilation = max(1, (T - 1) // max(length - 1, 1))
n_ch = int(rng.integers(1, min(C, 3) + 1))
channels = np.sort(rng.choice(C, size=n_ch, replace=False)).astype(np.int64)
weights = rng.normal(0, 1, size=(length, n_ch)).astype(np.float64)
weights -= weights.mean(axis=0, keepdims=True)
norm = np.linalg.norm(weights) + 1e-12
weights /= norm
bias = float(rng.normal(0, 0.25))
kernels.append({'length': length, 'dilation': dilation, 'channels': channels, 'weights': weights, 'bias': bias})
self.kernels_ = kernels
return self
def transform(self, X: Any) -> NDArray[np.float64]:
X3 = _as_3d(X)
if self.zscore:
X3 = _safe_zscore_per_window(X3)
n, T, _ = X3.shape
feats = np.empty((n, len(self.kernels_) * 4), dtype=np.float64)
for k, spec in enumerate(self.kernels_):
length = int(spec['length'])
dilation = int(spec['dilation'])
channels = np.asarray(spec['channels'], dtype=np.int64)
weights = np.asarray(spec['weights'], dtype=np.float64)
span = (length - 1) * dilation + 1
out_len = max(T - span + 1, 1)
resp = np.zeros((n, out_len), dtype=np.float64)
for ii in range(length):
start = ii * dilation
stop = start + out_len
resp += X3[:, start:stop, :][:, :, channels] @ weights[ii]
resp += float(spec['bias'])
feats[:, 4 * k + 0] = np.mean(resp > 0.0, axis=1)
feats[:, 4 * k + 1] = np.max(resp, axis=1)
feats[:, 4 * k + 2] = np.mean(resp, axis=1)
feats[:, 4 * k + 3] = np.std(resp, axis=1)
return np.nan_to_num(feats, nan=0.0, posinf=0.0, neginf=0.0)
def _quantile_block(X: NDArray[np.float64], qs: Sequence[float]) -> NDArray[np.float64]:
q = np.quantile(X, np.asarray(qs, dtype=np.float64), axis=1).transpose(1, 2, 0)
return q.reshape(X.shape[0], -1)
def _gram_eig_features(X: NDArray[np.float64]) -> NDArray[np.float64]:
n, _, c = X.shape
feats = []
for i in range(n):
Xi = X[i] - X[i].mean(axis=0, keepdims=True)
G = Xi.T @ Xi / max(Xi.shape[0] - 1, 1)
vals = np.linalg.eigvalsh(G)
vals = np.sort(np.maximum(vals, 0.0))[::-1]
total = float(np.sum(vals)) + 1e-12
ratios = vals / total
pad = np.zeros((max(6 - 2 * c, 0),), dtype=np.float64)
feats.append(np.concatenate([vals, ratios, pad], axis=0))
return np.stack(feats, axis=0)
@dataclass
class IntervalDistributionSketch(BaseEstimator, TransformerMixin):
n_random_intervals: int = 32
random_state: int = 42
quantiles: tuple[float, ...] = (0.1, 0.25, 0.5, 0.75, 0.9)
include_dyadic: bool = True
zscore: bool = True
intervals_: list[tuple[int, int]] = field(default_factory=list, init=False)
def fit(self, X: Any, y: Any | None=None) -> 'IntervalDistributionSketch':
X3 = _as_3d(X)
_, T, _ = X3.shape
rng = np.random.default_rng(self.random_state)
intervals: list[tuple[int, int]] = []
if self.include_dyadic:
for parts in (2, 4, 8):
width = max(2, int(np.ceil(T / parts)))
for start in range(0, T, width):
stop = min(T, start + width)
if stop - start >= 2:
intervals.append((start, stop))
for _ in range(int(self.n_random_intervals)):
lo = int(rng.integers(0, max(T - 2, 1)))
max_len = max(3, T - lo)
length = int(rng.integers(2, max_len + 1))
hi = min(T, lo + length)
if hi - lo >= 2:
intervals.append((lo, hi))
seen: set[tuple[int, int]] = set()
self.intervals_ = []
for it in intervals:
if it not in seen:
seen.add(it)
self.intervals_.append(it)
return self
def transform(self, X: Any) -> NDArray[np.float64]:
X3 = _as_3d(X)
if self.zscore:
X3 = _safe_zscore_per_window(X3)
blocks: list[NDArray[np.float64]] = []
for lo, hi in self.intervals_:
V = X3[:, lo:hi, :]
n = V.shape[0]
stats = [np.mean(V, axis=1), np.std(V, axis=1), np.max(V, axis=1) - np.min(V, axis=1), np.mean(V * V, axis=1), _slope(V), _quantile_block(V, self.quantiles)]
blocks.append(np.concatenate([s.reshape(n, -1) for s in stats], axis=1))
if not blocks:
return np.empty((X3.shape[0], 0), dtype=np.float64)
return np.nan_to_num(np.concatenate(blocks, axis=1), nan=0.0, posinf=0.0, neginf=0.0)
@dataclass
class InvariantPhysicsFeatureExtractor(BaseEstimator, TransformerMixin):
segment_sizes: tuple[int, ...] = (4, 8, 16)
symbolic_bins: int = 6
random_intervals: int = 24
random_state: int = 42
zscore: bool = True
include_axis_features: bool = True
interval_: IntervalDistributionSketch | None = field(default=None, init=False)
def fit(self, X: Any, y: Any | None=None) -> 'InvariantPhysicsFeatureExtractor':
X3 = _as_3d(X)
self.interval_ = IntervalDistributionSketch(n_random_intervals=self.random_intervals, random_state=self.random_state, zscore=self.zscore).fit(X3, y)
return self
def transform(self, X: Any) -> NDArray[np.float64]:
X3 = _as_3d(X)
Xn = _safe_zscore_per_window(X3) if self.zscore else np.nan_to_num(X3)
n, T, C = Xn.shape
blocks: list[NDArray[np.float64]] = []
if self.include_axis_features:
axis = WearableFeatureExtractor(zscore=False, include_raw_stats=True, include_magnitude=False, include_jerk=False, include_multiscale=True, segment_sizes=self.segment_sizes, include_spectral=False, include_autocorr=False, include_cross_channel=True, include_symbolic=False).fit_transform(Xn)
blocks.append(axis)
base = Xn[:, :, :min(3, C)]
mag = np.linalg.norm(base, axis=2, keepdims=True)
jerk = np.diff(base, axis=1, prepend=base[:, :1, :])
jerk_mag = np.linalg.norm(jerk, axis=2, keepdims=True)
invariant_series = np.concatenate([mag, jerk_mag], axis=2)
inv = WearableFeatureExtractor(zscore=False, include_raw_stats=True, include_magnitude=False, include_jerk=False, include_multiscale=True, segment_sizes=self.segment_sizes, include_spectral=True, include_autocorr=True, include_cross_channel=False, include_symbolic=True, symbolic_bins=self.symbolic_bins).fit_transform(invariant_series)
blocks.append(inv)
blocks.append(_gram_eig_features(base))
mag_energy = np.mean(mag * mag, axis=1) + 1e-12
jerk_energy = np.mean(jerk_mag * jerk_mag, axis=1)
blocks.append((jerk_energy / mag_energy).reshape(n, -1))
if self.interval_ is not None:
blocks.append(self.interval_.transform(Xn))
return np.nan_to_num(np.concatenate(blocks, axis=1), nan=0.0, posinf=0.0, neginf=0.0)
@dataclass
class RandomShapeletSketch(BaseEstimator, TransformerMixin):
n_shapelets: int = 48
lengths: tuple[int, ...] = (8, 12, 16, 24)
dilations: tuple[int, ...] = (1, 2, 4)
random_state: int = 42
zscore: bool = True
shapelets_: list[dict[str, Any]] = field(default_factory=list, init=False)
def fit(self, X: Any, y: Any | None=None) -> 'RandomShapeletSketch':
X3 = _as_3d(X)
if self.zscore:
X3 = _safe_zscore_per_window(X3)
n, T, C = X3.shape
rng = np.random.default_rng(self.random_state)
self.shapelets_ = []
for _ in range(int(self.n_shapelets)):
length = int(rng.choice(self.lengths))
dilation = int(rng.choice(self.dilations))
span = (length - 1) * dilation + 1
if span > T:
dilation = max(1, (T - 1) // max(length - 1, 1))
span = (length - 1) * dilation + 1
i = int(rng.integers(0, n))
c = int(rng.integers(0, C))
start = int(rng.integers(0, max(T - span + 1, 1)))
values = X3[i, start:start + span:dilation, c].astype(np.float64, copy=True)
values = values - float(values.mean())
sd = float(values.std()) or 1.0
values = values / sd
self.shapelets_.append({'values': values, 'channel': c, 'dilation': dilation})
return self
def transform(self, X: Any) -> NDArray[np.float64]:
X3 = _as_3d(X)
if self.zscore:
X3 = _safe_zscore_per_window(X3)
n, T, _ = X3.shape
F = np.empty((n, len(self.shapelets_) * 2), dtype=np.float64)
for k, spec in enumerate(self.shapelets_):
sh = np.asarray(spec['values'], dtype=np.float64)
c = int(spec['channel'])
dilation = int(spec['dilation'])
length = int(sh.shape[0])
span = (length - 1) * dilation + 1
out_len = max(T - span + 1, 1)
best = np.full((n,), np.inf, dtype=np.float64)
best_pos = np.zeros((n,), dtype=np.float64)
for start in range(out_len):
seg = X3[:, start:start + span:dilation, c]
seg = seg - seg.mean(axis=1, keepdims=True)
seg_sd = seg.std(axis=1, keepdims=True)
seg = seg / np.where(seg_sd < 1e-06, 1.0, seg_sd)
d = np.sqrt(np.mean((seg - sh[None, :]) ** 2, axis=1))
improved = d < best
best = np.where(improved, d, best)
best_pos = np.where(improved, start / max(out_len - 1, 1), best_pos)
F[:, 2 * k] = best
F[:, 2 * k + 1] = best_pos
return np.nan_to_num(F, nan=0.0, posinf=0.0, neginf=0.0)
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