Signature

polars_ts.imaging.signature

Path signature features and signature image visualization.

Computes truncated path signatures as feature vectors for time series, and reshapes them into 2D images for vision-based analysis.

Uses iisignature when available for fast computation; falls back to a pure-numpy implementation for basic signatures.

_time_augment(x)

Prepend a normalised time channel: path becomes 2D (t, x).

_leadlag_augment(x)

Lead-lag transform: (x_t, x_{t-1}) for richer path structure.

_basepoint_augment(path)

Prepend the origin as basepoint.

_apply_augmentations(x, augmentations)

Build a multi-dimensional path from a 1D series via augmentations.

_sig_numpy(path, depth)

Compute truncated signature using pure numpy (iterated integrals).

This is a reference implementation; for production use install iisignature.

_compute_signature(path, depth)

Compute the truncated signature, using iisignature if available.

signature_features(df, depth=3, augmentations=None, id_col='unique_id', target_col='y')

Extract truncated path signature features for each time series.

The signature is a sequence of iterated integrals that captures the shape of a path up to reparametrisation. Truncating at depth d gives a finite-dimensional feature vector.

Parameters

df DataFrame with columns id_col and target_col. depth Truncation depth. Controls feature dimensionality: depth 1 → d features, depth 2 → d + d², depth 3 → d + d² + d³. augmentations List of path augmentations to apply before computing the signature. Options: "time" (prepend time channel), "leadlag" (lead-lag transform), "basepoint" (prepend origin). Default: ["time"]. id_col Column identifying each time series. target_col Column with the time series values.

Returns

pl.DataFrame DataFrame with columns [id_col, sig_0, sig_1, ..., sig_d].

to_signature_image(df, depth=2, augmentations=None, id_col='unique_id', target_col='y')

Convert time series to signature images.

Computes the depth-2 signature and reshapes the d² terms into a d × d matrix for visualization. Higher-depth terms are discarded.

Parameters

df DataFrame with columns id_col and target_col. depth Signature depth (must be >= 2). Only the depth-2 terms are used for the image; depth-1 terms are discarded. augmentations Path augmentations. Default: ["time"]. id_col Column identifying each time series. target_col Column with the time series values.

Returns

dict[str, np.ndarray] Mapping from series ID to a d × d matrix of depth-2 signature terms.