pathsig.projections.anisotropic#

pathsig.projections.anisotropic(weights, weight_threshold, depth, path_dim, full_levels=())#

Projection selecting coordinates via an anisotropic truncation rule. It selects words \((i_1,\ldots,i_n)\) satisfying

\[\texttt{weights}[i_1] + \cdots + \texttt{weights}[i_n] \le \texttt{weight\_threshold},\]

together with all words at levels listed in full_levels.

Parameters:

  • weights (iterable of float or int) – Per-letter weights of length path_dim.

  • weight_threshold (float or int) – Non-strict threshold used by the selection rule.

  • depth (int) – Maximum word length (signature level) to include.

  • path_dim (int) – Path dimension (alphabet size).

  • full_levels (iterable of int) – (optional) Levels in \(\{1,2,\ldots,\mathrm{depth}\}\) that should be included in full in addition to the anisotropically selected set.

Returns:

Projection object to be used with pathsig.Signature and pathsig.LogSignature.

Return type:

Projection

Notes

It is preferable to specify weights and weight_threshold as integers. Floating-point inputs can make the cutoff weights[i_1] + ... + weights[i_n] <= weight_threshold unstable near the boundary due to inexact representation and accumulated rounding error. Integer arithmetic, by contrast, yields a deterministic, platform-independent truncation rule.

Examples

import pathsig

proj = pathsig.projections.anisotropic(
    weights=[1, 2, 3, 4],
    weight_threshold=6,
    depth=5,
    path_dim=4,
)
sig_size = proj.sig_size  # output feature dimension