SST

SST applies Singular Spectrum Transformation to a one-dimensional signal. It compares low-rank representations of past and future Hankel matrices and returns a structural-change score.

Use the tuning guide for a parameter-by-parameter workflow and runtime advice.

Parameters

window_length : int

Subsequence length in samples. This is the main temporal scale.

n_windows : int, optional

Number of subsequences in each Hankel matrix. Defaults to window_length.

lag : int, optional

Separation between compared matrices. Defaults to max(n_windows // 3, 1).

rank : int, default 5

Number of dominant past-subspace directions.

scale : bool, default True

Min-max scale the signal to [1, 2] before scoring.

method : str, default "ika"

Scoring/decomposition method: "ika", "svd", "rsvd", "fbrsvd", "naive", "naive updated", "weighted", or "symmetric".

lanczos_rank : int, optional

Krylov approximation size for method="ika". Derived from rank when omitted.

random_rank : int, optional

Sampled dimension for randomized methods. Defaults to at most rank + 10.

feedback_noise_level : float, default 1e-3

Noise added to the recycled future direction used by IKA-style scoring.

scoring_step : int, default 1

Distance in samples between evaluated positions.

use_fast_hankel : bool, default False

Use implicit FFT-based Hankel products where the selected method supports them.

mitigate_offset : bool, default False

Remove column-wise offsets. Cannot be combined with fast Hankel products.

Methods

transform(time_series)

time_series : numpy.ndarray, shape (n_samples,)

Signal to score.

Returns

score : numpy.ndarray, shape (n_samples,)

Structural-change score. Initial positions without enough context are zero.

Minimal Example

import numpy as np
from changepoynt.algorithms.sst import SST

signal = np.r_[np.sin(np.linspace(0, 8 * np.pi, 200)),
               np.sin(np.linspace(0, 20 * np.pi, 200))]
score = SST(window_length=40, method="rsvd").transform(signal)

References: Ide and Inoue (2005), Ide and Tsuda (2007).