pyhctsa.operations.correlation.embed2_basic¶

pyhctsa.operations.correlation.embed2_basic(y, tau=1)¶

Point-density statistics in a two-dimensional delay embedding.

Computes a set of point-density statistics in the embedding space formed by \((y_i, y_{i-\tau})\). The method quantifies how points cluster around specific geometric structures in this plane, including diagonals, parabolas, rings, and circles.

The embedding corresponds to a standard two-dimensional delay reconstruction with lag \(\tau\).

Parameters:¶

y : array-like¶

Input time series (1D array).

tau : int¶

Time delay used to construct the embedding \((y_i, y_{i-\tau})\).

Returns:¶

Dictionary of point-density statistics associated with different geometric regions in the embedding space.

Return type:¶

dict