pyhctsa.operations.correlation.embed2_shapes¶

pyhctsa.operations.correlation.embed2_shapes(y, tau='tau', shape='circle', r=1.0, theiler_win=('ac', 1))¶

Shape-based statistics in a 2-d embedding space.

Takes a shape and places it on each point in the two-dimensional time-delay embedding space sequentially. For each point it records the fraction of the other points (outside a Theiler window) that are inside the shape, giving a time series of the local density along the trajectory (the pointwise correlation sum, which is intensive and bounded in [0, 1]; raw counts would grow in direct proportion to N), and returns statistics on this extracted time series.

Parameters:¶

y : array-like¶

The input time-series (z-scored).

tau : int or str, optional¶

The time delay: an integer number of samples, or a rule that sets it from the series: 'tau' (or 'ac'; the first zero crossing of the autocorrelation function), 'ac1e' (the floor of its first 1/e crossing) or 'mi' (the smaller of the first minimum of the Kraskov automutual information and the 'ac1e' delay); see get_tau(). A delay set by a rule is capped at N/10; if it cannot be set the output is NaN. Default is 'tau'.

shape : str, optional¶

The shape to use. Currently only ‘circle’ is supported. Default is circle.

r : float, optional¶

The radius of the circle. Default is 1.0.

theiler_win : list, tuple, int or float, optional¶

The Theiler window: points closer in time than this are not counted as neighbors, since they are close in the embedding only because successive values are correlated. ['ac', k] for k times the first zero-crossing of the autocorrelation function, or a number of samples (see theiler_window(); 0 counts every other point). Default is ('ac', 1). NaN output if the window cannot be set.

Returns:¶

A dictionary containing various statistics of the constructed time series (ac1, ac2, ac3, tau, std, median, mean, iqr, iqronrange, mode_val, mode, hist_ent, statav5_m, statav5_s). hist_ent is sum(p * log(p)) over the bins of a histogram of the local densities (minus the Shannon entropy). As in hctsa, the maximum (max) is not returned. If no point has any neighbor within r, a fixed set of values is returned (std, median, mean, iqr, hist_ent = 0; mode_val = 1; mode = 0; the rest NaN).

Return type:¶

dict