pyhctsa.operations.symbolic.motif_two

pyhctsa.operations.symbolic.motif_two(y, binarize_how='diff', tau=1)

Compute local motifs in a binary symbolization of the input time series.

This function coarse-grains the input time series into a binary sequence using the specified binarization method, and computes the probabilities of binary words of lengths 1 through 4, along with their entropies.

Parameters:
y : array-like

The input time series.

binarize_how : str, optional

The method used for binary transformation. One of:

  • ’diff’: Encode increases in the time series as 1, and decreases or no change as 0.

  • ’mean’: Encode values above the mean as 1, and at or below the mean as 0.

  • ’median’: Encode values above the median as 1, and at or below the median as 0.

Default is 'diff'.

tau : int or str, optional

The lag of the words. The whole series is binarized to symbols s, and the words of length L are (s[t], s[t + tau], ..., s[t + (L-1)*tau]) for every t, as in a time-delay embedding; for ‘diff’ the symbols are the signs of the increments at lag tau, y[t + tau] - y[t]. An integer, or a rule that sets it from the series: '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), or one of these computed from the ranks of the series ('ac-rank', 'ac1e-rank', 'mi-rank'); see pyhctsa.utils.get_tau(). With the order-based symbols (‘diff’, ‘median’) and a rank-based rule, the result is unchanged by a strictly increasing transformation of the series. Default is 1. NaN is returned if tau cannot be determined, or leaves fewer than two words of length 4.

Returns:

The probability of each binary word of length 1 to 4, keyed by the word in the letters ‘u’ (1) and ‘d’ (0) (‘u’, ‘d’, ‘dd’, ‘du’, …, ‘uuuu’), and the Miller-Madow-corrected entropy of the words of each length (‘h’, ‘hh’, ‘hhh’, ‘hhhh’). NaN if the series is too short for two words of length 4.

Return type:

dict