I used a feature extraction code, where two of the features are unknown to me. They work well for my model but I don't know the formal names for them.

The first one has the following python implementation:

def LOG(y):
    n = len(y)
    return np.exp(np.sum(np.log(np.abs(y)))/n)

I didn't find any feature by LOG.

The other one was taken from tsfresh library,


def c3(x, lag):
    This function calculates the value of
    .. math::
        \\frac{1}{n-2lag} \\sum_{i=1}^{n-2lag} x_{i + 2 \\cdot lag} \\cdot x_{i + lag} \\cdot x_{i}
    which is
    .. math::
        \\mathbb{E}[L^2(X) \\cdot L(X) \\cdot X]
    where :math:`\\mathbb{E}` is the mean and :math:`L` is the lag operator. It was proposed in [1] as a measure of
    non linearity in the time series.
    .. rubric:: References
    |  [1] Schreiber, T. and Schmitz, A. (1997).
    |  Discrimination power of measures for nonlinearity in a time series
    :param x: the time series to calculate the feature of
    :type x: numpy.ndarray
    :param lag: the lag that should be used in the calculation of the feature
    :type lag: int
    :return: the value of this feature
    :return type: float
    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    n = x.size
    if 2 * lag >= n:
        return 0
        return np.mean((_roll(x, 2 * -lag) * _roll(x, -lag) * x)[0:(n - 2 * lag)])

It says C3, but in the paper, I didn't find any details about the feature (there were some t^(c3) mentioned in the paper, but I'm not sure, in one of the lines it says it's called third-order cumulant, but I couldn't confirm)

Can anyone tell me what are the common (more general) names of these two features?


LOG is the geometric mean of $|y|$: $$ \left(\prod_{i=1}^n |y_i|\right)^{\frac{1}{n}} = \exp\left(\frac{1}{n}\sum_{i=1}^n \log|y_i| \right) $$ This builds in a strong assumption that $y_i \neq 0\forall i$ because $\log(0)$ is not a real number.

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