# What are these features called (LOG and C3)?

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,

https://github.com/blue-yonder/tsfresh/blob/master/tsfresh/feature_extraction/feature_calculators.py?fbclid=IwAR0Qnh3X1t_2M9Y1bniEcMoyUUIiYwCS80Vj1D7_B5-hDHBBSyCiDKLOg4Q#L1480

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
|  PHYSICAL REVIEW E, VOLUME 55, NUMBER 5
: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
else:
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.