Skewness Function¶

The skew function computes the skewness of a window. When combined with the SlidingWindow abstraction, the skew function can be used to compute the skew feature of a time series. The skewness is defined as:

\[ \gamma = \frac{m_3}{m_2^{3/2}} \]

We use this and correct for statistical bias. The Fisher-Pearson standardized moment coefficient is defined as:

\[ \Gamma = \gamma \sqrt{\frac{N(N-1)}{N-2}} \]

where \(m_2\) and \(m_3\) are the second and third central moments, respectively. They are defined as:

\[ m_2 = \frac{1}{N} \sum_{i=1}^N (x_i - \bar{x})^2 \]

\[ m_3 = \frac{1}{N} \sum_{i=1}^N (x_i - \bar{x})^3 \]

where \(N\) is the number of samples in the window and \(\bar{x}\) is the mean of the window.

Compute the skewness of the values in x where where is True. The skewness is computed using the Fisher-Pearson standardized coefficient of skewness. The skewness is only computed for valid values i.e. values where where is True. The skewness computed is corrected for statistical bias.

Parameters:

Name	Type	Description	Default
`x`	`ndarray`	The array to compute the skewness of.	required
`where`	`Callable[[Union[int, float, int_, float_]], Union[bool, bool_]]`	A function that takes a value and returns `True` or `False`. Default is `lambda x: not np.isnan(x)` i.e. a measurement is valid if it is not a `NaN` value.	`lambda : not numpy.isnan(x)`

Returns:

Type	Description
`Union[float, float_]`	The skewness of the values in `x` where `where` is `True`.

Examples¶

import numpy as np
import autonfeat as aft
import autonfeat.functional as F

# Random data
n_samples = 100
x = np.random.rand(n_samples)

# Create sliding window
ws = 10
ss = 10
window = aft.SlidingWindow(window_size=ws, step_size=ss)

# Get featurizer
featurizer = window.use(F.skewness_tf)

# Get features
features = featurizer(x)

# Print features
print(features)

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