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Median Transform

The median transform computes the median of a window. When combined with the SlidingWindow abstraction, the median transform can be used to compute the median feature of a time series. The median is defined as: (write the formula as two cases for even and odd length vectors and index with i for each case)

\[ \text{median}(x) = \begin{cases} 0.5 \cdot (x_{\lfloor n/2 \rfloor} + x_{\lceil n/2 \rceil}) & \text{if $n$ is even} \\ x_{\lfloor n/2 \rfloor} & \text{if $n$ is odd} \end{cases} \]

where \(x\) is a vector of length \(n\).

Bases: Transform

Compute the median of the values.

__call__(signal_window, method='linear', where=lambda : not np.isnan(x))

Compute the median of the values in x.

Parameters:

Name Type Description Default
signal_window ndarray

The array to compute the median of.

 required
method str

The method to use when computing the quantile. Default is 'linear'. See numpy.quantile for more information.

 'linear'
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_, int_]

A scalar value representing the median of the signal.

Examples

import numpy as np
import autonfeat as aft

# 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)

# Create transform
tf = aft.MedianTransform()

# Get featurizer
featurizer = window.use(tf)

# Get features
features = featurizer(x)

# Print features
print(window)
print(tf)
print(features)

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