Median Function¶

The median function computes the median of a window. When combined with the SlidingWindow abstraction, the median function 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 $n$.

Compute the median of the values in x.

Parameters:

Name	Type	Description	Default
`x`	`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, float_]`	The median of the values in `x`.

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.median_tf)

# Get features
features = featurizer(x)

# Print features
print(features)

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