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Delta Var Preprocessor Transform

The Delta Var Preprocessor Transform shifts the input signal by the var of the signal. The is defined as:

\[ x_{shifted_{i}} = x_{i} - \sigma^{2}_{x}, \quad \forall i \in \{1, \dots, N\} \]

For shifting signals by a custom \(\delta\), see the Delta Transform Preprocessor. For more on how we compute the var of a signal, check out var function.

Bases: Preprocess

Preprocess the signal by shifting each element in the signal by the variance of the signal.

__call__(signal, ddof=0, where=lambda : not np.isnan(x))

Compute the variance of the signal and shift the signal by this variance.

Parameters:

Name Type Description Default
signal ndarray

The array to compute the delta with.

 required
ddof Union[int, int_]

The delta degrees of freedom. Default is 0. See numpy.var for more information.

 0
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
ndarray

The shifted signal.

Examples

Here we look at an example where we shift two signals by their var to demonstrate the effect of the Delta Var Preprocessor Transform.

Transform Signal

First, we define the signals as two normal distributions with different means and variances. Then, we apply the Delta Var Preprocessor Transform to both signals.

A univariate normal distribution with mean \(\mu\) and var \(\sigma\) is defined as:

\[ \mathcal{N}(\mu, \sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x - \mu)^{2}}{2 \sigma^{2}}} \]
import numpy as np
import autonfeat as aft

# Number of samples
n_samples = 100

# Generate sample data
x1 = np.random.normal(0, 1, n_samples)
x2 = np.random.normal(5, 5, n_samples)

# Define preprocessor
preprocessor = aft.preprocess.DeltaVarPreprocessor()

shifted_x1 = preprocessor(x1)
shifted_x2 = preprocessor(x2)

Visualize Transform

Next, we visualize the effect of the transform on the signals.

import matplotlib.pyplot as plt

# Plot original data
plt.figure(figsize=(8, 4))
plt.subplot(1, 2, 1)
plt.plot(x1, '.', color='green', label='x1')
plt.plot(x2, '.', color='orange', label='x2')
plt.legend()
plt.title('Original Data')

# Plot shifted data
plt.subplot(1, 2, 2)
plt.plot(shifted_x1, '.', color='green', label='x1 shifted')
plt.plot(shifted_x2, '.', color='orange', label='x2 shifted')
plt.legend()
plt.title('Shifted Data')

plt.tight_layout()
plt.show()

This can be seen in the figure below.

DeltaVar

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