medusa.local_activation package

Submodules

medusa.local_activation.nonlinear_parameters module

medusa.local_activation.nonlinear_parameters.central_tendency_measure(signal, r)

This method implements the central tendency measure (CTM). This parameter is useful to quantify the variability of a signal. It is based on calculating the second-order differences diagram of the time series and then counting the points within a radius “r”. CTM assigns higher values to less variable signals

References

Cohen, M. E., Hudson, D. L., & Deedwania, P. C. (1996). Applying continuous chaotic modeling to cardiac signal analysis. IEEE Engineering in Medicine and Biology Magazine, 15(5), 97-102.

Parameters

• signal (numpy.ndarray) – Signal with shape [n_epochs, n_samples, n_channels].

• r (double) – Radius used to compute the CTM.

Returns

ctm – CTM values for each channel in “signal”. [n_epochs, n_channels].

Return type

numpy.ndarray

medusa.local_activation.nonlinear_parameters.lempelziv_complexity(signal)

Calculate the signal binarisation and the Lempel-Ziv’s complexity.

This function takes advantage of its implementation in C to achieve a high performance.

Parameters

signal (numpy.ndarray) – MEEG Signal [n_epochs, n_samples, n_channels]

Returns

lz_result – Lempel-Ziv values for each epoch and each channel. [n_epochs, n_channels].

Return type

numpy.ndarray

medusa.local_activation.nonlinear_parameters.multiscale_entropy(signal, max_scale, m, r)

This method implements the Multiscale Entropy (MSE). MSE is a measurement of complexity which measures the irregularity of a signal over multiple time-scales. This is accomplished through estimation of the Sample Entropy (SampEn) on coarse-grained versions of the original signal. As a result of the these calculations, MSE curves are obtained and can be used to compare the complexity of time-series. The MSE curve whose entropy values are higher for the most of time-scales is considered more complex.

References

Costa, M., Goldberger, A. L., & Peng, C. K. (2005). Multiscale entropy analysis of biological signals, Physical review E, 71(2), 021906.

Parameters

• signal (numpy.ndarray) – MEEG Signal. [n_epochs, n_samples, n_channels].

• max_scale (int) – Maximum scale value

• m (int) – Sequence length

• r (float) – Tolerance

Returns

mse_result – SampEn values for each scale for each channel in “signal” . [n_epochs, max_scale, n_channels].

Return type

numpy.ndarray

medusa.local_activation.nonlinear_parameters.multiscale_lempelziv_complexity(signal, W)

Calculate the multiscale signal binarisation and the Multiscale Lempel-Ziv’s complexity.

References

Ibáñez-Molina, A. J., Iglesias-Parro, S., Soriano, M. F., & Aznarte, J. I, Multiscale Lempel-Ziv complexity for EEG measures. Clinical Neurophysiology, (2015), 126(3), 541–548.

Parameters

• signal (numpy.ndarray) – MEEG Signal [n_epochs, n_samples, n_channels]

• W (list or numpy 1D array) – Set of window length to consider at multiscale binarisation stage. Values must be odd.

Returns

result – Matrix of results with shape [n_epochs, n_window_length, n_channels]

Return type

numpy.ndarray

medusa.local_activation.nonlinear_parameters.sample_entropy(signal, m, r, dist_type='chebyshev')

This method implements the sample entropy (SampEn). SampEn is an irregularity measure that assigns higher values to more irregular time sequences. It has two tuning parameters: the sequence length (m) and the tolerance (r)

Notes: IF A = 0 or B = 0, SamEn would return an infinite value. However, the lowest non-zero conditional probability that SampEn should report is A/B = 2/[(N-m-1)*(N-m)]. SampEn has the following limits:

• Lower bound: 0

• Upper bound : log(N-m) + log(N-m-1) - log(2)

References

Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology.

Parameters

• signal (numpy.ndarray) – Signal with shape [n_epochs, n_samples, n_channels].

• m (int) – Sequence length

• r (float) – Tolerance

• dist_type (string) – Distance metric

Returns

sampen – SampEn value. [n_epochs, n_channels]

Return type

numpy.ndarray

medusa.local_activation.spectral_parameteres module

medusa.local_activation.spectral_parameteres.absolute_band_power(psd, fs, target_band)

This method computes the absolute band power of the signal in the given band using the power spectral density (PSD).

Parameters

• psd (numpy array) – PSD of the signal with shape [n_epochs, n_samples, n_channels]. Some of these dimensions may not exist in advance. In these case, create new axis using np.newaxis. E.g., non-epoched single-channel psd with shape [n_samples] can be passed to this function with psd[numpy.newaxis, …, numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate those axes.

• fs (int) – Sampling frequency of the signal

• target_band (numpy 2D array) – Frequency band where to calculate the power in Hz. E.g., [8, 13]

Returns

powers – RP value for eachh epoch and channel. [n_epochs, n_channels]

Return type

numpy 2D array

medusa.local_activation.spectral_parameteres.median_frequency(psd, fs, target_band=(1, 70))

This method computes the median frequency (MF) of the signal in the given band.

Parameters

• psd (numpy array) – PSD of the signal with shape [n_epochs, n_samples, n_channels]. Some of these dimensions may not exist in advance. In these case, create new axis using np.newaxis. E.g., non-epoched single-channel psd with shape [n_samples] can be passed to this function with psd[numpy.newaxis, …, numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate those axes.

• fs (int) – Sampling frequency of the signal

• target_band (numpy array) – Frequency band where the MF will be computed. [b1_start, b1_end]. Default [1, 70].

Returns

median_freqs – MF value for each epoch and channel with shape [n_epochs x n_channels].

Return type

numpy 2D array

medusa.local_activation.spectral_parameteres.relative_band_power(psd, fs, target_band, baseline_band=None)

This method computes the relative band power of the signal in the given band using the power spectral density (PSD). Do not use this method on PSDs that are already normalized! In this case, use absolute_band_power function.

Parameters

• psd (numpy array) – PSD with shape [n_epochs, n_samples, n_channels]. Some of these dimensions may not exist in advance. In these case, create new axis using np.newaxis. E.g., non-epoched single-channel psd with shape [n_samples] can be passed to this function with psd[numpy.newaxis, …, numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate those axes.

• fs (int) – Sampling frequency of the signal

• target_band (numpy nd array) – Frequency band where to calculate the power in Hz. E.g., [8, 13]

• baseline_band (numpy nd array or None) – Frequency band where used as baseline in Hz. Leave to None to normalize by the whole spectrum, which is preferred in most cases

Returns

powers – RP value for each epoch and channel. [n_epochs, n_channels]

Return type

numpy 2D array

medusa.local_activation.spectral_parameteres.shannon_spectral_entropy(psd, fs, target_band=(1, 70))

Computes the Shannon spectral entropy of the power spectral density (PSD)

in the given band.

Parameters

psdnumpy array

PSD of the signal with shape [n_epochs, n_samples, n_channels]. Some of these dimensions may not exist in advance. In these case, create new axis using np.newaxis. E.g., non-epoched single-channel psd with shape [n_samples] can be passed to this function with psd[numpy.newaxis, …, numpy.newaxis]. Afterwards, you may use numpy.squeeze to eliminate those axes.

fsint

Sampling frequency of the signal

target_bandnumpy array

Frequency band where the SE will be computed. [b1_start, b1_end]. Default [1, 70]

sample_entropynumpy 2D array

SE value for each epoch and channel with shape [n_epochs x n_channels].

medusa.local_activation.statistics module

medusa.local_activation.statistics.signed_r2(class1, class2, signed=True, axis=0)

This function computes the basic form of the squared point biserial correlation coefficient (r2-value).

Parameters

• class1 (list or numpy.ndarray) – Data that belongs to the first class

• class1 – Data that belongs to the second class

• signed (bool (Optional, default=True)) – Controls if the sign should be mantained.

• axis (int (Optional, default=0)) – Dimension along which the r2-value is computed. Therefore, if class1 and class2 has dimensions of [observations x samples] and dim=0, the r2-value will have dimensions [1 x samples].

Returns

r2 – (Signed) r2-value.

Return type

numpy.ndarray