Calculate temporal cross correlation coefficients (Pearson’s coefficient) on a TimeSeries datatype and return a graph.CorrelationCoefficients dataype. The correlation matrix is widely used to represent functional connectivity (FC).
Compute the node-pairwise pearson correlation coefficient of the given input 4D TimeSeries datatype.
Return a CrossCorrelation datatype, whose values of are between -1 and 1, inclusive.
See: http://docs.scipy.org/doc/numpy/reference/generated/numpy.corrcoef.html
traits on this class:
- t_end (\(t_{end}\))
- t_start (\(t_{start}\))
- time_series (Time Series)
Calculate temporal cross correlation on a TimeSeries datatype and return a temporal_correlations.CrossCorrelation dataype.
Compute the node-pairwise cross-correlation of the given input 4D TimeSeries DataType.
Return a CrossCorrelation DataType. It contains the cross-correlation sequences for all possible combinations of the nodes.
See: http://www.scipy.org/doc/api_docs/SciPy.signal.signaltools.html#correlate
traits on this class:
- time_series (Time Series)
Adapter that uses the traits module to generate interfaces for ... Analyzer.
The present class will do the following actions:
the time series is divided in time window of fixed length and with an overlapping of fixed length. The data-points within each window, centered at time ti, are used to calculate FC(ti) as Pearson correlation. The ij element of the FCD matrix is calculated as the Pearson correlation between FC(ti) and FC(tj) -in a vector
(length of time during which FC matrix are high correlated).
The algorithm can produce 2 kind of results:
– fcs calculated over the epochs of stability (excluded the first one = artifact, due to initial conditions) – 3 eigenvectors, associated to the 3 largest eigenvalues, of the fcs are extracted
– fc over the all time series is calculated – 3 first eigenvectors, associated to the 3 largest eigenvalues, of the fcs are extracted
fcd matrix whose values are between -1 and 1, inclusive.
(Value=1.1 for time not belonging to epochs of stability identified with spectral embedding algorithm) in case 2: fcd matrix segmented identical to the fcd matrix not segmented
dictionary containing the eigenvectors.
dictionary containing the eigenvalues
connectivity associated to the TimeSeriesRegions
traits on this class:
- sp (Spanning between two consecutive sliding window (ms))
- sw (Sliding window length (ms))
- time_series (Time Series)
Calculate an FFT on a TimeSeries DataType and return a FourierSpectrum DataType.
A class for calculating the FFT of a TimeSeries object of TVB and returning a FourierSpectrum object. A segment length and windowing function can be optionally specified. By default the time series is segmented into 1 second blocks and no windowing function is applied.
traits on this class:
- detrend (Detrending)
- segment_length (Segment(window) length (ms))
- time_series (Time Series)
- window_function (Windowing function)
Implementation of differet BOLD signal models. Four different models are distinguished:
Classical means that the coefficients used to compute the BOLD signal are derived as described in [Obata2004] . Revised coefficients are defined in [Stephan2007]
References:
| [Stephan2007] | Stephan KE, Weiskopf N, Drysdale PM, Robinson PA, Friston KJ (2007) Comparing hemodynamic models with DCM. NeuroImage 38: 387-401. |
| [Obata2004] | Obata, T.; Liu, T. T.; Miller, K. L.; Luh, W. M.; Wong, E. C.; Frank, L. R. & Buxton, R. B. (2004) Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the balloon model to the interpretation of BOLD transients. Neuroimage, 21:144-153 |
A class for calculating the simulated BOLD signal given a TimeSeries object of TVB and returning another TimeSeries object.
The haemodynamic model parameters based on constants for a 1.5 T scanner.
traits on this class:
- E0 (\(E_0\))
- RBM (Revised BOLD Model)
- TE (\(TE\))
- V0 (\(V_0\))
- alpha (\(\tau_f\))
- bold_model (Select BOLD model equations)
- dt (\(dt\))
- epsilon (\(\epsilon\))
- integrator (Integration scheme)
- neural_input_transformation (Neural input transformation)
- nu_0 (\(\nu_0\))
- r_0 (\(r_0\))
- tau_f (\(\tau_f\))
- tau_o (\(\tau_o\))
- tau_s (\(\tau_s\))
- time_series (Time Series)
Useful graph analyses.
Node betweenness centrality is the fraction of all shortest paths in the network that contain a given node. Nodes with high values of betweenness centrality participate in a large number of shortest paths.
| Parameters: | A – binary (directed/undirected) connection matrix (array) |
|---|---|
| Returns: | BC: a vector representing node between centrality vector. |
Notes:
Betweenness centrality may be normalised to the range [0,1] as BC/[(N-1)(N-2)], where N is the number of nodes in the network.
Original Mika Rubinov, UNSW/U Cambridge, 2007-2012 - From BCT 2012-12-04
Reference: [1] Kintali (2008) arXiv:0809.1906v2 [cs.DS] (generalization to directed and disconnected graphs)
Author: Paula Sanz Leon
Compute the inverse shortest path lengths of G.
| Parameters: | G – binary undirected connection matrix |
|---|---|
| Returns: | D: matrix of inverse distances |
Computes global efficiency or local efficiency of a connectivity matrix. The global efficiency is the average of inverse shortest path length, and is inversely related to the characteristic path length.
The local efficiency is the global efficiency computed on the neighborhood of the node, and is related to the clustering coefficient.
| Parameters: |
|
|---|---|
| Returns: |
|
References: [1] Latora and Marchiori (2001) Phys Rev Lett 87:198701.
Note
Algorithm: algebraic path count
Note
Original: Mika Rubinov, UNSW, 2008-2010 - From BCT 2012-12-04
Note
Tested with Numpy 1.7
Warning
tested against Matlab version... needs indexing improvement
Example:
>>> import numpy.random
>>> A = np.random.rand(5, 5)
>>> E = efficiency_bin(A)
>>> E.shape == (1, )
>>> True
If you want to compute the local efficiency for every node in the network:
>>> E = efficiency_bin(A, compute_local_efficiency=True)
>>> E.shape == (5, 1)
>>> True
Author: Paula Sanz Leon
Get connected components sizes. Returns the size of the largest component of an undirected graph specified by the binary and undirected connection matrix A.
| Parameters: | A – array - binary undirected (BU) connectivity matrix. |
|---|---|
| Returns: |
|
| Raises: | Value Error - If A is not square. |
Warning
Requires NetworkX
Author: Paula Sanz Leon
A strategy to lesion a connectivity matrix.
A single node is removed at each step until the network is reduced to only 2 nodes. This method represents a structural failure analysis and it should be run several times with different random sequences.
| Parameters: |
|
|---|---|
| Returns: |
|
References: Alstott et al. (2009).
Author: Paula Sanz Leon
A strategy to lesion a connectivity matrix.
A single node is removed at each step until the network is reduced to only 2 nodes. At each step different graph metrics are computed (degree, strength and betweenness centrality). The single node with the highest degree, strength or centrality is removed.
| Parameters: |
|
|---|---|
| Returns: |
|
See also: sequential_random_deletion, localized_area_deletion
References: Alstott et al. (2009).
Author: Paula Sanz Leon
Perform Independent Component Analysis on a TimeSeries Object and returns an IndependentComponents datatype.
Takes a TimeSeries datatype (x) and returns the unmixed temporal sources (S) and the estimated mixing matrix (A).
| Math: | x = A S |
|---|
ICA takes time-points as observations and nodes as variables.
It uses the FastICA algorithm implemented in the scikit-learn toolkit, and its intended usage is as a blind source separation method.
traits on this class:
- n_components (Number of principal components to unmix.)
- time_series (Time Series)
This module implements information theoretic analyses.
TODO: Fix docstring of sampen TODO: Convert sampen to a traited class
Computes (quadratic) sample entropy of a given input signal y, with embedding dimension n, and a match tolerance of r (ref 2). If an array of scale factors, taus, are given, the signal will be coarsened by each factor and a corresponding entropy will be computed (ref 1). If no value for r is given, it will be set to 0.15*y.std().
Currently, the implementation is lazy and expects or coerces scale factors to integer values.
With qse=True (default) the probability p is normalized for the value of r, giving the quadratic sample entropy, such that results from different values of r can be meaningfully compared (ref 2).
To check that algorithm is working, look at ref 1, fig 1, and run
>>> sampen(randn(3*10000), r=.15, taus=r_[1:20], qse=False, m=2)
Filler analyzer: Takes a TimeSeries object and returns a Float.
Return the Kuramoto synchronization index.
Useful metric for a parameter analysis when the collective brain dynamics represent coupled oscillatory processes.
The order parameters are \(r\) and \(Psi\).
The first is the phase coherence of the population of oscillators (KSI) and the second is the average phase.
When \(r=0\) means 0 coherence among oscillators.
Input: TimeSeries DataType
Output: Float
This is a crude indicator of synchronization among nodes over the entire network.
#NOTE: For the time being it is meant to be another global metric. However, it should be consider to have a sort of TimeSeriesDatatype for this analyzer.
traits on this class:
- segment (Segmentation factor)
- start_point (Start point (ms))
- time_series (Time Series)
Filler analyzer: Takes a TimeSeries object and returns two Floats.
These metrics are described and used in:
Hellyer et al. The Control of Global Brain Dynamics: Opposing Actions of Frontoparietal Control and Default Mode Networks on Attention. The Journal of Neuroscience, January 8, 2014, 34(2):451– 461
Proxy of spatial coherence (V):
Proxy metastability (M): the variability in spatial coherence of the signal globally or locally (within a network) over time.
Proxy synchrony (S) : the reciprocal of mean spatial variance across time.
Subtract the mean time-series and compute.
Input: TimeSeries DataType
Output: Float, Float
The two metrics given by this analyzers are a proxy for metastability and synchrony. The underlying dynamical model used in the article was the Kuramoto model.
traits on this class:
- segment (Segmentation factor)
- start_point (Start point (ms))
- time_series (Time Series)
Filler analyzer: Takes a TimeSeries object and returns a Float.
Zero-centres all the time-series and then calculates the variance over all data points.
Input: TimeSeries DataType
Output: Float
This is a crude indicator of “excitability” or oscillation amplitude of the models over the entire network.
traits on this class:
- segment (Segmentation factor)
- start_point (Start point (ms))
- time_series (Time Series)
Filler analyzer: Takes a TimeSeries object and returns a Float.
Zero-centres all the time-series, calculates the variance for each node time-series and returns the variance of the node variances.
Input: TimeSeries DataType
Output: Float
This is a crude indicator of how different the “excitability” of the model is from node to node.
traits on this class:
- segment (Segmentation factor)
- start_point (Start point (ms))
- time_series (Time Series)
This is a base class for all metrics on timeSeries dataTypes. Metric means an algorithm computing a single value for an entire TimeSeries.
traits on this class:
- segment (Segmentation factor)
- start_point (Start point (ms))
- time_series (Time Series)
Compute cross coherence between all nodes in a time series.
Adapter for cross-coherence algorithm(s) traits on this class:
- nfft (Data-points per block)
- time_series (Time Series)
Calculate the cross spectrum and complex coherence on a TimeSeries datatype and return a ComplexCoherence datatype.
A class for calculating the FFT of a TimeSeries and returning a ComplexCoherenceSpectrum datatype.
| [Freyer_2012] | Freyer, F.; Reinacher, M.; Nolte, G.; Dinse, H. R. and Ritter, P. Repetitive tactile stimulation changes resting-state functional connectivity-implications for treatment of sensorimotor decline. Front Hum Neurosci, Bernstein Focus State Dependencies of Learning and Bernstein Center for Computational Neuroscience Berlin, Germany., 2012, 6, 144 |
Input: originally the input could be 2D (tpts x nodes/channels), and it was possible to give a 3D array (e.g., tpspt x nodes/cahnnels x trials) via the segment_length attribute. Current TVB implementation can handle 4D or 2D TimeSeries datatypes. Be warned: the 4D TimeSeries will be averaged and squeezed.
Output: (main arrays) - the cross-spectrum - the complex coherence, from which the imaginary part can be extracted
By default the time series is segmented into 1 second epoch blocks and 0.5 second 50% overlapping segments to which a Hanning function is applied.
traits on this class:
- average_segments (Average across segments)
- detrend_ts (Detrend time series)
- epoch_length (Epoch length [ms])
- max_freq (Maximum frequency)
- npat (dummy variable)
- segment_length (Segment length [ms])
- segment_shift (Segment shift [ms])
- subtract_epoch_average (Subtract average across epochs)
- time_series (Time Series)
- window_function (Windowing function)
- zeropad (Zeropadding)
Calculate a ... on a .. datatype and return a ...
Compute the temporal covariance of nodes in a TimeSeries dataType. A nodes x nodes matrix is returned for each (state-variable, mode).
traits on this class:
- time_series (Time Series)
Perform Principal Component Analysis (PCA) on a TimeSeries datatype and return a PrincipalComponents datatype.
Return principal component weights and the fraction of the variance that they explain.
PCA takes time-points as observations and nodes as variables.
traits on this class:
- time_series (Time Series)
Calculate a wavelet transform on a TimeSeries datatype and return a WaveletSpectrum datatype.
A class for calculating the wavelet transform of a TimeSeries object of TVB and returning a WaveletSpectrum object. The sampling period and frequency range of the result can be specified. The mother wavelet can also be specified... (So far, only Morlet.)
| [TBetal_1996] | C. Tallon-Baudry et al, Stimulus Specificity of Phase-Locked and Non-Phase-Locked 40 Hz Visual Responses in Human., J Neurosci 16(13):4240-4249, 1996. |
| [Mallat_1999] | S. Mallat, A wavelet tour of signal processing., book, Academic Press, 1999. |
traits on this class:
- frequencies (Frequency range of result (kHz).)
- mother (Wavelet function)
- normalisation (Normalisation)
- q_ratio (Q-ratio)
- sample_period (Sample period of result (ms))
- time_series (Time Series)