WIP: functional connectivity

[ncullen93]

Hi all,

This is a duplicate of my mne-python PR, where I propose an expansion of the scope of mne-python's functional connectivity (FC) measures. I have just started my PhD and am working on EEG-based Connectomics, so it is ideal for me to incorporate my connectivity code to the mne-python package over the next few years.

Correlation-based and mutual information-based measures are quite common in the literature and easy to implement, so I've submitted some examples of those first. A good reference for FC measures is Wang et al (2014) "A systematic framework for functional connectivity measures."

For now, I will plan to continually implement various FC measures as I've found in the literature while awaiting discussion on where to take this. I will also continue learning the mne-python API so I can integrate my code better.

Again, ideally it would make sense to have measures from the 7 major categories of FC measures. The current functionality from "spectral.py" belongs to the 4th category in my understanding:

    1) correlation
    2) h^2
    3) mutual information
    4) coherence
    5) Granger
    6) transfer entropy
    7) MVAR-frequency domain-based techniques

To note, I would also like to incorporate dynamic functional connectivity (FC over multiple epochs) and more causal effective connectivity, so an entire discussion on connectivity overall might be worthwhile.

Best Nick