navis.form_factor

navis.form_factor(x, start=-3, stop=3, num=601, parallel=False, n_cores=1, progress=True)

Calculate form factor for given neuron.

The form factor F(q) is a Fourier transform of density-density correlation of particles used to classify objects in polymer physics. Based on Choi et al., 2022 (bioRxiv). Code adapted from github.com/kirichoi/FqClustering.

Parameters:

• x (TreeNeuron | Meshneuron | Dotprops | NeuronList) –

  Neurons to calculate form factor for. A few notes:

  • data should be in micron - if not, you might want to adjust start/stop/min!

  • since this is all about density, it may make sense to resample neurons

• start/stop/num (int) – Start/stop/num describe the (log) space over which to calculate the form factor. Effectively determining the resolution. Assuming x is in microns the defaults mean we pay attention to densities between 1 nm (1e-3 microns) and 1 mm (1e+3 microns). The x-value corresponding to the form factor(s) in Fq will be np.logspace(start, stop, num).

• parallel (bool) – Whether to use multiple cores when x is a NeuronList.

• n_cores (bool) – Number of cores to use when x is a NeuronList and parallel=True. Even on a single core this function makes heavy use of numpy which itself uses multiple threads - it is therefore not

• progress (bool) – Whether to show a progress bar.

Returns:

Fq – For single neurons: (num,) array For Neuronlists: (len(x), num) array

Return type:

np.ndarray

References

Polymer physics-based classification of neurons Kiri Choi, Won Kyu Kim, Changbong Hyeon bioRxiv 2022.04.07.487455; doi: https://doi.org/10.1101/2022.04.07.487455

Examples

>>> import navis
>>> nl = navis.example_neurons(3)
>>> # Resample to 1 node / micron
>>> rs = navis.resample_skeleton(nl, '1 micron')
>>> # Calculate form factor
>>> Fq = navis.form_factor(rs, start=-3, stop=3, num=301,
...                        parallel=True, n_cores=3)
>>> # Plot
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> x = np.logspace(-3, 3,  301)
>>> fig, ax = plt.subplots()
>>> for i in range(len(Fq)):
...     _ = ax.plot(x, Fq[i])
>>> # Make log-log
>>> ax.set_xscale('log')
>>> ax.set_yscale('log')
>>> plt.show()                                              
>>> # Cluster
>>> from scipy.spatial.distance import pdist
>>> from scipy.cluster.hierarchy import dendrogram, linkage
>>> dists = pdist(Fq)
>>> Z = linkage(dists, method='ward')
>>> dn = dendrogram(Z)