def density_thresholding(conn_matrix, thr, max_iters=10000, interval=0.01):
"""
Iteratively apply an absolute threshold to achieve a target density.
Parameters
----------
conn_matrix : np.ndarray
Weighted connectivity matrix
thr : float
Density value between 0-1.
max_iters : int
Maximum number of iterations for performing absolute thresholding. Default is 1000.
interval : float
Interval for increasing the absolute threshold for each iteration. Default is 0.01.
Returns
-------
conn_matrix : np.ndarray
Thresholded connectivity matrix
References
----------
.. [1] van Wijk, B. C. M., Stam, C. J., & Daffertshofer, A. (2010).
Comparing brain networks of different size and connectivity
density using graph theory. PLoS ONE.
https://doi.org/10.1371/journal.pone.0013701
.. [2] Complex network measures of brain connectivity: Uses and interpretations.
Rubinov M, Sporns O (2010) NeuroImage 52:1059-69.
"""
from pynets.core import thresholding
np.fill_diagonal(conn_matrix, 0)
work_thr = 0
i = 1
density = nx.density(nx.from_numpy_matrix(conn_matrix))
if float(thr) < float(density):
while float(i) < max_iters and float(work_thr) < float(1):
work_thr = float(work_thr) + float(interval)
density = nx.density(
nx.from_numpy_matrix(
thresholding.threshold_absolute(conn_matrix, work_thr)))
print("%s%d%s%.2f%s%.2f%s" %
('Iteration ', i, ' -- with Thresh: ', float(work_thr),
' and Density: ', float(density), '...'))
if float(thr) >= float(density):
conn_matrix = thresholding.threshold_absolute(
conn_matrix, work_thr)
break
i = i + 1
else:
print(
'Density of raw matrix is already greater than or equal to the target density requested'
)
return conn_matrix
def density_thresholding(conn_matrix, thr, max_iters=10000, interval=0.01):
"""
Iteratively apply an absolute threshold to achieve a target density.
Parameters
----------
conn_matrix : np.ndarray
Weighted connectivity matrix
thr : float
Density value between 0-1.
max_iters : int
Maximum number of iterations for performing absolute thresholding. Default is 1000.
interval : float
Interval for increasing the absolute threshold for each iteration. Default is 0.01.
Returns
-------
conn_matrix : np.ndarray
Thresholded connectivity matrix
References
----------
.. Adapted from Adapted from bctpy
"""
from pynets.core import thresholding
np.fill_diagonal(conn_matrix, 0)
work_thr = 0
i = 1
density = nx.density(nx.from_numpy_matrix(conn_matrix))
if float(thr) < float(density):
while float(i) < max_iters and float(work_thr) < float(1):
work_thr = float(work_thr) + float(interval)
density = nx.density(
nx.from_numpy_matrix(
thresholding.threshold_absolute(conn_matrix, work_thr)))
print("%s%d%s%.2f%s%.2f%s" %
('Iteration ', i, ' -- with Thresh: ', float(work_thr),
' and Density: ', float(density), '...'))
if float(thr) >= float(density):
conn_matrix = thresholding.threshold_absolute(
conn_matrix, work_thr)
break
i = i + 1
else:
print(
'Density of raw matrix is already greater than or equal to the target density requested'
)
return conn_matrix
def test_thr2prob(x, thr):
s = thresholding.threshold_absolute(thresholding.normalize(x), thr)
s[0][0] = 0.0000001
t = thresholding.thr2prob(s)
assert float(len(t[np.logical_and(t < 0.001, t > 0)])) == float(0.0)
def test_density(x, thr):
d_known = thresholding.est_density(
thresholding.threshold_absolute(x, thr, copy=True))
x = thresholding.density_thresholding(x, d_known)
d_test = thresholding.est_density(x)
assert np.equal(np.round(d_known, 1), np.round(d_test, 1))
def test_threshold_absolute(x, thr, cp):
s = thresholding.threshold_absolute(x, thr, copy=cp)
s_test = [val for arr in s for val in arr
if val >= thr] # search for value > thr
assert round(np.sum(s), 10) == round(np.sum(s_test), 10)
def compare_motifs(struct_mat, func_mat, name, namer_dir, bins=20, N=4):
'''
Compare motif structure and population across structural and functional
graphs to achieve a homeostatic absolute threshold of each that optimizes
multiplex community detection and analysis.
Parameters
----------
in_mat : ndarray
M x M Connectivity matrix
thr : float
Absolute threshold [0, 1].
mlib : list
List of motif classes.
Returns
-------
mf : ndarray
1D vector listing the total motifs of size N for each
class of mlib.
References
----------
.. [1] Battiston, F., Nicosia, V., Chavez, M., & Latora, V. (2017).
Multilayer motif analysis of brain networks. Chaos.
https://doi.org/10.1063/1.4979282
'''
from pynets.stats.netmotifs import adaptivethresh
from pynets.core.thresholding import threshold_absolute
from pynets.core.thresholding import standardize
from scipy import spatial
from nilearn.connectome import sym_matrix_to_vec
import pandas as pd
import gc
mlib = ['1113', '1122', '1223', '2222', '2233', '3333']
# Standardize structural graph
struct_mat = standardize(struct_mat)
dims_struct = struct_mat.shape[0]
struct_mat[range(dims_struct), range(dims_struct)] = 0
at_struct = adaptivethresh(struct_mat, float(0.0), mlib, N)
print("%s%s%s" %
('Layer 1 (structural) has: ', np.sum(at_struct), ' total motifs'))
# Functional graph threshold window
func_mat = standardize(func_mat)
dims_func = func_mat.shape[0]
func_mat[range(dims_func), range(dims_func)] = 0
tmin_func = func_mat.min()
tmax_func = func_mat.max()
threshes_func = np.linspace(tmin_func, tmax_func, bins)
assert np.all(
struct_mat == struct_mat.T), "Structural Matrix must be symmetric"
assert np.all(
func_mat == func_mat.T), "Functional Matrix must be symmetric"
# Count motifs
print("%s%s%s%s" % ('Mining ', N, '-node motifs: ', mlib))
motif_dict = {}
motif_dict['struct'] = {}
motif_dict['func'] = {}
mat_dict = {}
mat_dict['struct'] = sym_matrix_to_vec(struct_mat, discard_diagonal=True)
mat_dict['funcs'] = {}
for thr_func in threshes_func:
# Count
at_func = adaptivethresh(func_mat, float(thr_func), mlib, N)
motif_dict['struct']["%s%s" %
('thr-', np.round(thr_func, 4))] = at_struct
motif_dict['func']["%s%s" % ('thr-', np.round(thr_func, 4))] = at_func
mat_dict['funcs']["%s%s" %
('thr-', np.round(thr_func, 4))] = sym_matrix_to_vec(
threshold_absolute(func_mat, thr_func),
discard_diagonal=True)
print("%s%s%s%s%s" %
('Layer 2 (functional) with absolute threshold of: ',
np.round(thr_func,
2), ' yields ', np.sum(at_func), ' total motifs'))
gc.collect()
df = pd.DataFrame(motif_dict)
for idx in range(len(df)):
df.set_value(
df.index[idx], 'motif_dist',
spatial.distance.cosine(df['struct'][idx], df['func'][idx]))
df = df[pd.notnull(df['motif_dist'])]
for idx in range(len(df)):
df.set_value(
df.index[idx], 'graph_dist_cosine',
spatial.distance.cosine(
mat_dict['struct'].reshape(-1, 1),
mat_dict['funcs'][df.index[idx]].reshape(-1, 1)))
df.set_value(
df.index[idx], 'graph_dist_correlation',
spatial.distance.correlation(
mat_dict['struct'].reshape(-1, 1),
mat_dict['funcs'][df.index[idx]].reshape(-1, 1)))
df['struct_func_3333'] = np.zeros(len(df))
df['struct_func_2233'] = np.zeros(len(df))
df['struct_func_2222'] = np.zeros(len(df))
df['struct_func_1223'] = np.zeros(len(df))
df['struct_func_1122'] = np.zeros(len(df))
df['struct_func_1113'] = np.zeros(len(df))
df['struct_3333'] = np.zeros(len(df))
df['func_3333'] = np.zeros(len(df))
df['struct_2233'] = np.zeros(len(df))
df['func_2233'] = np.zeros(len(df))
df['struct_2222'] = np.zeros(len(df))
df['func_2222'] = np.zeros(len(df))
df['struct_1223'] = np.zeros(len(df))
df['func_1223'] = np.zeros(len(df))
df['struct_1122'] = np.zeros(len(df))
df['func_1122'] = np.zeros(len(df))
df['struct_1113'] = np.zeros(len(df))
df['func_1113'] = np.zeros(len(df))
for idx in range(len(df)):
df.set_value(df.index[idx], 'struct_3333', df['struct'][idx][-1])
df.set_value(df.index[idx], 'func_3333', df['func'][idx][-1])
df.set_value(df.index[idx], 'struct_2233', df['struct'][idx][-2])
df.set_value(df.index[idx], 'func_2233', df['func'][idx][-2])
df.set_value(df.index[idx], 'struct_2222', df['struct'][idx][-3])
df.set_value(df.index[idx], 'func_2222', df['func'][idx][-3])
df.set_value(df.index[idx], 'struct_1223', df['struct'][idx][-4])
df.set_value(df.index[idx], 'func_1223', df['func'][idx][-4])
df.set_value(df.index[idx], 'struct_1122', df['struct'][idx][-5])
df.set_value(df.index[idx], 'func_1122', df['func'][idx][-5])
df.set_value(df.index[idx], 'struct_1113', df['struct'][idx][-6])
df.set_value(df.index[idx], 'func_1113', df['func'][idx][-6])
df['struct_func_3333'] = np.abs(df['struct_3333'] - df['func_3333'])
df['struct_func_2233'] = np.abs(df['struct_2233'] - df['func_2233'])
df['struct_func_2222'] = np.abs(df['struct_2222'] - df['func_2222'])
df['struct_func_1223'] = np.abs(df['struct_1223'] - df['func_1223'])
df['struct_func_1122'] = np.abs(df['struct_1122'] - df['func_1122'])
df['struct_func_1113'] = np.abs(df['struct_1113'] - df['func_1113'])
df = df.drop(columns=['struct', 'func'])
df = df.loc[~(df == 0).all(axis=1)]
df = df.sort_values(by=[
'motif_dist', 'graph_dist_cosine', 'graph_dist_correlation',
'struct_func_3333', 'struct_func_2233', 'struct_func_2222',
'struct_func_1223', 'struct_func_1122', 'struct_func_1113',
'struct_3333', 'func_3333', 'struct_2233', 'func_2233', 'struct_2222',
'func_2222', 'struct_1223', 'func_1223', 'struct_1122', 'func_1122',
'struct_1113', 'func_1113'
],
ascending=[
True, True, False, False, False, False, False,
False, False, False, False, False, False, False,
False, False, False, False, False, False, False
])
# Take the top 25th percentile
df = df.head(int(0.25 * len(df)))
best_threshes = []
best_mats = []
best_multigraphs = []
for key in list(df.index):
func_mat_tmp = func_mat.copy()
struct_mat_tmp = struct_mat.copy()
struct_thr = float(key.split('-')[-1])
func_thr = float(key.split('-')[-1])
best_threshes.append(str(func_thr))
func_mat_tmp[func_mat_tmp < func_thr] = 0
struct_mat_tmp[struct_mat_tmp < struct_thr] = 0
best_mats.append((func_mat_tmp, struct_mat_tmp))
mG = build_mx_multigraph(func_mat, struct_mat, f"{name}_{key}",
namer_dir)
best_multigraphs.append(mG)
mg_dict = dict(zip(best_threshes, best_multigraphs))
g_dict = dict(zip(best_threshes, best_mats))
return mg_dict, g_dict
