def local_thresholding_prop(conn_matrix, coords, labels, thr):
"""
Threshold the adjacency matrix by building from the minimum spanning tree (MST) and adding
successive N-nearest neighbour degree graphs to achieve target proportional threshold.
Parameters
----------
conn_matrix : array
Weighted NxN matrix.
thr : float
A proportional threshold, between 0 and 1, to achieve through local thresholding.
Returns
-------
conn_matrix_thr : array
Weighted, MST local-thresholded, NxN matrix.
"""
from pynets.core import thresholding
from pynets.stats import netstats
fail_tol = 100
conn_matrix = np.nan_to_num(conn_matrix)
G = nx.from_numpy_matrix(np.abs(conn_matrix))
if not nx.is_connected(G):
[G, pruned_nodes] = netstats.prune_disconnected(G)
pruned_nodes.sort(reverse=True)
coords_pre = list(coords)
labels_pre = list(labels)
if len(pruned_nodes) > 0:
for j in pruned_nodes:
labels_pre.pop(j)
coords_pre.pop(j)
conn_matrix = nx.to_numpy_array(G)
labels = labels_pre
coords = coords_pre
maximum_edges = G.number_of_edges()
min_t = nx.minimum_spanning_tree(thresholding.weight_to_distance(G),
weight="distance")
len_edges = min_t.number_of_edges()
upper_values = np.triu_indices(np.shape(conn_matrix)[0], k=1)
weights = np.array(conn_matrix[upper_values])
edgenum = int(float(thr) * float(len(weights[~np.isnan(weights)])))
if len_edges > edgenum:
print("%s%s%s" % (
'Warning: The minimum spanning tree already has: ', len_edges,
' edges, select more edges. Local Threshold will be applied by just retaining the Minimum '
'Spanning Tree'))
conn_matrix_thr = nx.to_numpy_array(G)
return conn_matrix_thr, coords, labels
k = 1
len_edge_list = []
while len_edges < edgenum and k <= np.shape(conn_matrix)[0] and (
len(len_edge_list[-fail_tol:]) -
len(set(len_edge_list[-fail_tol:]))) < (fail_tol - 1):
# print(k)
# print(len_edges)
len_edge_list.append(len_edges)
# Create nearest neighbour graph
nng = thresholding.knn(conn_matrix, k)
# Remove edges from the NNG that exist already in the new graph/MST
nng.remove_edges_from(min_t.edges())
number_before = nng.number_of_edges()
if nng.number_of_edges() == 0 and number_before >= maximum_edges:
break
# Add weights to NNG
for e in nng.edges():
nng.edges[e[0], e[1]]['weight'] = float(conn_matrix[e[0], e[1]])
# Obtain list of edges from the NNG in order of weight
edge_list = sorted(nng.edges(data=True),
key=lambda t: t[2]['weight'],
reverse=True)
# Add edges in order of connectivity strength
for edge in edge_list:
# print("%s%s" % ('Adding edge to mst: ', edge))
min_t.add_edges_from([edge])
len_edges = min_t.number_of_edges()
if len_edges >= edgenum:
print(len_edges)
break
k += 1
conn_matrix_bin = thresholding.binarize(
nx.to_numpy_array(min_t,
nodelist=sorted(min_t.nodes()),
dtype=np.float64))
# Enforce original dimensionality by padding with zeros.
if conn_matrix_bin.shape != conn_matrix.shape:
if conn_matrix.shape[0] > conn_matrix_bin.shape[0]:
result = np.zeros(conn_matrix.shape)
result[:conn_matrix_bin.shape[0], :conn_matrix_bin.
shape[1]] = conn_matrix_bin
conn_matrix_thr = np.multiply(conn_matrix, result)
else:
result = np.zeros(conn_matrix_bin.shape)
result[:conn_matrix.shape[0], :conn_matrix.shape[1]] = conn_matrix
conn_matrix_thr = np.multiply(conn_matrix_bin, result)
else:
conn_matrix_thr = np.multiply(conn_matrix, conn_matrix_bin)
return conn_matrix_thr, coords, labels
def test_knn(x, thr):
k = int(thr * 10)
gra = thresholding.knn(x, k)
def local_thresholding_prop(conn_matrix, thr):
"""
Threshold the adjacency matrix by building from the minimum spanning tree (MST) and adding
successive N-nearest neighbour degree graphs to achieve target proportional threshold.
Parameters
----------
conn_matrix : array
Weighted NxN matrix.
thr : float
A proportional threshold, between 0 and 1, to achieve through local thresholding.
Returns
-------
conn_matrix_thr : array
Weighted local-thresholding using MST, NxN matrix.
References
----------
.. [1] Alexander-Bloch, A. F., Gogtay, N., Meunier, D., Birn, R., Clasen, L.,
Lalonde, F., … Bullmore, E. T. (2010). Disrupted modularity and local
connectivity of brain functional networks in childhood-onset schizophrenia.
Frontiers in Systems Neuroscience. https://doi.org/10.3389/fnsys.2010.00147
.. [2] Tewarie, P., van Dellen, E., Hillebrand, A., & Stam, C. J. (2015).
The minimum spanning tree: An unbiased method for brain network analysis.
NeuroImage. https://doi.org/10.1016/j.neuroimage.2014.10.015
"""
from pynets.core import thresholding
fail_tol = 100
conn_matrix = np.nan_to_num(conn_matrix)
G = nx.from_numpy_matrix(np.abs(conn_matrix))
maximum_edges = G.number_of_edges()
Gcc = sorted(nx.connected_components(G), key=len, reverse=True)
G0 = G.subgraph(Gcc[0])
min_t = nx.minimum_spanning_tree(thresholding.weight_to_distance(G0),
weight="distance")
min_t.add_nodes_from(G.nodes())
len_edges = min_t.number_of_edges()
upper_values = np.triu_indices(np.shape(conn_matrix)[0], k=1)
weights = np.array(conn_matrix[upper_values])
edgenum = int(float(thr) * float(len(weights[~np.isnan(weights)])))
if len_edges > edgenum:
print(
f"Warning: The minimum spanning tree already has: {len_edges} edges, select more edges. Local Threshold "
f"will be applied by just retaining the Minimum Spanning Tree")
conn_matrix_thr = nx.to_numpy_array(G)
return conn_matrix_thr
k = 1
len_edge_list = []
while (len_edges < edgenum and k <= np.shape(conn_matrix)[0]
and (len(len_edge_list[-fail_tol:]) -
len(set(len_edge_list[-fail_tol:]))) < (fail_tol - 1)):
# print(k)
# print(len_edges)
len_edge_list.append(len_edges)
# Create nearest neighbour graph
nng = thresholding.knn(conn_matrix, k)
# Remove edges from the NNG that exist already in the new graph/MST
nng.remove_edges_from(min_t.edges())
number_before = nng.number_of_edges()
if nng.number_of_edges() == 0 and number_before >= maximum_edges:
break
# Add weights to NNG
for e in nng.edges():
nng.edges[e[0], e[1]]["weight"] = float(conn_matrix[e[0], e[1]])
# Obtain list of edges from the NNG in order of weight
edge_list = sorted(nng.edges(data=True),
key=lambda t: t[2]["weight"],
reverse=True)
# Add edges in order of connectivity strength
for edge in edge_list:
# print(f"Adding edge to mst: {edge}")
min_t.add_edges_from([edge])
len_edges = min_t.number_of_edges()
if len_edges >= edgenum:
# print(len_edges)
break
k += 1
conn_matrix_bin = thresholding.binarize(
nx.to_numpy_array(min_t, nodelist=sorted(G.nodes()), dtype=np.float64))
try:
conn_matrix_thr = np.multiply(conn_matrix, conn_matrix_bin)
return conn_matrix_thr
except ValueError:
print(
"MST thresholding failed. Check raw graph output manually for debugging."
)