def _gen_mat_data(n: int = 20,
m: int = 20,
p: int = 0.50,
mat_type: str = 'sb',
binary: bool = False,
asfile: bool = True,
n_graphs: int = 1):
if binary is True:
wt = 1
else:
wt = np.random.uniform
mat_list = []
mat_file_list = []
for nm in range(n_graphs):
if mat_type == 'er':
mat = largest_connected_component(
symmetrize(
remove_loops(
er_nm(n,
m,
wt=np.random.uniform,
wtargs=dict(low=0, high=1)))))
elif mat_type == 'sb':
if p is None:
raise ValueError(
f"for mat_type {mat_type}, p cannot be None")
mat = largest_connected_component(
symmetrize(
remove_loops(
sbm(np.array([n]),
np.array([[p]]),
wt=wt,
wtargs=dict(low=0, high=1)))))
else:
raise ValueError(f"mat_type {mat_type} not recognized!")
mat_list.append(mat)
if asfile is True:
mat_path_tmp = tempfile.NamedTemporaryFile(mode='w+',
suffix='.npy',
delete=False)
mat_path = str(mat_path_tmp.name)
np.save(mat_path, mat)
mat_file_list.append(mat_path)
mat_path_tmp.close()
return {'mat_list': mat_list, 'mat_file_list': mat_file_list}
def __init__(self,
est_path,
prune,
norm,
out_fmt="gpickle",
remove_self_loops=True):
import graspologic.utils as gu
self.est_path = est_path
self.prune = prune
self.norm = norm
self.out_fmt = out_fmt
self.in_mat = None
# Load and threshold matrix
self.in_mat_raw = utils.load_mat(self.est_path)
# De-diagnal and remove nan's and inf's, ensure edge weights are
# positive
self.in_mat = np.array(
np.array(thresholding.autofix(np.array(np.abs(self.in_mat_raw)))))
# Remove self-loops and ensure symmetry
if remove_self_loops is True:
self.in_mat = gu.remove_loops(gu.symmetrize(self.in_mat))
else:
self.in_mat = gu.symmetrize(self.in_mat)
self.in_mat[np.where(np.isnan(self.in_mat)
| np.isinf(self.in_mat))] = 0
# Create nx graph
self.G = nx.from_numpy_array(self.in_mat)
def signal_flow(A):
"""Implementation of the signal flow metric from Varshney et al 2011
Parameters
----------
A : [type]
[description]
Returns
-------
[type]
[description]
"""
A = A.copy()
A = remove_loops(A)
W = (A + A.T) / 2
D = np.diag(np.sum(W, axis=1))
L = D - W
b = np.sum(W * np.sign(A - A.T), axis=1)
L_pinv = np.linalg.pinv(L)
z = L_pinv @ b
return z
def calculate_p_upper(A):
A = remove_loops(A)
n = len(A)
triu_inds = np.triu_indices(n, k=1)
upper_triu_sum = A[triu_inds].sum()
total_sum = A.sum()
upper_triu_p = upper_triu_sum / total_sum
return upper_triu_p
def _augment_graph(
graph: Union[nx.Graph, nx.OrderedGraph, nx.DiGraph, nx.OrderedDiGraph],
node_ids: Set[Hashable],
weight_attribute: Optional[str],
perform_augment_diagonal: bool = True,
) -> np.ndarray:
graph_sparse = nx.to_scipy_sparse_matrix(graph,
weight=weight_attribute,
nodelist=node_ids)
graphs_loops_removed: np.ndarray = remove_loops(graph_sparse)
graphs_ranked: np.ndarray = pass_to_ranks(graphs_loops_removed)
if perform_augment_diagonal:
graphs_diag_augmented: np.ndarray = augment_diagonal(graphs_ranked)
return graphs_diag_augmented
return graphs_ranked
def _gen_mat_data(n: int=20, m: int=20, p: int=0.50,
mat_type: str='sb', binary: bool=False,
asfile: bool=True, n_graphs: int=1,
lcc: bool=False, modality: str='func'):
if binary is True:
wt = 1
else:
wt = np.random.uniform
mat_list = []
mat_file_list = []
if n_graphs > 0:
for nm in range(n_graphs):
if mat_type == 'er':
mat = symmetrize(
remove_loops(er_nm(n, m, wt=np.random.uniform,
wtargs=dict(low=0, high=1))))
elif mat_type == 'sb':
if p is None:
raise ValueError(
f"for mat_type {mat_type}, p cannot be None")
mat = symmetrize(
remove_loops(sbm(np.array([n]), np.array([[p]]),
wt=wt, wtargs=dict(low=0,
high=1))))
else:
raise ValueError(f"mat_type {mat_type} not recognized!")
if lcc is True:
mat = largest_connected_component(mat)
mat_list.append(autofix(mat))
if asfile is True:
path_tmp = tempfile.NamedTemporaryFile(mode='w+',
suffix='.npy',
delete=False)
mat_path_tmp = str(path_tmp.name)
out_folder = f"{str(Path.home())}/test_mats"
os.makedirs(out_folder, exist_ok=True)
if modality == 'func':
mat_path = f"{out_folder}/graph_sub-999_modality-func_" \
f"model-corr_template-" \
f"MNI152_2mm_" \
f"parc_tol-6fwhm_hpass-" \
f"0Hz_" \
f"signal-mean_thrtype-prop_thr-" \
f"{round(random.uniform(0, 1),2)}.npy"
elif modality == 'dwi':
mat_path = f"{out_folder}/graph_sub-999_modality-func_" \
f"model-csa_template-" \
f"MNI152_2mm_tracktype-local_" \
f"traversal-det_minlength-30_" \
f"tol-5_thrtype-prop_thr-" \
f"{round(random.uniform(0, 1),2)}.npy"
shutil.copyfile(mat_path_tmp, mat_path)
np.save(mat_path, mat)
mat_file_list.append(mat_path)
path_tmp.close()
return {'mat_list': mat_list, 'mat_file_list': mat_file_list}
def motif_matching(
paths,
ID,
atlas,
namer_dir,
name_list,
metadata_list,
multigraph_list_all,
graph_path_list_all,
rsn=None,
):
import networkx as nx
import numpy as np
import glob
import pickle
from pynets.core import thresholding
from pynets.stats.netmotifs import compare_motifs
from sklearn.metrics.pairwise import cosine_similarity
from pynets.stats.netstats import community_resolution_selection
from graspologic.utils import remove_loops, symmetrize
from pynets.core.nodemaker import get_brainnetome_node_attributes
[struct_graph_path, func_graph_path] = paths
struct_mat = np.load(struct_graph_path)
func_mat = np.load(func_graph_path)
[struct_coords, struct_labels, struct_label_intensities] = \
get_brainnetome_node_attributes(glob.glob(
f"{str(Path(struct_graph_path).parent.parent)}/nodes/*.json"),
struct_mat.shape[0])
[func_coords, func_labels, func_label_intensities] = \
get_brainnetome_node_attributes(glob.glob(
f"{str(Path(func_graph_path).parent.parent)}/nodes/*.json"),
func_mat.shape[0])
# Find intersecting nodes across modalities (i.e. assuming the same
# parcellation, but accomodating for the possibility of dropped nodes)
diff1 = list(set(struct_label_intensities) - set(func_label_intensities))
diff2 = list(set(func_label_intensities) - set(struct_label_intensities))
G_struct = nx.from_numpy_array(struct_mat)
G_func = nx.from_numpy_array(func_mat)
bad_idxs = []
for val in diff1:
bad_idxs.append(struct_label_intensities.index(val))
bad_idxs = sorted(list(set(bad_idxs)), reverse=True)
if type(struct_coords) is np.ndarray:
struct_coords = list(tuple(x) for x in struct_coords)
for j in bad_idxs:
G_struct.remove_node(j)
print(f"Removing: {(struct_labels[j], struct_coords[j])}...")
del struct_labels[j], struct_coords[j]
bad_idxs = []
for val in diff2:
bad_idxs.append(func_label_intensities.index(val))
bad_idxs = sorted(list(set(bad_idxs)), reverse=True)
if type(func_coords) is np.ndarray:
func_coords = list(tuple(x) for x in func_coords)
for j in bad_idxs:
G_func.remove_node(j)
print(f"Removing: {(func_labels[j], func_coords[j])}...")
del func_labels[j], func_coords[j]
struct_mat = nx.to_numpy_array(G_struct)
func_mat = nx.to_numpy_array(G_func)
struct_mat = thresholding.autofix(symmetrize(remove_loops(struct_mat)))
func_mat = thresholding.autofix(symmetrize(remove_loops(func_mat)))
if func_mat.shape == struct_mat.shape:
func_mat[~struct_mat.astype("bool")] = 0
struct_mat[~func_mat.astype("bool")] = 0
print(
"Edge disagreements after matching: ",
sum(sum(abs(func_mat - struct_mat))),
)
metadata = {}
assert (len(struct_coords) == len(struct_labels) == len(func_coords) ==
len(func_labels) == func_mat.shape[0])
metadata["coords"] = struct_coords
metadata["labels"] = struct_labels
metadata_list.append(metadata)
struct_mat = np.maximum(struct_mat, struct_mat.T)
func_mat = np.maximum(func_mat, func_mat.T)
struct_mat = thresholding.standardize(struct_mat)
func_mat = thresholding.standardize(func_mat)
struct_node_comm_aff_mat = community_resolution_selection(
nx.from_numpy_matrix(np.abs(struct_mat)))[1]
func_node_comm_aff_mat = community_resolution_selection(
nx.from_numpy_matrix(np.abs(func_mat)))[1]
struct_comms = []
for i in np.unique(struct_node_comm_aff_mat):
struct_comms.append(struct_node_comm_aff_mat == i)
func_comms = []
for i in np.unique(func_node_comm_aff_mat):
func_comms.append(func_node_comm_aff_mat == i)
sims = cosine_similarity(struct_comms, func_comms)
try:
struct_comm = struct_comms[np.argmax(sims, axis=0)[0]]
except BaseException:
print('Matching by structural communities failed...')
struct_comm = struct_mat
try:
func_comm = func_comms[np.argmax(sims, axis=0)[0]]
except BaseException:
print('Matching by functional communities failed...')
func_comm = func_mat
comm_mask = np.equal.outer(struct_comm, func_comm).astype(bool)
try:
assert comm_mask.shape == struct_mat.shape == func_mat.shape
except AssertionError as e:
e.args += (comm_mask, comm_mask.shape, struct_mat,
struct_mat.shape, func_mat, func_mat.shape)
try:
struct_mat[~comm_mask] = 0
except BaseException:
print('Skipping community masking...')
try:
func_mat[~comm_mask] = 0
except BaseException:
print('Skipping community masking...')
struct_name = struct_graph_path.split("/rawgraph_")[-1].split(
".npy")[0]
func_name = func_graph_path.split("/rawgraph_")[-1].split(".npy")[0]
name = f"sub-{ID}_{atlas}_mplx_Layer-1_{struct_name}_" \
f"Layer-2_{func_name}"
name_list.append(name)
struct_mat = np.maximum(struct_mat, struct_mat.T)
func_mat = np.maximum(func_mat, func_mat.T)
try:
[mldict, g_dict] = compare_motifs(struct_mat, func_mat, name,
namer_dir)
except BaseException:
print(f"Adaptive thresholding by motif comparisons failed "
f"for {name}. This usually happens when no motifs are found")
return [], [], [], []
multigraph_list_all.append(list(mldict.values())[0])
graph_path_list = []
for thr in list(g_dict.keys()):
multigraph_path_list_dict = {}
[struct, func] = g_dict[thr]
struct_out = f"{namer_dir}/struct_{atlas}_{struct_name}.npy"
func_out = f"{namer_dir}/struct_{atlas}_{func_name}_" \
f"motif-{thr}.npy"
np.save(struct_out, struct)
np.save(func_out, func)
multigraph_path_list_dict[f"struct_{atlas}_{thr}"] = struct_out
multigraph_path_list_dict[f"func_{atlas}_{thr}"] = func_out
graph_path_list.append(multigraph_path_list_dict)
graph_path_list_all.append(graph_path_list)
else:
print(
f"Skipping {rsn} rsn, since structural and functional graphs are "
f"not identical shapes.")
return name_list, metadata_list, multigraph_list_all, graph_path_list_all
def adjacency_spectral_embedding(
graph: Union[nx.Graph, nx.DiGraph, nx.OrderedGraph, nx.OrderedDiGraph],
dimensions: int = 100,
elbow_cut: Optional[int] = None,
svd_solver_algorithm: SvdAlgorithmType = "randomized",
svd_solver_iterations: int = 5,
svd_seed: Optional[int] = None,
weight_attribute: str = "weight",
) -> Embeddings:
"""
Given a directed or undirected networkx graph (*not* multigraph), generate an
Embeddings object.
Adjacency spectral embeddings are extremely egocentric, implying that results are
slanted toward the core-periphery of each node. This is in contrast to Laplacian
spectral embeddings, which look further into the latent space when it captures
change.
`Adjacency Spectral Embedding Tutorial
<https://microsoft.github.io/graspologic/tutorials/embedding/AdjacencySpectralEmbed.html>`_
Graphs will always have their diagonal augmented. In other words, a self-loop
will be created for each node with a weight corresponding to the weighted degree.
Lastly, all weights will be rescaled based on their relative rank in the graph,
which is beneficial in minimizing anomalous results if some edge weights are
extremely atypical of the rest of the graph.
Parameters
----------
graph : Union[nx.Graph, nx.OrderedGraph, nx.DiGraph, nx.OrderedDiGraph]
An undirected or directed graph. The graph **must**:
- be fully numerically weighted (every edge must have a real, numeric weight
or else it will be treated as an unweighted graph)
- be a basic graph (meaning it should not be a multigraph; if you have a
multigraph you must first decide how you want to handle the weights of the
edges between two nodes, whether summed, averaged, last-wins,
maximum-weight-only, etc)
dimensions : int (default=100)
Dimensions to use for the svd solver.
For undirected graphs, if ``elbow_cut==None``, you will receive an embedding
that has ``nodes`` rows and ``dimensions`` columns.
For directed graphs, if ``elbow_cut==None``, you will receive an embedding that
has ``nodes`` rows and ``2*dimensions`` columns.
If ``elbow_cut`` is specified to be not ``None``, we will cut the embedding at
``elbow_cut`` elbow, but the provided ``dimensions`` will be used in the
creation of the SVD.
elbow_cut : Optional[int] (default=None)
Using a process described by Zhu & Ghodsi in their paper "Automatic
dimensionality selection from the scree plot via the use of profile likelihood",
truncate the dimensionality of the return on the ``elbow_cut``-th elbow.
By default this value is ``None`` but can be used to reduce the dimensionality
of the returned tensors.
svd_solver_algorithm : str (default="randomized")
allowed values: {'randomized', 'full', 'truncated'}
SVD solver to use:
- 'randomized'
Computes randomized svd using
:func:`sklearn.utils.extmath.randomized_svd`
- 'full'
Computes full svd using :func:`scipy.linalg.svd`
Does not support ``graph`` input of type scipy.sparse.csr_matrix
- 'truncated'
Computes truncated svd using :func:`scipy.sparse.linalg.svds`
svd_solver_iterations : int (default=5)
Number of iterations for randomized SVD solver. Not used by 'full' or
'truncated'. The default is larger than the default in randomized_svd
to handle sparse matrices that may have large slowly decaying spectrum.
svd_seed : Optional[int] (default=None)
Used to seed the PRNG used in the ``randomized`` svd solver algorithm.
weight_attribute : str (default="weight")
The edge dictionary key that contains the weight of the edge.
Returns
-------
Embeddings
Raises
------
beartype.roar.BeartypeCallHintParamViolation if parameters do not match type hints
ValueError if values are not within appropriate ranges or allowed values
See Also
--------
graspologic.pipeline.embed.Embeddings
graspologic.embed.AdjacencySpectralEmbed
graspologic.embed.select_svd
Notes
-----
The singular value decomposition:
.. math:: A = U \Sigma V^T
is used to find an orthonormal basis for a matrix, which in our case is the
adjacency matrix of the graph. These basis vectors (in the matrices U or V) are
ordered according to the amount of variance they explain in the original matrix.
By selecting a subset of these basis vectors (through our choice of dimensionality
reduction) we can find a lower dimensional space in which to represent the graph.
References
----------
.. [1] Sussman, D.L., Tang, M., Fishkind, D.E., Priebe, C.E. "A
Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs,"
Journal of the American Statistical Association, Vol. 107(499), 2012
.. [2] Levin, K., Roosta-Khorasani, F., Mahoney, M. W., & Priebe, C. E. (2018).
Out-of-sample extension of graph adjacency spectral embedding. PMLR: Proceedings
of Machine Learning Research, 80, 2975-2984.
.. [3] Zhu, M. and Ghodsi, A. (2006). Automatic dimensionality selection from the
scree plot via the use of profile likelihood. Computational Statistics & Data
Analysis, 51(2), pp.918-930.
"""
check_argument(dimensions >= 1, "dimensions must be positive")
check_argument(elbow_cut is None or elbow_cut >= 1, "elbow_cut must be positive")
check_argument(
svd_solver_algorithm in __SVD_SOLVER_TYPES,
f"svd_solver_algorithm must be one of the values in {','.join(__SVD_SOLVER_TYPES)}",
)
check_argument(svd_solver_iterations >= 1, "svd_solver_iterations must be positive")
check_argument(
svd_seed is None or 0 <= svd_seed <= 2**32 - 1,
"svd_seed must be a nonnegative, 32-bit integer",
)
check_argument(
not graph.is_multigraph(),
"Multigraphs are not supported; you must determine how to represent at most "
"one edge between any two nodes, and handle the corresponding weights "
"accordingly",
)
used_weight_attribute: Optional[str] = weight_attribute
if not is_real_weighted(graph, weight_attribute=weight_attribute):
warnings.warn(
f"Graphs with edges that do not have a real numeric weight set for every "
f"{weight_attribute} attribute on every edge are treated as an unweighted "
f"graph - which presumes all weights are `1.0`. If this is incorrect, "
f"please add a '{weight_attribute}' attribute to every edge with a real, "
f"numeric value (e.g. an integer or a float) and call this function again."
)
used_weight_attribute = None # this supercedes what the user said, because
# not all of the weights are real numbers, if they exist at all
# this weight=1.0 treatment actually happens in nx.to_scipy_sparse_matrix()
node_labels = np.array(list(graph.nodes()))
graph_as_csr = nx.to_scipy_sparse_matrix(
graph, weight=used_weight_attribute, nodelist=node_labels
)
if not is_fully_connected(graph):
warnings.warn("More than one connected component detected")
graph_sans_loops = remove_loops(graph_as_csr)
ranked_graph = pass_to_ranks(graph_sans_loops)
augmented_graph = augment_diagonal(ranked_graph)
embedder = AdjacencySpectralEmbed(
n_components=dimensions,
n_elbows=None, # in the short term, we do our own elbow finding
algorithm=svd_solver_algorithm,
n_iter=svd_solver_iterations,
svd_seed=svd_seed,
concat=False,
diag_aug=False,
)
results = embedder.fit_transform(augmented_graph)
results_arr: np.ndarray
if elbow_cut is None:
if isinstance(results, tuple) or graph.is_directed():
results_arr = np.concatenate(results, axis=1)
else:
results_arr = results
else:
column_index = _index_of_elbow(embedder.singular_values_, elbow_cut)
if isinstance(results, tuple):
left, right = results
left = left[:, :column_index]
right = right[:, :column_index]
results_arr = np.concatenate((left, right), axis=1)
else:
results_arr = results[:, :column_index]
embeddings = Embeddings(node_labels, results_arr)
return embeddings
#%% [markdown]
# ### Load the data
#%%
mg = load_maggot_graph()
mg = mg[mg.nodes["paper_clustered_neurons"]]
# mg = mg[mg.nodes["left"]]
# mg = mg[mg.nodes["class1"] == "KC"]
#%%
import networkx as nx
adj = mg.sum.adj.copy()
adj = remove_loops(adj)
adj = binarize(adj)
g = nx.from_numpy_array(adj, create_using=nx.DiGraph)
nodelist = sorted(g.nodes)
incidence = nx.incidence_matrix(g, nodelist=nodelist, oriented=True).T
weights = np.ones(incidence.shape[0])
from sklearn.linear_model import LinearRegression
lr = LinearRegression(fit_intercept=False, n_jobs=-1)
lr.fit(incidence, weights)
lr_score = lr.coef_
mg.nodes["lr_score"] = lr_score
mg.nodes.sort_values("lr_score", inplace=True)
from src.visualization import adjplot, CLASS_COLOR_DICT
def laplacian_spectral_embedding(
graph: Union[nx.Graph, nx.OrderedGraph, nx.DiGraph, nx.OrderedDiGraph],
form: LaplacianFormType = "R-DAD",
dimensions: int = 100,
elbow_cut: Optional[int] = None,
svd_solver_algorithm: SvdAlgorithmType = "randomized",
svd_solver_iterations: int = 5,
svd_seed: Optional[int] = None,
weight_attribute: str = "weight",
regularizer: Optional[numbers.Real] = None,
) -> Embeddings:
"""
Given a directed or undirected networkx graph (*not* multigraph), generate an
Embeddings object.
The laplacian spectral embedding process is similar to the adjacency spectral
embedding process, with the key differentiator being that the LSE process looks
further into the latent space when it captures changes, whereas the ASE process
is egocentric and focused on immediate differentiators in a node's periphery.
All weights will be rescaled based on their relative rank in the graph,
which is beneficial in minimizing anomalous results if some edge weights are
extremely atypical of the rest of the graph.
Parameters
----------
graph : Union[nx.Graph, nx.OrderedGraph, nx.DiGraph, nx.OrderedDiGraph]
An undirected or directed graph. The graph **must**:
- be fully numerically weighted (every edge must have a real, numeric weight
or else it will be treated as an unweighted graph)
- be a basic graph (meaning it should not be a multigraph; if you have a
multigraph you must first decide how you want to handle the weights of the
edges between two nodes, whether summed, averaged, last-wins,
maximum-weight-only, etc)
form : str (default="R-DAD")
Specifies the type of Laplacian normalization to use. Allowed values are:
{ "DAD", "I-DAD", "R-DAD" }. See
:func:`~graspologic.utils.to_laplacian` for more details regarding form.
dimensions : int (default=100)
Dimensions to use for the svd solver.
For undirected graphs, if ``elbow_cut==None``, you will receive an embedding
that has ``nodes`` rows and ``dimensions`` columns.
For directed graphs, if ``elbow_cut==None``, you will receive an embedding that
has ``nodes`` rows and ``2*dimensions`` columns.
If ``elbow_cut`` is specified to be not ``None``, we will cut the embedding at
``elbow_cut`` elbow, but the provided ``dimensions`` will be used in the
creation of the SVD.
elbow_cut : Optional[int] (default=None)
Using a process described by Zhu & Ghodsi in their paper "Automatic
dimensionality selection from the scree plot via the use of profile likelihood",
truncate the dimensionality of the return on the ``elbow_cut``-th elbow.
By default this value is ``None`` but can be used to reduce the dimensionality
of the returned tensors.
svd_solver_algorithm : str (default="randomized")
allowed values: {'randomized', 'full', 'truncated'}
SVD solver to use:
- 'randomized'
Computes randomized svd using
:func:`sklearn.utils.extmath.randomized_svd`
- 'full'
Computes full svd using :func:`scipy.linalg.svd`
Does not support ``graph`` input of type scipy.sparse.csr_matrix
- 'truncated'
Computes truncated svd using :func:`scipy.sparse.linalg.svds`
svd_solver_iterations : int (default=5)
Number of iterations for randomized SVD solver. Not used by 'full' or
'truncated'. The default is larger than the default in randomized_svd
to handle sparse matrices that may have large slowly decaying spectrum.
svd_seed : Optional[int] (default=None)
Used to seed the PRNG used in the ``randomized`` svd solver algorithm.
weight_attribute : str (default="weight")
The edge dictionary key that contains the weight of the edge.
regularizer : Optional[numbers.Real] (default=None)
Only used when form="R-DAD". Must be None or nonnegative.
Constant to be added to the diagonal of degree matrix. If None, average
node degree is added. If int or float, must be >= 0.
Returns
-------
Embeddings
Raises
------
beartype.roar.BeartypeCallHintParamViolation if parameters do not match type hints
ValueError if values are not within appropriate ranges or allowed values
See Also
--------
graspologic.pipeline.embed.Embeddings
graspologic.embed.LaplacianSpectralEmbed
graspologic.embed.select_svd
graspologic.utils.to_laplacian
Notes
-----
The singular value decomposition:
.. math:: A = U \Sigma V^T
is used to find an orthonormal basis for a matrix, which in our case is the
Laplacian matrix of the graph. These basis vectors (in the matrices U or V) are
ordered according to the amount of variance they explain in the original matrix.
By selecting a subset of these basis vectors (through our choice of dimensionality
reduction) we can find a lower dimensional space in which to represent the graph.
References
----------
.. [1] Sussman, D.L., Tang, M., Fishkind, D.E., Priebe, C.E. "A
Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs,"
Journal of the American Statistical Association, Vol. 107(499), 2012.
.. [2] Von Luxburg, Ulrike. "A tutorial on spectral clustering," Statistics
and computing, Vol. 17(4), pp. 395-416, 2007.
.. [3] Rohe, Karl, Sourav Chatterjee, and Bin Yu. "Spectral clustering and
the high-dimensional stochastic blockmodel," The Annals of Statistics,
Vol. 39(4), pp. 1878-1915, 2011.
.. [4] Zhu, M. and Ghodsi, A. (2006). Automatic dimensionality selection from the
scree plot via the use of profile likelihood. Computational Statistics & Data
Analysis, 51(2), pp.918-930.
"""
check_argument(form in __FORMS,
f"form must be one of the values in {','.join(__FORMS)}")
check_argument(dimensions >= 1, "dimensions must be positive")
check_argument(elbow_cut is None or elbow_cut >= 1,
"elbow_cut must be positive")
check_argument(
svd_solver_algorithm in __SVD_SOLVER_TYPES,
f"svd_solver_algorithm must be one of the values in {','.join(__SVD_SOLVER_TYPES)}",
)
check_argument(svd_solver_iterations >= 1,
"svd_solver_iterations must be positive")
check_argument(
svd_seed is None or 0 <= svd_seed <= 2**32 - 1,
"svd_seed must be a nonnegative, 32-bit integer",
)
check_argument(
regularizer is None or float(regularizer) >= 0,
"regularizer must be nonnegative",
)
check_argument(
not graph.is_multigraph(),
"Multigraphs are not supported; you must determine how to represent at most "
"one edge between any two nodes, and handle the corresponding weights "
"accordingly",
)
used_weight_attribute: Optional[str] = weight_attribute
if not is_real_weighted(graph, weight_attribute=weight_attribute):
warnings.warn(
f"Graphs with edges that do not have a real numeric weight set for every "
f"{weight_attribute} attribute on every edge are treated as an unweighted "
f"graph - which presumes all weights are `1.0`. If this is incorrect, "
f"please add a '{weight_attribute}' attribute to every edge with a real, "
f"numeric value (e.g. an integer or a float) and call this function again."
)
used_weight_attribute = None # this supercedes what the user said, because
# not all of the weights are real numbers, if they exist at all
# this weight=1.0 treatment actually happens in nx.to_scipy_sparse_matrix()
node_labels = np.array(list(graph.nodes()))
graph_as_csr = nx.to_scipy_sparse_matrix(graph,
weight=used_weight_attribute,
nodelist=node_labels)
if not is_fully_connected(graph):
warnings.warn("More than one connected component detected")
graph_sans_loops = remove_loops(graph_as_csr)
ranked_graph = pass_to_ranks(graph_sans_loops)
embedder = LaplacianSpectralEmbed(
form=form,
n_components=dimensions,
n_elbows=None, # in the short term, we do our own elbow finding
algorithm=svd_solver_algorithm,
n_iter=svd_solver_iterations,
svd_seed=svd_seed,
concat=False,
)
results = embedder.fit_transform(ranked_graph)
results_arr: np.ndarray
if elbow_cut is None:
if isinstance(results, tuple) or graph.is_directed():
results_arr = np.concatenate(results, axis=1)
else:
results_arr = results
else:
column_index = _index_of_elbow(embedder.singular_values_, elbow_cut)
if isinstance(results, tuple):
left, right = results
left = left[:, :column_index]
right = right[:, :column_index]
results_arr = np.concatenate((left, right), axis=1)
else:
results_arr = results[:, :column_index]
embeddings = Embeddings(node_labels, results_arr)
return embeddings
def matching(
paths,
atlas,
namer_dir,
):
import glob
import networkx as nx
import numpy as np
from pynets.core import thresholding
from pynets.statistics.utils import parse_closest_ixs
from graspologic.utils import remove_loops, symmetrize, \
multigraph_lcc_intersection
[dwi_graph_path, func_graph_path] = paths
dwi_mat = np.load(dwi_graph_path)
func_mat = np.load(func_graph_path)
dwi_mat = thresholding.autofix(symmetrize(remove_loops(dwi_mat)))
func_mat = thresholding.autofix(symmetrize(remove_loops(func_mat)))
dwi_mat = thresholding.standardize(dwi_mat)
func_mat = thresholding.standardize(func_mat)
node_dict_dwi = parse_closest_ixs(
glob.glob(f"{str(Path(dwi_graph_path).parent.parent)}"
f"/nodes/*.json"), dwi_mat.shape[0])[1]
node_dict_func = parse_closest_ixs(
glob.glob(f"{str(Path(func_graph_path).parent.parent)}"
f"/nodes/*.json"), func_mat.shape[0])[1]
G_dwi = nx.from_numpy_array(dwi_mat)
nx.set_edge_attributes(G_dwi, 'structural',
nx.get_edge_attributes(G_dwi, 'weight').values())
nx.set_node_attributes(G_dwi, dict(node_dict_dwi), name='dwi')
#G_dwi.nodes(data=True)
G_func = nx.from_numpy_array(func_mat)
nx.set_edge_attributes(G_func, 'functional',
nx.get_edge_attributes(G_func, 'weight').values())
nx.set_node_attributes(G_func, dict(node_dict_func), name='func')
#G_func.nodes(data=True)
R = G_dwi.copy()
R.remove_nodes_from(n for n in G_dwi if n not in G_func)
R.remove_edges_from(e for e in G_dwi.edges if e not in G_func.edges)
G_dwi = R.copy()
R = G_func.copy()
R.remove_nodes_from(n for n in G_func if n not in G_dwi)
R.remove_edges_from(e for e in G_func.edges if e not in G_dwi.edges)
G_func = R.copy()
[G_dwi, G_func] = multigraph_lcc_intersection([G_dwi, G_func])
def writeJSON(metadata_str, outputdir):
import json
import uuid
modality = metadata_str.split('modality-')[1].split('_')[0]
metadata_list = [
i for i in metadata_str.split('modality-')[1].split('_')
if '-' in i
]
hash = str(uuid.uuid4())
filename = f"{outputdir}/sidecar_modality-{modality}_{hash}.json"
metadata_dict = {}
for meta in metadata_list:
k, v = meta.split('-')
metadata_dict[k] = v
with open(filename, 'w+') as jsonfile:
json.dump(metadata_dict, jsonfile, indent=4)
jsonfile.close()
return hash
dwi_name = dwi_graph_path.split("/")[-1].split(".npy")[0]
func_name = func_graph_path.split("/")[-1].split(".npy")[0]
dwi_hash = writeJSON(dwi_name, namer_dir)
func_hash = writeJSON(func_name, namer_dir)
name = f"{atlas}_mplx_layer1-dwi_ensemble-{dwi_hash}_" \
f"layer2-func_ensemble-{func_hash}"
dwi_opt, func_opt, best_mi = optimize_mutual_info(
nx.to_numpy_array(G_dwi), nx.to_numpy_array(G_func), bins=50)
func_mat_final = list(func_opt.values())[0]
dwi_mat_final = list(dwi_opt.values())[0]
G_dwi_final = nx.from_numpy_array(dwi_mat_final)
G_func_final = nx.from_numpy_array(func_mat_final)
G_multi = nx.OrderedMultiGraph(nx.compose(G_dwi_final, G_func_final))
out_name = f"{name}_matchthr-{list(dwi_opt.keys())[0]}_" \
f"{list(func_opt.keys())[0]}"
mG = build_mx_multigraph(nx.to_numpy_array(G_func_final),
nx.to_numpy_array(G_dwi_final), out_name,
namer_dir)
mG_nx = f"{namer_dir}/{out_name}.gpickle"
nx.write_gpickle(G_multi, mG_nx)
dwi_file_out = f"{namer_dir}/{dwi_name}.npy"
func_file_out = f"{namer_dir}/{func_name}.npy"
np.save(dwi_file_out, dwi_mat_final)
np.save(func_file_out, func_mat_final)
return mG_nx, mG, dwi_file_out, func_file_out
