def _dwpc_general_case(graph, metapath, damping=0, dtype=numpy.float64):
"""
A slow but general function to compute the degree-weighted
path count. Works by splitting the metapath at junctions
where one node is joined to multiple nodes over a metaedge.
Parameters
----------
graph : hetio.hetnet.Graph
metapath : hetio.hetnet.MetaPath
damping : float
dtype : dtype object
"""
dwpc_step = functools.partial(_node_to_children,
graph=graph,
metapath=metapath,
damping=damping,
dtype=dtype)
start_nodes, cols, adj = metaedge_to_adjacency_matrix(graph, metapath[0])
rows, fin_nodes, adj = metaedge_to_adjacency_matrix(graph, metapath[-1])
number_start = len(start_nodes)
number_end = len(fin_nodes)
dwpc_matrix = []
if len(metapath) > 1:
for i in range(number_start):
search = numpy.zeros(number_start, dtype=dtype)
search[i] = 1
step1 = [dwpc_step(node=search, metapath_index=0, history=None)]
k = 1
while k < len(metapath):
k += 1
step2 = []
for group in step1:
for child in group['children']:
hist = copy.deepcopy(group['history'])
out = dwpc_step(node=child,
metapath_index=group['next_index'],
history=hist)
if out['children']:
step2.append(out)
step1 = step2
final_children = [
group for group in step2 if group['children'] != []
]
end_nodes = sum([
child for group in final_children
for child in group['children']
])
if type(end_nodes) not in (list, numpy.ndarray):
end_nodes = numpy.zeros(number_end)
dwpc_matrix.append(end_nodes)
else:
dwpc_matrix = _degree_weight(adj, damping=damping, dtype=dtype)
dwpc_matrix = numpy.array(dwpc_matrix, dtype=dtype)
return start_nodes, fin_nodes, dwpc_matrix
def metapath_to_degree_dicts(graph, metapath):
metapath = graph.metagraph.get_metapath(metapath)
_, _, source_adj_mat = metaedge_to_adjacency_matrix(graph, metapath[0], dense_threshold=0.7)
_, _, target_adj_mat = metaedge_to_adjacency_matrix(graph, metapath[-1], dense_threshold=0.7)
source_degrees = source_adj_mat.sum(axis=1).flat
target_degrees = target_adj_mat.sum(axis=0).flat
source_degree_to_ind = degrees_to_degree_to_ind(source_degrees)
target_degree_to_ind = degrees_to_degree_to_ind(target_degrees)
return source_degree_to_ind, target_degree_to_ind
def _node_to_children(graph,
metapath,
node,
metapath_index,
damping=0,
history=None,
dtype=numpy.float64):
"""
Returns a history adjusted list of child nodes. Used in _dwpc_general_case.
Parameters
----------
graph : hetio.hetnet.Graph
metapath : hetio.hetnet.MetaPath
node : numpy.ndarray
metapath_index : int
damping : float
history : numpy.ndarray
dtype : dtype object
Returns
-------
dict
List of child nodes and a single numpy.ndarray of the newly
updated history vector.
"""
metaedge = metapath[metapath_index]
metanodes = list(metapath.get_nodes())
freq = collections.Counter(metanodes)
repeated = {i for i in freq.keys() if freq[i] > 1}
if history is None:
history = {
i.target:
numpy.ones(len(metaedge_to_adjacency_matrix(graph, i)[1]),
dtype=dtype)
for i in metapath if i.target in repeated
}
history = history.copy()
if metaedge.source in history:
history[metaedge.source] -= numpy.array(node != 0, dtype=dtype)
rows, cols, adj = metaedge_to_adjacency_matrix(graph,
metaedge,
dtype=dtype)
adj = _degree_weight(adj, damping, dtype=dtype)
vector = node @ adj
if metaedge.target in history:
vector *= history[metaedge.target]
children = [i for i in numpy.diag(vector) if i.any()]
return {
'children': children,
'history': history,
'next_index': metapath_index + 1
}
def dwwc_sequential(graph,
metapath,
damping=0.5,
dense_threshold=0,
dtype=numpy.float64):
"""
Compute the degree-weighted walk count (DWWC) in which nodes can be
repeated within a path.
Parameters
----------
graph : hetio.hetnet.Graph
metapath : hetio.hetnet.MetaPath
damping : float
dense_threshold : float (0 <= dense_threshold <= 1)
sets the density threshold at which a sparse matrix will be
converted to a dense automatically.
dtype : dtype object
"""
dwwc_matrix = None
row_names = None
for metaedge in metapath:
rows, cols, adj_mat = metaedge_to_adjacency_matrix(
graph, metaedge, dense_threshold=dense_threshold, dtype=dtype)
adj_mat = _degree_weight(adj_mat, damping, dtype=dtype)
if dwwc_matrix is None:
row_names = rows
dwwc_matrix = adj_mat
else:
dwwc_matrix = dwwc_matrix @ adj_mat
dwwc_matrix = sparsify_or_densify(dwwc_matrix, dense_threshold)
return row_names, cols, dwwc_matrix
def dwpc_to_degrees(graph, metapath, damping=0.5, ignore_zeros=False):
"""
Yield a description of each cell in a DWPC matrix adding source and target
node degree info as well as the corresponding path count.
"""
metapath = graph.metagraph.get_metapath(metapath)
_, _, source_adj_mat = metaedge_to_adjacency_matrix(graph, metapath[0], dense_threshold=0.7)
_, _, target_adj_mat = metaedge_to_adjacency_matrix(graph, metapath[-1], dense_threshold=0.7)
source_degrees = source_adj_mat.sum(axis=1).flat
target_degrees = target_adj_mat.sum(axis=0).flat
del source_adj_mat, target_adj_mat
source_path = graph.get_nodes_path(metapath.source(), file_format='tsv')
source_node_df = pandas.read_table(source_path)
source_node_names = list(source_node_df['name'])
target_path = graph.get_nodes_path(metapath.target(), file_format='tsv')
target_node_df = pandas.read_table(target_path)
target_node_names = list(target_node_df['name'])
row_names, col_names, dwpc_matrix = graph.read_path_counts(metapath, 'dwpc', damping)
dwpc_matrix = numpy.arcsinh(dwpc_matrix / dwpc_matrix.mean())
if scipy.sparse.issparse(dwpc_matrix):
dwpc_matrix = dwpc_matrix.toarray()
_, _, path_count = graph.read_path_counts(metapath, 'dwpc', 0.0)
if scipy.sparse.issparse(path_count):
path_count = path_count.toarray()
row_inds, col_inds = range(len(row_names)), range(len(col_names))
for row_ind, col_ind in itertools.product(row_inds, col_inds):
dwpc_value = dwpc_matrix[row_ind, col_ind]
if ignore_zeros and dwpc_value == 0:
continue
row = {
'source_id': row_names[row_ind],
'target_id': col_names[col_ind],
'source_name': source_node_names[row_ind],
'target_name': target_node_names[col_ind],
'source_degree': source_degrees[row_ind],
'target_degree': target_degrees[col_ind],
'path_count': path_count[row_ind, col_ind],
'dwpc': dwpc_value,
}
yield collections.OrderedDict(row)
def _multi_dot(metapath, order, i, j, graph, damping, dense_threshold, dtype):
"""
Perform matrix multiplication with the given order. Modified from
numpy.linalg.linalg._multi_dot (https://git.io/vh31f) which is released
under a 3-Clause BSD License (https://git.io/vhCDC).
"""
if i == j:
_, _, adj_mat = metaedge_to_adjacency_matrix(
graph, metapath[i], dense_threshold=dense_threshold, dtype=dtype)
adj_mat = _degree_weight(adj_mat, damping=damping, dtype=dtype)
return adj_mat
return _multi_dot(metapath, order, i, order[i, j], graph, damping, dense_threshold, dtype) \
@ _multi_dot(metapath, order, order[i, j] + 1, j, graph, damping, dense_threshold, dtype)
def metaedge_to_data_array(graph, metaedge, dtype=numpy.bool_):
"""
Return an xarray.DataArray that's an adjacency matrix where source nodes
are columns and target nodes are rows.
"""
source_node_ids, target_node_ids, adjacency_matrix = (
metaedge_to_adjacency_matrix(graph, metaedge, dtype=dtype))
dims = metaedge.source.identifier, metaedge.target.identifier
coords = source_node_ids, target_node_ids
data_array = xarray.DataArray(adjacency_matrix,
coords=coords,
dims=dims,
name=metaedge.get_unicode_str())
return data_array
def _dwpc_short_repeat(graph,
metapath,
damping=0.5,
dense_threshold=0,
dtype=numpy.float64):
"""
One metanode repeated 3 or fewer times (A-A-A), not (A-A-A-A)
This can include other random inserts, so long as they are not
repeats. Must start and end with the repeated node. Acceptable
examples: (A-B-A-A), (A-B-A-C-D-E-F-A), (A-B-A-A), etc.
"""
segments = get_segments(graph.metagraph, metapath)
assert len(segments) <= 3
# Account for different head and tail possibilities.
head_segment = None
tail_segment = None
dwpc_matrix = None
dwpc_tail = None
# Label the segments as head, tail, and repeat
for i, segment in enumerate(segments):
if segment.source() == segment.target():
repeat_segment = segment
else:
if i == 0:
head_segment = segment
else:
tail_segment = segment
# Calculate DWPC for the middle ("repeat") segment
repeated_metanode = repeat_segment.source()
index_of_repeats = [
i for i, v in enumerate(repeat_segment.get_nodes())
if v == repeated_metanode
]
for metaedge in repeat_segment[:index_of_repeats[1]]:
rows, cols, adj = metaedge_to_adjacency_matrix(
graph, metaedge, dtype=dtype, dense_threshold=dense_threshold)
adj = _degree_weight(adj, damping, dtype=dtype)
if dwpc_matrix is None:
row_names = rows
dwpc_matrix = adj
else:
dwpc_matrix = dwpc_matrix @ adj
dwpc_matrix = remove_diag(dwpc_matrix, dtype=dtype)
# Extra correction for random metanodes in the repeat segment
if len(index_of_repeats) == 3:
for metaedge in repeat_segment[index_of_repeats[1]:]:
rows, cols, adj = metaedge_to_adjacency_matrix(
graph, metaedge, dtype=dtype, dense_threshold=dense_threshold)
adj = _degree_weight(adj, damping, dtype=dtype)
if dwpc_tail is None:
dwpc_tail = adj
else:
dwpc_tail = dwpc_tail @ adj
dwpc_tail = remove_diag(dwpc_tail, dtype=dtype)
dwpc_matrix = dwpc_matrix @ dwpc_tail
dwpc_matrix = remove_diag(dwpc_matrix, dtype=dtype)
col_names = cols
if head_segment:
row_names, cols, head_dwpc = dwpc(graph,
head_segment,
damping=damping,
dense_threshold=dense_threshold,
dtype=dtype)
dwpc_matrix = head_dwpc @ dwpc_matrix
if tail_segment:
rows, col_names, tail_dwpc = dwpc(graph,
tail_segment,
damping=damping,
dense_threshold=dense_threshold,
dtype=dtype)
dwpc_matrix = dwpc_matrix @ tail_dwpc
return row_names, col_names, dwpc_matrix