# -*- coding: utf-8 -*-
#
# Copyright 2017-2020 Data61, CSIRO
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
__all__ = [
"UniformRandomWalk",
"BiasedRandomWalk",
"UniformRandomMetaPathWalk",
"SampledBreadthFirstWalk",
"SampledHeterogeneousBreadthFirstWalk",
"TemporalRandomWalk",
"DirectedBreadthFirstNeighbours",
]
import numpy as np
import warnings
from collections import defaultdict, deque
from scipy import stats
from scipy.special import softmax
from ..core.schema import GraphSchema
from ..core.graph import StellarGraph
from ..core.utils import is_real_iterable
from ..core.validation import require_integer_in_range, comma_sep
from ..random import random_state
from abc import ABC, abstractmethod
def _default_if_none(value, default, name, ensure_not_none=True):
value = value if value is not None else default
if ensure_not_none and value is None:
raise ValueError(
f"{name}: expected a value to be specified in either `__init__` or `run`, found None in both"
)
return value
class RandomWalk(ABC):
"""
Abstract base class for Random Walk classes. A Random Walk class must implement a ``run`` method
which takes an iterable of node IDs and returns a list of walks. Each walk is a list of node IDs
that contains the starting node as its first element.
"""
def __init__(self, graph, seed=None):
if not isinstance(graph, StellarGraph):
raise TypeError("Graph must be a StellarGraph or StellarDiGraph.")
self.graph = graph
self._random_state, self._np_random_state = random_state(seed)
def _get_random_state(self, seed):
"""
Args:
seed: The optional seed value for a given run.
Returns:
The random state as determined by the seed.
"""
if seed is None:
# Restore the random state
return self._random_state
# seed the random number generator
require_integer_in_range(seed, "seed", min_val=0)
rs, _ = random_state(seed)
return rs
@staticmethod
def _validate_walk_params(nodes, n, length):
if not is_real_iterable(nodes):
raise ValueError(f"nodes: expected an iterable, found: {nodes}")
if len(nodes) == 0:
warnings.warn(
"No root node IDs given. An empty list will be returned as a result.",
RuntimeWarning,
stacklevel=3,
)
require_integer_in_range(n, "n", min_val=1)
require_integer_in_range(length, "length", min_val=1)
@abstractmethod
def run(self, nodes, **kwargs):
pass
class GraphWalk(object):
"""
Base class for exploring graphs.
"""
def __init__(self, graph, graph_schema=None, seed=None):
self.graph = graph
# Initialize the random state
self._check_seed(seed)
self._random_state, self._np_random_state = random_state(seed)
# We require a StellarGraph for this
if not isinstance(graph, StellarGraph):
raise TypeError("Graph must be a StellarGraph or StellarDiGraph.")
if not graph_schema:
self.graph_schema = self.graph.create_graph_schema()
else:
self.graph_schema = graph_schema
if type(self.graph_schema) is not GraphSchema:
self._raise_error(
"The parameter graph_schema should be either None or of type GraphSchema."
)
def get_adjacency_types(self):
# Allow additional info for heterogeneous graphs.
adj = getattr(self, "adj_types", None)
if not adj:
# Create a dict of adjacency lists per edge type, for faster neighbour sampling from graph in SampledHeteroBFS:
self.adj_types = adj = self.graph._adjacency_types(
self.graph_schema, use_ilocs=True
)
return adj
def _check_seed(self, seed):
if seed is not None:
if type(seed) != int:
self._raise_error(
"The random number generator seed value, seed, should be integer type or None."
)
if seed < 0:
self._raise_error(
"The random number generator seed value, seed, should be non-negative integer or None."
)
def _get_random_state(self, seed):
"""
Args:
seed: The optional seed value for a given run.
Returns:
The random state as determined by the seed.
"""
if seed is None:
# Use the class's random state
return self._random_state
# seed the random number generator
rs, _ = random_state(seed)
return rs
def neighbors(self, node):
return self.graph.neighbor_arrays(node, use_ilocs=True)
def run(self, *args, **kwargs):
"""
To be overridden by subclasses. It is the main entry point for performing random walks on the given
graph.
It should return the sequences of nodes in each random walk.
"""
raise NotImplementedError
def _raise_error(self, msg):
raise ValueError("({}) {}".format(type(self).__name__, msg))
def _check_common_parameters(self, nodes, n, length, seed):
"""
Checks that the parameter values are valid or raises ValueError exceptions with a message indicating the
parameter (the first one encountered in the checks) with invalid value.
Args:
nodes: <list> A list of root node ids from which to commence the random walks.
n: <int> Number of walks per node id.
length: <int> Maximum length of each walk.
seed: <int> Random number generator seed.
"""
self._check_nodes(nodes)
self._check_repetitions(n)
self._check_length(length)
self._check_seed(seed)
def _check_nodes(self, nodes):
if nodes is None:
self._raise_error("A list of root node IDs was not provided.")
if not is_real_iterable(nodes):
self._raise_error("Nodes parameter should be an iterable of node IDs.")
if (
len(nodes) == 0
): # this is not an error but maybe a warning should be printed to inform the caller
warnings.warn(
"No root node IDs given. An empty list will be returned as a result.",
RuntimeWarning,
stacklevel=3,
)
def _check_repetitions(self, n):
if type(n) != int:
self._raise_error(
"The number of walks per root node, n, should be integer type."
)
if n <= 0:
self._raise_error(
"The number of walks per root node, n, should be a positive integer."
)
def _check_length(self, length):
if type(length) != int:
self._raise_error("The walk length, length, should be integer type.")
if length <= 0:
# Technically, length 0 should be okay, but by consensus is invalid.
self._raise_error("The walk length, length, should be a positive integer.")
# For neighbourhood sampling
def _check_sizes(self, n_size):
err_msg = "The neighbourhood size must be a list of non-negative integers."
if not isinstance(n_size, list):
self._raise_error(err_msg)
if len(n_size) == 0:
# Technically, length 0 should be okay, but by consensus it is invalid.
self._raise_error("The neighbourhood size list should not be empty.")
for d in n_size:
if type(d) != int or d < 0:
self._raise_error(err_msg)
def naive_weighted_choices(rs, weights):
"""
Select an index at random, weighted by the iterator `weights` of
arbitrary (non-negative) floats. That is, `x` will be returned
with probability `weights[x]/sum(weights)`.
For doing a single sample with arbitrary weights, this is much (5x
or more) faster than numpy.random.choice, because the latter
requires a lot of preprocessing (normalized probabilties), and
does a lot of conversions/checks/preprocessing internally.
"""
probs = np.cumsum(weights)
idx = np.searchsorted(probs, rs.random() * probs[-1], side="left")
return idx
[docs]class BiasedRandomWalk(RandomWalk):
"""
Performs biased second order random walks (like those used in Node2Vec algorithm
https://snap.stanford.edu/node2vec/) controlled by the values of two parameters p and q.
Args:
graph (StellarGraph): Graph to traverse
n (int, optional): Total number of random walks per root node
length (int, optional): Maximum length of each random walk
p (float, optional): Defines probability, 1/p, of returning to source node
q (float, optional): Defines probability, 1/q, for moving to a node away from the source node
weighted (bool, optional): Indicates whether the walk is unweighted or weighted
seed (int, optional): Random number generator seed
"""
def __init__(
self, graph, n=None, length=None, p=1.0, q=1.0, weighted=False, seed=None,
):
super().__init__(graph, seed=seed)
self.n = n
self.length = length
self.p = p
self.q = q
self.weighted = weighted
self._checked_weights = False
if weighted:
self._check_weights_valid()
def _check_weights_valid(self):
if self._checked_weights:
# we only need to check the weights once, either in the constructor or in run, whichever
# sets `weighted=True` first
return
# Check that all edge weights are greater than or equal to 0.
source, target, _, weights = self.graph.edge_arrays(
include_edge_weight=True, use_ilocs=True
)
(invalid,) = np.where((weights < 0) | ~np.isfinite(weights))
if len(invalid) > 0:
def format(idx):
s = source[idx]
t = target[idx]
w = weights[idx]
return f"{s!r} to {t!r} (weight = {w})"
raise ValueError(
f"graph: expected all edge weights to be non-negative and finite, found some negative or infinite: {comma_sep(invalid, stringify=format)}"
)
self._checked_weights = True
[docs] def run(
self, nodes, *, n=None, length=None, p=None, q=None, seed=None, weighted=None
):
"""
Perform a random walk starting from the root nodes. Optional parameters default to using the
values passed in during construction.
Args:
nodes (list): The root nodes as a list of node IDs
n (int, optional): Total number of random walks per root node
length (int, optional): Maximum length of each random walk
p (float, optional): Defines probability, 1/p, of returning to source node
q (float, optional): Defines probability, 1/q, for moving to a node away from the source node
seed (int, optional): Random number generator seed; default is None
weighted (bool, optional): Indicates whether the walk is unweighted or weighted
Returns:
List of lists of nodes ids for each of the random walks
"""
n = _default_if_none(n, self.n, "n")
length = _default_if_none(length, self.length, "length")
p = _default_if_none(p, self.p, "p")
q = _default_if_none(q, self.q, "q")
weighted = _default_if_none(weighted, self.weighted, "weighted")
self._validate_walk_params(nodes, n, length)
self._check_weights(p, q, weighted)
rs = self._get_random_state(seed)
nodes = self.graph.node_ids_to_ilocs(nodes)
if weighted:
self._check_weights_valid()
weight_dtype = self.graph._edges.weights.dtype
cast_func = np.cast[weight_dtype]
ip = cast_func(1.0 / p)
iq = cast_func(1.0 / q)
if np.isinf(ip):
raise ValueError(
f"p: value ({p}) is too small. It must be possible to represent 1/p in {weight_dtype}, but this value overflows to infinity."
)
if np.isinf(iq):
raise ValueError(
f"q: value ({q}) is too small. It must be possible to represent 1/q in {weight_dtype}, but this value overflows to infinity."
)
walks = []
for node in nodes: # iterate over root nodes
for walk_number in range(n): # generate n walks per root node
# the walk starts at the root
walk = [node]
previous_node = None
previous_node_neighbours = []
current_node = node
for _ in range(length - 1):
# select one of the neighbours using the
# appropriate transition probabilities
if weighted:
neighbours, weights = self.graph.neighbor_arrays(
current_node, include_edge_weight=True, use_ilocs=True
)
else:
neighbours = self.graph.neighbor_arrays(
current_node, use_ilocs=True
)
weights = np.ones(neighbours.shape, dtype=weight_dtype)
if len(neighbours) == 0:
break
mask = neighbours == previous_node
weights[mask] *= ip
mask |= np.isin(neighbours, previous_node_neighbours)
weights[~mask] *= iq
choice = naive_weighted_choices(rs, weights)
previous_node = current_node
previous_node_neighbours = neighbours
current_node = neighbours[choice]
walk.append(current_node)
walks.append(list(self.graph.node_ilocs_to_ids(walk)))
return walks
def _check_weights(self, p, q, weighted):
"""
Checks that the parameter values are valid or raises ValueError exceptions with a message indicating the
parameter (the first one encountered in the checks) with invalid value.
Args:
p: <float> The backward walk 'penalty' factor.
q: <float> The forward walk 'penalty' factor.
weighted: <False or True> Indicates whether the walk is unweighted or weighted.
"""
if p <= 0.0:
raise ValueError(f"p: expected positive numeric value, found {p}")
if q <= 0.0:
raise ValueError(f"q: expected positive numeric value, found {q}")
if type(weighted) != bool:
raise ValueError(f"weighted: expected boolean value, found {weighted}")
[docs]class SampledBreadthFirstWalk(GraphWalk):
"""
Breadth First Walk that generates a sampled number of paths from a starting node.
It can be used to extract a random sub-graph starting from a set of initial nodes.
"""
[docs] def run(self, nodes, n_size, n=1, seed=None):
"""
Performs a sampled breadth-first walk starting from the root nodes.
Args:
nodes (list): A list of root node ids such that from each node a BFWs will be generated up to the
given depth. The depth of each of the walks is inferred from the length of the ``n_size``
list parameter.
n_size (list of int): The number of neighbouring nodes to expand at each depth of the walk.
Sampling of neighbours is always done with replacement regardless of the node degree and
number of neighbours requested.
n (int): Number of walks per node id.
seed (int, optional): Random number generator seed; Default is None.
Returns:
A list of lists such that each list element is a sequence of ids corresponding to a BFW.
"""
self._check_sizes(n_size)
self._check_common_parameters(nodes, n, len(n_size), seed)
rs = self._get_random_state(seed)
walks = []
max_hops = len(n_size) # depth of search
for node in nodes: # iterate over root nodes
for _ in range(n): # do n bounded breadth first walks from each root node
q = deque() # the queue of neighbours
walk = list() # the list of nodes in the subgraph of node
# extend() needs iterable as parameter; we use list of tuples (node id, depth)
q.append((node, 0))
while len(q) > 0:
# remove the top element in the queue
# index 0 pop the item from the front of the list
cur_node, cur_depth = q.popleft()
depth = cur_depth + 1 # the depth of the neighbouring nodes
walk.append(cur_node) # add to the walk
# consider the subgraph up to and including max_hops from root node
if depth > max_hops:
continue
neighbours = (
self.graph.neighbor_arrays(cur_node, use_ilocs=True)
if cur_node != -1
else []
)
if len(neighbours) == 0:
# Either node is unconnected or is in directed graph with no out-nodes.
_size = n_size[cur_depth]
neighbours = [-1] * _size
else:
# sample with replacement
neighbours = rs.choices(neighbours, k=n_size[cur_depth])
# add them to the back of the queue
q.extend((sampled_node, depth) for sampled_node in neighbours)
# finished i-th walk from node so add it to the list of walks as a list
walks.append(walk)
return walks
[docs]class SampledHeterogeneousBreadthFirstWalk(GraphWalk):
"""
Breadth First Walk for heterogeneous graphs that generates a sampled number of paths from a starting node.
It can be used to extract a random sub-graph starting from a set of initial nodes.
"""
[docs] def run(self, nodes, n_size, n=1, seed=None):
"""
Performs a sampled breadth-first walk starting from the root nodes.
Args:
nodes (list): A list of root node ids such that from each node n BFWs will be generated
with the number of samples per hop specified in n_size.
n_size (int): The number of neighbouring nodes to expand at each depth of the walk. Sampling of
n (int, default 1): Number of walks per node id. Neighbours with replacement is always used regardless
of the node degree and number of neighbours requested.
seed (int, optional): Random number generator seed; default is None
Returns:
A list of lists such that each list element is a sequence of ids corresponding to a sampled Heterogeneous
BFW.
"""
self._check_sizes(n_size)
self._check_common_parameters(nodes, n, len(n_size), seed)
rs = self._get_random_state(seed)
adj = self.get_adjacency_types()
walks = []
d = len(n_size) # depth of search
for node in nodes: # iterate over root nodes
for _ in range(n): # do n bounded breadth first walks from each root node
q = list() # the queue of neighbours
walk = list() # the list of nodes in the subgraph of node
# Start the walk by adding the head node, and node type to the frontier list q
node_type = self.graph.node_type(node, use_ilocs=True)
q.extend([(node, node_type, 0)])
# add the root node to the walks
walk.append([node])
while len(q) > 0:
# remove the top element in the queue and pop the item from the front of the list
frontier = q.pop(0)
current_node, current_node_type, depth = frontier
depth = depth + 1 # the depth of the neighbouring nodes
# consider the subgraph up to and including depth d from root node
if depth <= d:
# Find edge types for current node type
current_edge_types = self.graph_schema.schema[current_node_type]
# Create samples of neigbhours for all edge types
for et in current_edge_types:
neigh_et = adj[et][current_node]
# If there are no neighbours of this type then we return None
# in the place of the nodes that would have been sampled
# YT update: with the new way to get neigh_et from adj[et][current_node], len(neigh_et) is always > 0.
# In case of no neighbours of the current node for et, neigh_et == [None],
# and samples automatically becomes [None]*n_size[depth-1]
if len(neigh_et) > 0:
samples = rs.choices(neigh_et, k=n_size[depth - 1])
else: # this doesn't happen anymore, see the comment above
_size = n_size[depth - 1]
samples = [-1] * _size
walk.append(samples)
q.extend(
[
(sampled_node, et.n2, depth)
for sampled_node in samples
]
)
# finished i-th walk from node so add it to the list of walks as a list
walks.append(walk)
return walks
class DirectedBreadthFirstNeighbours(GraphWalk):
"""
Breadth First sampler that generates the composite of a number of sampled paths from a starting node.
It can be used to extract a random sub-graph starting from a set of initial nodes.
"""
def __init__(self, graph, graph_schema=None, seed=None):
super().__init__(graph, graph_schema, seed)
if not graph.is_directed():
self._raise_error("Graph must be directed")
def run(self, nodes, in_size, out_size, n=1, seed=None):
"""
Performs a sampled breadth-first walk starting from the root nodes.
Args:
nodes (list): A list of root node ids such that from each node n BFWs will be generated up to the
given depth d.
in_size (int): The number of in-directed nodes to sample with replacement at each depth of the walk.
out_size (int): The number of out-directed nodes to sample with replacement at each depth of the walk.
n (int, default 1): Number of walks per node id.
seed (int, optional): Random number generator seed; default is None
Returns:
A list of multi-hop neighbourhood samples. Each sample expresses multiple undirected walks, but the in-node
neighbours and out-node neighbours are sampled separately. Each sample has the format:
[[node]
[in_1...in_n] [out_1...out_m]
[in_1.in_1...in_n.in_p] [in_1.out_1...in_n.out_q]
[out_1.in_1...out_m.in_p] [out_1.out_1...out_m.out_q]
[in_1.in_1.in_1...in_n.in_p.in_r] [in_1.in_1.out_1...in_n.in_p.out_s] ...
...]
where a single, undirected walk might be, for example:
[node out_i out_i.in_j out_i.in_j.in_k ...]
"""
self._check_neighbourhood_sizes(in_size, out_size)
self._check_common_parameters(nodes, n, len(in_size), seed)
rs = self._get_random_state(seed)
max_hops = len(in_size)
# A binary tree is a graph of nodes; however, we wish to avoid overusing the term 'node'.
# Consider that each binary tree node carries some information.
# We uniquely and deterministically number every node in the tree, so we
# can represent the information stored in the tree via a flattened list of 'slots'.
# Each slot (and corresponding binary tree node) now has a unique index in the flattened list.
max_slots = 2 ** (max_hops + 1) - 1
samples = []
for node in nodes: # iterate over root nodes
for _ in range(n): # do n bounded breadth first walks from each root node
q = list() # the queue of neighbours
# the list of sampled node-lists:
sample = [[] for _ in range(max_slots)]
# Add node to queue as (node, depth, slot)
q.append((node, 0, 0))
while len(q) > 0:
# remove the top element in the queue
# index 0 pop the item from the front of the list
cur_node, cur_depth, cur_slot = q.pop(0)
sample[cur_slot].append(cur_node) # add to the walk
depth = cur_depth + 1 # the depth of the neighbouring nodes
# consider the subgraph up to and including max_hops from root node
if depth > max_hops:
continue
# get in-nodes
neighbours = self._sample_neighbours(
rs, cur_node, 0, in_size[cur_depth]
)
# add them to the back of the queue
slot = 2 * cur_slot + 1
q.extend(
[(sampled_node, depth, slot) for sampled_node in neighbours]
)
# get out-nodes
neighbours = self._sample_neighbours(
rs, cur_node, 1, out_size[cur_depth]
)
# add them to the back of the queue
slot = slot + 1
q.extend(
[(sampled_node, depth, slot) for sampled_node in neighbours]
)
# finished multi-hop neighbourhood sampling
samples.append(sample)
return samples
def _sample_neighbours(self, rs, node, idx, size):
"""
Samples (with replacement) the specified number of nodes
from the directed neighbourhood of the given starting node.
If the neighbourhood is empty, then the result will contain
only None values.
Args:
rs: The random state used for sampling.
node: The starting node.
idx: <int> The index specifying the direction of the
neighbourhood to be sampled: 0 => in-nodes;
1 => out-nodes.
size: <int> The number of nodes to sample.
Returns:
The fixed-length list of neighbouring nodes (or None values
if the neighbourhood is empty).
"""
if node == -1:
# Non-node, e.g. previously sampled from empty neighbourhood
return [-1] * size
if idx == 0:
neighbours = self.graph.in_node_arrays(node, use_ilocs=True)
else:
neighbours = self.graph.out_node_arrays(node, use_ilocs=True)
if len(neighbours) == 0:
# Sampling from empty neighbourhood
return [-1] * size
# Sample with replacement
return rs.choices(neighbours, k=size)
def _check_neighbourhood_sizes(self, in_size, out_size):
"""
Checks that the parameter values are valid or raises ValueError exceptions with a message indicating the
parameter (the first one encountered in the checks) with invalid value.
Args:
nodes: <list> A list of root node ids such that from each node n BFWs will be generated up to the
given depth d.
n_size: <list> The number of neighbouring nodes to expand at each depth of the walk.
seed: <int> Random number generator seed; default is None
"""
self._check_sizes(in_size)
self._check_sizes(out_size)
if len(in_size) != len(out_size):
self._raise_error(
"The number of hops for the in and out neighbourhoods must be the same."
)
[docs]class TemporalRandomWalk(GraphWalk):
"""
Performs temporal random walks on the given graph. The graph should contain numerical edge
weights that correspond to the time at which the edge was created. Exact units are not relevant
for the algorithm, only the relative differences (e.g. seconds, days, etc).
Args:
graph (StellarGraph): Graph to traverse
cw_size (int, optional): Size of context window. Also used as the minimum walk length,
since a walk must generate at least 1 context window for it to be useful.
max_walk_length (int, optional): Maximum length of each random walk. Should be greater
than or equal to the context window size.
initial_edge_bias (str, optional): Distribution to use when choosing a random
initial temporal edge to start from. Available options are:
* None (default) - The initial edge is picked from a uniform distribution.
* "exponential" - Heavily biased towards more recent edges.
walk_bias (str, optional): Distribution to use when choosing a random
neighbour to walk through. Available options are:
* None (default) - Neighbours are picked from a uniform distribution.
* "exponential" - Exponentially decaying probability, resulting in a bias towards shorter time gaps.
p_walk_success_threshold (float, optional): Lower bound for the proportion of successful
(i.e. longer than minimum length) walks. If the 95% percentile of the
estimated proportion is less than the provided threshold, a RuntimeError
will be raised. The default value of 0.01 means an error is raised if less than 1%
of the attempted random walks are successful. This parameter exists to catch any
potential situation where too many unsuccessful walks can cause an infinite or very
slow loop.
seed (int, optional): Random number generator seed.
"""
def __init__(
self,
graph,
cw_size=None,
max_walk_length=80,
initial_edge_bias=None,
walk_bias=None,
p_walk_success_threshold=0.01,
seed=None,
):
super().__init__(graph, graph_schema=None, seed=seed)
self.cw_size = cw_size
self.max_walk_length = max_walk_length
self.initial_edge_bias = initial_edge_bias
self.walk_bias = walk_bias
self.p_walk_success_threshold = p_walk_success_threshold
[docs] def run(
self,
num_cw,
cw_size=None,
max_walk_length=None,
initial_edge_bias=None,
walk_bias=None,
p_walk_success_threshold=None,
seed=None,
):
"""
Perform a time respecting random walk starting from randomly selected temporal edges.
Optional parameters default to using the values passed in during construction.
Args:
num_cw (int): Total number of context windows to generate. For comparable
results to most other random walks, this should be a multiple of the number
of nodes in the graph.
cw_size (int, optional): Size of context window. Also used as the minimum walk length,
since a walk must generate at least 1 context window for it to be useful.
max_walk_length (int, optional): Maximum length of each random walk. Should be greater
than or equal to the context window size.
initial_edge_bias (str, optional): Distribution to use when choosing a random
initial temporal edge to start from. Available options are:
* None (default) - The initial edge is picked from a uniform distribution.
* "exponential" - Heavily biased towards more recent edges.
walk_bias (str, optional): Distribution to use when choosing a random
neighbour to walk through. Available options are:
* None (default) - Neighbours are picked from a uniform distribution.
* "exponential" - Exponentially decaying probability, resulting in a bias towards shorter time gaps.
p_walk_success_threshold (float, optional): Lower bound for the proportion of successful
(i.e. longer than minimum length) walks. If the 95% percentile of the
estimated proportion is less than the provided threshold, a RuntimeError
will be raised. The default value of 0.01 means an error is raised if less than 1%
of the attempted random walks are successful. This parameter exists to catch any
potential situation where too many unsuccessful walks can cause an infinite or very
slow loop.
seed (int, optional): Random number generator seed; default is None.
Returns:
List of lists of node ids for each of the random walks.
"""
cw_size = _default_if_none(cw_size, self.cw_size, "cw_size")
max_walk_length = _default_if_none(
max_walk_length, self.max_walk_length, "max_walk_length"
)
initial_edge_bias = _default_if_none(
initial_edge_bias,
self.initial_edge_bias,
"initial_edge_bias",
ensure_not_none=False,
)
walk_bias = _default_if_none(
walk_bias, self.walk_bias, "walk_bias", ensure_not_none=False
)
p_walk_success_threshold = _default_if_none(
p_walk_success_threshold,
self.p_walk_success_threshold,
"p_walk_success_threshold",
)
if cw_size < 2:
raise ValueError(
f"cw_size: context window size should be greater than 1, found {cw_size}"
)
if max_walk_length < cw_size:
raise ValueError(
f"max_walk_length: maximum walk length should not be less than the context window size, found {max_walk_length}"
)
np_rs = self._np_random_state if seed is None else np.random.RandomState(seed)
walks = []
num_cw_curr = 0
sources, targets, _, times = self.graph.edge_arrays(include_edge_weight=True)
edge_biases = self._temporal_biases(
times, None, bias_type=initial_edge_bias, is_forward=False,
)
successes = 0
failures = 0
def not_progressing_enough():
# Estimate the probability p of a walk being long enough; the 95% percentile is used to
# be more stable with respect to randomness. This uses Beta(1, 1) as the prior, since
# it's uniform on p
posterior = stats.beta.ppf(0.95, 1 + successes, 1 + failures)
return posterior < p_walk_success_threshold
# loop runs until we have enough context windows in total
while num_cw_curr < num_cw:
first_edge_index = self._sample(len(times), edge_biases, np_rs)
src = sources[first_edge_index]
dst = targets[first_edge_index]
t = times[first_edge_index]
remaining_length = num_cw - num_cw_curr + cw_size - 1
walk = self._walk(
src, dst, t, min(max_walk_length, remaining_length), walk_bias, np_rs
)
if len(walk) >= cw_size:
walks.append(walk)
num_cw_curr += len(walk) - cw_size + 1
successes += 1
else:
failures += 1
if not_progressing_enough():
raise RuntimeError(
f"Discarded {failures} walks out of {failures + successes}. "
"Too many temporal walks are being discarded for being too short. "
f"Consider using a smaller context window size (currently cw_size={cw_size})."
)
return walks
def _sample(self, n, biases, np_rs):
if biases is not None:
assert len(biases) == n
return naive_weighted_choices(np_rs, biases)
else:
return np_rs.choice(n)
def _exp_biases(self, times, t_0, decay):
# t_0 assumed to be smaller than all time values
return softmax(t_0 - np.array(times) if decay else np.array(times) - t_0)
def _temporal_biases(self, times, time, bias_type, is_forward):
if bias_type is None:
# default to uniform random sampling
return None
# time is None indicates we should obtain the minimum available time for t_0
t_0 = time if time is not None else min(times)
if bias_type == "exponential":
# exponential decay bias needs to be reversed if looking backwards in time
return self._exp_biases(times, t_0, decay=is_forward)
else:
raise ValueError("Unsupported bias type")
def _step(self, node, time, bias_type, np_rs):
"""
Perform 1 temporal step from a node. Returns None if a dead-end is reached.
"""
neighbours, times = self.graph.neighbor_arrays(node, include_edge_weight=True)
neighbours = neighbours[times > time]
times = times[times > time]
if len(neighbours) > 0:
biases = self._temporal_biases(times, time, bias_type, is_forward=True)
chosen_neighbour_index = self._sample(len(neighbours), biases, np_rs)
next_node = neighbours[chosen_neighbour_index]
next_time = times[chosen_neighbour_index]
return next_node, next_time
else:
return None
def _walk(self, src, dst, t, length, bias_type, np_rs):
walk = [src, dst]
node, time = dst, t
for _ in range(length - 2):
result = self._step(node, time=time, bias_type=bias_type, np_rs=np_rs)
if result is not None:
node, time = result
walk.append(node)
else:
break
return walk
