def test_delete_and_pickle():
'''
Deleting an element doesn't affect the remaining elements'
indices.
'''
s = OrderedSet(['dog', 'cat', 'banana'])
del s[1]
eq_(s[1], None)
eq_(s.index('banana'), 2)
# Pickling doesn't change things.
s2 = pickle.loads(pickle.dumps(s))
eq_(s, s2)
eq_(s2[1], None)
eq_(s2.index('banana'), 2)
assert None not in s2
assert None not in s2
def test_delete_and_pickle():
'''
Deleting an element doesn't affect the remaining elements'
indices.
'''
s = OrderedSet(['dog','cat','banana'])
del s[1]
eq_(s[1], None)
eq_(s.index('banana'), 2)
# Pickling doesn't change things.
s2 = pickle.loads(pickle.dumps(s))
eq_(s, s2)
eq_(s2[1], None)
eq_(s2.index('banana'), 2)
assert None not in s2
assert None not in s2
class TrustNetwork(object):
def __init__(self, output=None):
self.nodes = OrderedSet()
self._node_matrix = None
self._node_conjunctions = None
self._fast_matrix_up = None
self._fast_matrix_down = None
self._fast_conjunctions = None
@staticmethod
def load(node_file, matrix_up, matrix_down, conjunction_file):
trust = TrustNetwork()
nodes = divisi2.load(node_file)
trust.nodes = OrderedSet(nodes)
trust._fast_matrix_up = divisi2.load(matrix_up)
trust._fast_matrix_down = divisi2.load(matrix_down)
trust._fast_conjunctions = divisi2.load(conjunction_file)
return trust
def add_nodes(self, nodes):
for node in nodes:
self.nodes.add(node)
def scan_edge(self, source, dest):
self.nodes.add(source)
self.nodes.add(dest)
def make_matrices(self):
self._node_matrix = sparse.dok_matrix((len(self.nodes), len(self.nodes)))
self._node_conjunctions = sparse.dok_matrix((len(self.nodes), len(self.nodes)))
def add_edge(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
#self._node_matrix[source_idx, dest_idx] = weight
self._node_matrix[dest_idx, source_idx] = weight
def add_conjunction(self, sources, dest, weight):
dest_idx = self.nodes.index(dest)
for i, source in enumerate(sources):
self.add_edge(source, dest, weight)
source_idx = self.nodes.index(source)
self._node_conjunctions[dest_idx, source_idx] = 1.0
def add_conjunction_piece(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
self._node_matrix[dest_idx, source_idx] = weight
self._node_conjunctions[dest_idx, source_idx] = 1.0
def make_fast_matrix(self):
self._fast_matrix = self._node_matrix.tocsr()
for i in xrange(self._node_matrix.shape[0]):
self._node_matrix[0, i] += EPS
self._node_matrix[i, 0] += EPS
abs_matrix = np.abs(self._fast_matrix)
rowsums = 1.0 / (EPS + (abs_matrix).sum(axis=1))
rowsums = np.asarray(rowsums)[:,0]
rowdiag = make_diag(rowsums)
self._fast_matrix_down = (rowdiag * self._fast_matrix).tocsr()
#self._fast_matrix_up = self._fast_matrix_down.T.tocsr()
colsums = 1.0 / (EPS + (abs_matrix).sum(axis=0))
colsums = np.asarray(colsums)[0,:]
coldiag = make_diag(colsums)
self._fast_matrix_up = (coldiag * self._fast_matrix.T).tocsr()
def make_fast_conjunctions(self):
csr_conjunctions = self._node_conjunctions.tocsr()
n = csr_conjunctions.shape[0]
scale_vec = np.zeros((n,))
for row in xrange(n):
nnz = csr_conjunctions[row].nnz
if nnz > 0:
scale_vec[row] = 1.0/nnz
self._fast_conjunctions = make_diag(scale_vec) * csr_conjunctions
def get_matrices(self):
if self._fast_matrix_up is None:
self.make_fast_matrix()
return self._fast_matrix_up, self._fast_matrix_down
def get_conjunctions(self):
if self._fast_conjunctions is None:
self.make_fast_conjunctions()
return self._fast_conjunctions
def corona(self):
cmat = self.get_conjunctions()
mat_up, mat_down = self.get_matrices()
hub = np.ones((mat_up.shape[0],))
authority = np.ones((mat_up.shape[0],))
for iter in xrange(100):
vec = authority + hub
vec /= np.max(vec)
root = vec * 0
root[0] = 1.0
conj_sums = cmat * vec
conj_par = 1.0/(np.maximum(EPS, cmat * (1.0 / np.maximum(EPS, vec))))
conj_factor = np.minimum(1.0, conj_par / (conj_sums+EPS))
conj_diag = make_diag(conj_factor)
combined = conj_diag * (mat_up + mat_down) + make_diag(np.ones(len(vec)))
#combined = (mat_up + mat_down) * 0.5
u, sigma, v = sparse_svd(combined, k=4)
activation = np.dot(u, u[0])
#w, v = eigen(combined, k=3, v0=root)
#activation = v[:, np.argmax(w)]
#activation = (activation / (activation[0]+EPS)).real
print activation
print sigma
print conj_factor
print
hub += self._fast_matrix.T * conj_diag * activation
authority += conj_diag * self._fast_matrix * activation
hub /= np.max(hub)
authority /= np.max(authority)
return zip(self.nodes, hub, authority)
class BeliefNetwork(object):
def __init__(self, output=None):
self.nodes = OrderedSet()
self.node_objs = {} #dict mapping node name to Node object
self._node_conjunctions = None
self._fast_matrix = None
self._fast_conjunctions = None
@staticmethod
def load(node_file, matrix_file, conjunction_file):
trust = BeliefNetwork()
nodes = divisi2.load(node_file)
for node in nodes:
trust.nodes.add(node)
trust.node_objs[node] = Node(node)
trust._fast_matrix = divisi2.load(matrix_file)
trust._fast_conjunctions = divisi2.load(conjunction_file)
return trust
def add_nodes(self, nodes):
for node in nodes:
self.nodes.add(node)
self.node_objs[node] = Node(node)
def scan_edge(self, source, dest):
self.nodes.add(source)
self.nodes.add(dest)
self.node_objs[source] = Node(source)
self.node_objs[dest] = Node(dest)
def initialize_matrices(self):
self.justification = ReconstructedMatrix.make_random(self.nodes, self.nodes, 3)
self.justification.right = self.justification.left.T
self.justification.left.fill(0.01)
self.justification.right.fill(0.01)
def add_edge(self, source, dest, weight, conjunction = False):
self.node_objs[source].add_outgoing_edge(dest, weight)
if conjunction:
self.node_objs[dest].add_incoming_edge(source, weight) #weight here?
def add_conjunction(self, sources, dest, weight):
for i, source in enumerate(sources):
self.add_edge(source, dest, weight, conjunction = True)
def add_conjunction_piece(self, source, dest, weight):
self.add_edge(source, dest, weight, conjunction = True)
def iterate(self, n=1000):
for iter in xrange(n):
for node in self.nodes:
print node, '=>',
self.activate_node(node)
print
return self.justification
def activate_node(self, node):
index = self.nodes.index(node)
activation = None
self.learn_justification(index, index, 1.0)
curr = node
for iter in xrange(20):
#get the nodes that this node has outgoing edges to
nz = self.node_objs[curr].outgoing_edges
if len(nz) == 0:
break
choice = random.choice(xrange(len(nz)))
next, weight = nz[choice]
if activation is None:
activation = weight
else:
activation = parallel(activation, weight)
assert next != curr
assert activation is not None
conj = self.node_objs[next].incoming_edges
for con in conj:
conj_index = self.nodes.index(con[0])
if conj_index != curr:
#FIXME: unsure of how to calculate this value
factor = self.justification[index, conj_index] #* conj[0, conj_index]
activation = parallel(activation, factor)
print self.nodes[self.nodes.index(next)], ('(%4.4f) =>' % activation),
self.learn_justification(index, self.nodes.index(next), activation)
if activation <= 0:
break
curr = next
def learn_justification(self, source, target, activation=1.0):
self.justification.hebbian_step(source, target, activation)
class TrustNetwork(object):
def __init__(self, output=None):
self.nodes = OrderedSet()
self._node_matrix = None
self._node_conjunctions = None
self._fast_matrix_up = None
self._transition_matrix = None
self._fast_conjunctions = None
@staticmethod
def load(node_file, matrix_up, matrix_down, conjunction_file):
trust = TrustNetwork()
nodes = divisi2.load(node_file)
trust.nodes = OrderedSet(nodes)
trust._fast_matrix_up = divisi2.load(matrix_up)
trust._transition_matrix = divisi2.load(matrix_down)
trust._fast_conjunctions = divisi2.load(conjunction_file)
return trust
def add_nodes(self, nodes):
for node in nodes:
self.nodes.add(node)
def scan_edge(self, source, dest):
self.nodes.add(source)
self.nodes.add(dest)
def make_matrices(self):
self._node_matrix = sparse.dok_matrix((len(self.nodes), len(self.nodes)))
self._node_conjunctions = sparse.dok_matrix((len(self.nodes), len(self.nodes)))
def add_edge(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
#self._node_matrix[source_idx, dest_idx] = weight
self._node_matrix[dest_idx, source_idx] = weight
def add_conjunction(self, sources, dest, weight):
dest_idx = self.nodes.index(dest)
for i, source in enumerate(sources):
self.add_edge(source, dest, weight)
source_idx = self.nodes.index(source)
self._node_conjunctions[dest_idx, source_idx] = 1.0
def add_conjunction_piece(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
self._node_matrix[dest_idx, source_idx] = weight
self._node_conjunctions[dest_idx, source_idx] = 1.0
def make_fast_matrix(self):
self._fast_matrix = self._node_matrix.tocsr()
for i in xrange(self._node_matrix.shape[0]):
self._node_matrix[0, i] += 1.0/self._node_matrix.shape[0]
self._node_matrix[i, 0] += 1.0/self._node_matrix.shape[0]
csr_matrix = self._node_matrix.tocsr()
abs_matrix = csr_matrix.multiply(csr_matrix)
rowsums = np.sqrt(1.0 / (EPS + (abs_matrix).sum(axis=1)))
rowsums = np.asarray(rowsums)[:,0]
rowdiag = make_diag(rowsums)
colsums = np.sqrt(1.0 / (EPS + (abs_matrix).sum(axis=0)))
colsums = np.asarray(colsums)[0,:]
coldiag = make_diag(colsums)
self._transition_matrix = (csr_matrix * coldiag).tocsr()
self._transition_matrix_T = self._transition_matrix.T.tocsr()
self._final_matrix = (self._fast_matrix * coldiag).tocsr()
self._final_matrix_T = (coldiag * self._fast_matrix.T).tocsr()
def make_fast_conjunctions(self):
csr_conjunctions = self._node_conjunctions.tocsr()
n = csr_conjunctions.shape[0]
scale_vec = np.zeros((n,))
for row in xrange(n):
nnz = csr_conjunctions[row].nnz
if nnz > 0:
scale_vec[row] = 1.0/nnz
self._fast_conjunctions = make_diag(scale_vec) * csr_conjunctions
def get_matrices(self):
if self._final_matrix is None:
self.make_fast_matrix()
return self._transition_matrix_T, self._transition_matrix
def get_conjunctions(self):
if self._fast_conjunctions is None:
self.make_fast_conjunctions()
return self._fast_conjunctions
def corona(self):
cmat = self.get_conjunctions()
mat_up, mat_down = self.get_matrices()
hub = np.ones((mat_up.shape[0],)) / mat_up.shape[0] / 100
authority = np.ones((mat_up.shape[0],)) / mat_up.shape[0] / 100
prev_activation = np.zeros((mat_up.shape[0],))
prev_err = 1.0
for iter in xrange(100):
vec = authority + hub
vec /= np.max(vec)
root = np.zeros(len(vec), 'f')
root[0] = 1.0
conj_sums = cmat * vec
conj_par = 1.0/(np.maximum(EPS, cmat * (1.0 / np.maximum(EPS, vec))))
conj_factor = np.minimum(1.0, conj_par / (conj_sums+EPS))
conj_diag = make_diag(conj_factor)
combined = conj_diag * (mat_up + mat_down) * 0.25 + make_diag(np.ones(len(vec))*0.5)
#combined = (mat_up + mat_down) * 0.5
u, sigma, v = sparse_svd(combined, k=1)
activation = u[:, 0]
#activation = np.dot(u, u[0])
#w, v = eigen(combined.T, k=1, v0=root, which='LR')
#activation = v[:, np.argmax(w)].real
activation *= np.sign(np.sum(activation))
activation /= (np.sum(np.abs(activation)) + EPS)
hub += (hub + self._final_matrix_T * conj_diag * activation) / 2
authority += (authority + conj_diag * self._final_matrix * activation) / 2
print activation
err = np.max(np.abs(activation - prev_activation))\
/ np.max(np.abs(activation))
print err
if iter >= 3 and err + prev_err < 1e-9:
print "converged on iteration %d" % iter
break
prev_err = err
prev_activation = activation.copy()
print sigma
print conj_factor
print
hub = self._final_matrix_T * conj_diag * activation
authority = conj_diag * self._final_matrix * activation
return zip(self.nodes, hub, authority)
class BeliefNetwork(object):
def __init__(self, ground_weight=1.0, output=None):
self.graph = nx.Graph()
self.conjunctions = set()
self.ground_weight = ground_weight
self.nodes = OrderedSet()
self.edges = OrderedSet()
self._edge_matrix = None
self._conjunction_matrix = None
self._node_matrix = None
self._node_conjunctions = None
self._edge_conductance = None
self.output = output
def add_edge(self, source, dest, weight, dependencies=None):
self.nodes.add(source)
self.nodes.add(dest)
self.edges.add((source, dest))
props = {'weight': weight}
if dependencies is not None:
props['dependencies'] = dependencies
self.graph.add_edge(source, dest, **props)
if self.output:
self.output.write("%s\t%s\t%r\n" % (source, dest, props))
def add_conjunction(self, sources, dest, weight):
sources = tuple(sources)
self.conjunctions.add((sources, dest, weight))
for i, source in enumerate(sources):
self.add_edge(source, dest, weight, dependencies=sources)
def ordered_nodes(self):
return sorted(self.graph.nodes())
def update_arrays(self):
n_edges = len(self.edges) + len(self.nodes)
n_nodes = len(self.nodes)
offset = len(self.edges)
mat = sparse.dok_matrix((n_edges, n_nodes))
conjunction_mat = sparse.dok_matrix((n_edges, n_nodes))
vec = np.zeros((n_edges, ))
for source, dest in self.graph.edges():
if (source, dest) not in self.edges:
(source, dest) = (dest, source)
edge_num = self.edges.index((source, dest))
weight = self.graph.get_edge_data(source, dest)['weight']
source_idx = self.nodes.index(source)
mat[edge_num, source_idx] = -1.0
dest_idx = self.nodes.index(dest)
mat[edge_num, dest_idx] = 1.0
vec[edge_num] = weight
# Add edges to ground
for node in self.graph.nodes():
node_num = self.nodes.index(node)
adjusted_node_num = node_num + offset
mat[adjusted_node_num, node_num] = -1.0
vec[adjusted_node_num] = self.ground_weight
# Make matrix of conjunctions, edges -> input nodes
for sources, dest, weight in self.conjunctions:
edge_indices = []
node_indices = []
for source in sources:
if (source, dest) in self.edges:
edge_num = self.edges.index((source, dest))
else:
edge_num = self.edges.index((dest, source))
edge_indices.append(edge_num)
node_indices.append(self.nodes.index(source))
conjunction_mat[edge_indices, node_indices] = 1
#for node_index in node_indices:
# unconnected_edges = [e for e in edge_indices if mat[e, node_index] == 0.0]
self._edge_matrix = mat.tocsr()
self._edge_matrix_transpose = mat.T.tocsr()
self._edge_conductance = vec
self._conjunction_matrix = conjunction_mat.tocsr()
return mat, vec
def make_node_matrix(self):
n_nodes = len(self.nodes)
self._node_matrix = nx.to_scipy_sparse_matrix(self.graph, self.nodes)
def make_node_conjunctions(self):
n_nodes = len(self.nodes)
node_conjunctions = sparse.dok_matrix((n_nodes, n_nodes))
for sources, dest, weight in self.conjunctions:
node_indices = [self.nodes.index(source) for source in sources]
node_conjunctions[self.nodes.index(dest), node_indices] = 1.0
self._node_conjunctions = node_conjunctions.tocsr()
def get_node_matrix(self):
if self._node_matrix is None:
self.make_node_matrix()
return self._node_matrix
def get_node_conjunctions(self):
if self._node_conjunctions is None:
self.make_node_conjunctions()
return self._node_conjunctions
def spreading_activation(self, vec=None, root=None):
if vec is None:
vec = np.ones((len(self.nodes), ))
cmat = self.get_node_conjunctions()
nmat = self.get_node_matrix()
for iter in xrange(100):
conj_sums = cmat * vec
conj_par = 1.0 / (cmat * (1.0 / np.maximum(0, vec)))
conj_factor = np.minimum(1.0, conj_par / conj_sums)
newvec = nmat.dot(vec) * conj_factor + vec
if root is not None and newvec[self.nodes.index(root)] < 0.0:
newvec = -newvec
newvec /= np.max(newvec)
print newvec
vec = newvec
return vec
def get_edge_matrix(self):
if self._edge_matrix is None:
self.update_arrays()
return self._edge_matrix
def get_edge_matrix_transpose(self):
if self._edge_matrix is None:
self.update_arrays()
return self._edge_matrix_transpose
def get_conductance(self):
if self._edge_conductance is None:
self.update_arrays()
return self._edge_conductance
def adjusted_conductances(self, equiv_conductances):
assert len(equiv_conductances) == len(self.nodes)
equiv_resistances = 1.0 / np.maximum(0, equiv_conductances)
edge_resistances = 1.0 / self._edge_conductance
combined_resistances = self._conjunction_matrix.dot(equiv_resistances)
new_resistances = (edge_resistances + combined_resistances)
adjusted_conductances = 1.0 / new_resistances
print adjusted_conductances
return adjusted_conductances
def get_system_matrix(self, conductances):
A_T = self.get_edge_matrix_transpose()
A = self.get_edge_matrix()
G = self.adjusted_conductances(conductances)
return make_product_operator(A_T, make_diag(G), A)
def solve_system(self, known_conductances, current_source):
"""
Get the conductance from root to each node by solving the electrical
system.
"""
current = np.zeros((len(self.nodes), ))
current[current_source] = 1.0
system = self.get_system_matrix(known_conductances)
A = self.get_edge_matrix()
# Solve the sparse system of linear equations using cg
new_potentials = sparse_linalg.cg(system, current)[0]
# A = edges by nodes
currents = -A.dot(new_potentials)
potential_differences = new_potentials[current_source] - new_potentials
current_magnitude = np.abs(
self.get_edge_matrix_transpose()).dot(currents)
conductance = 1.0 / potential_differences
return conductance
def run_analog(self, root, epsilon=1e-6):
conductance = np.ones((len(self.nodes), ))
converged = False
root_index = self.nodes.index(root)
for i in xrange(100):
new_conductance = self.solve_system(conductance, root_index)
diff = (np.minimum(conductance, 1000000.0) -
np.minimum(new_conductance, 1000000.0))
conductance = new_conductance
print conductance
if np.linalg.norm(diff) < epsilon:
converged = True
break
if not converged: print "Warning: failed to converge"
return zip(self.nodes, conductance)
class TrustNetwork(object):
def __init__(self, output=None):
self.nodes = OrderedSet()
self._node_matrix = None
self._node_conjunctions = None
self._fast_matrix_up = None
self._transition_matrix = None
self._fast_conjunctions = None
@staticmethod
def load(node_file, matrix_up, matrix_down, conjunction_file):
trust = TrustNetwork()
nodes = divisi2.load(node_file)
trust.nodes = OrderedSet(nodes)
trust._fast_matrix_up = divisi2.load(matrix_up)
trust._transition_matrix = divisi2.load(matrix_down)
trust._fast_conjunctions = divisi2.load(conjunction_file)
return trust
def add_nodes(self, nodes):
for node in nodes:
self.nodes.add(node)
def scan_edge(self, source, dest):
self.nodes.add(source)
self.nodes.add(dest)
def make_matrices(self):
self._node_matrix = sparse.dok_matrix(
(len(self.nodes), len(self.nodes)))
self._node_conjunctions = sparse.dok_matrix(
(len(self.nodes), len(self.nodes)))
def add_edge(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
#self._node_matrix[source_idx, dest_idx] = weight
self._node_matrix[dest_idx, source_idx] = weight
def add_conjunction(self, sources, dest, weight):
dest_idx = self.nodes.index(dest)
for i, source in enumerate(sources):
self.add_edge(source, dest, weight)
source_idx = self.nodes.index(source)
self._node_conjunctions[dest_idx, source_idx] = 1.0
def add_conjunction_piece(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
self._node_matrix[dest_idx, source_idx] = weight
self._node_conjunctions[dest_idx, source_idx] = 1.0
def make_fast_matrix(self):
self._fast_matrix = self._node_matrix.tocsr()
for i in xrange(self._node_matrix.shape[0]):
self._node_matrix[0, i] += 1.0 / self._node_matrix.shape[0]
self._node_matrix[i, 0] += 1.0 / self._node_matrix.shape[0]
csr_matrix = self._node_matrix.tocsr()
abs_matrix = csr_matrix.multiply(csr_matrix)
rowsums = np.sqrt(1.0 / (EPS + (abs_matrix).sum(axis=1)))
rowsums = np.asarray(rowsums)[:, 0]
rowdiag = make_diag(rowsums)
colsums = np.sqrt(1.0 / (EPS + (abs_matrix).sum(axis=0)))
colsums = np.asarray(colsums)[0, :]
coldiag = make_diag(colsums)
self._transition_matrix = (csr_matrix * coldiag).tocsr()
self._transition_matrix_T = self._transition_matrix.T.tocsr()
self._final_matrix = (self._fast_matrix * coldiag).tocsr()
self._final_matrix_T = (coldiag * self._fast_matrix.T).tocsr()
def make_fast_conjunctions(self):
csr_conjunctions = self._node_conjunctions.tocsr()
n = csr_conjunctions.shape[0]
scale_vec = np.zeros((n, ))
for row in xrange(n):
nnz = csr_conjunctions[row].nnz
if nnz > 0:
scale_vec[row] = 1.0 / nnz
self._fast_conjunctions = make_diag(scale_vec) * csr_conjunctions
def get_matrices(self):
if self._final_matrix is None:
self.make_fast_matrix()
return self._transition_matrix_T, self._transition_matrix
def get_conjunctions(self):
if self._fast_conjunctions is None:
self.make_fast_conjunctions()
return self._fast_conjunctions
def corona(self):
cmat = self.get_conjunctions()
mat_up, mat_down = self.get_matrices()
hub = np.ones((mat_up.shape[0], )) / mat_up.shape[0] / 100
authority = np.ones((mat_up.shape[0], )) / mat_up.shape[0] / 100
prev_activation = np.zeros((mat_up.shape[0], ))
prev_err = 1.0
for iter in xrange(100):
vec = authority + hub
vec /= np.max(vec)
root = np.zeros(len(vec), 'f')
root[0] = 1.0
conj_sums = cmat * vec
conj_par = 1.0 / (np.maximum(EPS,
cmat * (1.0 / np.maximum(EPS, vec))))
conj_factor = np.minimum(1.0, conj_par / (conj_sums + EPS))
conj_diag = make_diag(conj_factor)
combined = conj_diag * (mat_up + mat_down) * 0.25 + make_diag(
np.ones(len(vec)) * 0.5)
#combined = (mat_up + mat_down) * 0.5
u, sigma, v = sparse_svd(combined, k=1)
activation = u[:, 0]
#activation = np.dot(u, u[0])
#w, v = eigen(combined.T, k=1, v0=root, which='LR')
#activation = v[:, np.argmax(w)].real
activation *= np.sign(np.sum(activation))
activation /= (np.sum(np.abs(activation)) + EPS)
hub += (hub + self._final_matrix_T * conj_diag * activation) / 2
authority += (authority +
conj_diag * self._final_matrix * activation) / 2
print activation
err = np.max(np.abs(activation - prev_activation))\
/ np.max(np.abs(activation))
print err
if iter >= 3 and err + prev_err < 1e-9:
print "converged on iteration %d" % iter
break
prev_err = err
prev_activation = activation.copy()
print sigma
print conj_factor
print
hub = self._final_matrix_T * conj_diag * activation
authority = conj_diag * self._final_matrix * activation
return zip(self.nodes, hub, authority)
class BeliefNetwork(object):
def __init__(self, ground_weight=1.0, output=None):
self.graph = nx.Graph()
self.conjunctions = set()
self.ground_weight = ground_weight
self.nodes = OrderedSet()
self.edges = OrderedSet()
self._edge_matrix = None
self._conjunction_matrix = None
self._node_matrix = None
self._node_conjunctions = None
self._edge_conductance = None
self.output = output
def add_edge(self, source, dest, weight, dependencies=None):
self.nodes.add(source)
self.nodes.add(dest)
self.edges.add((source, dest))
props = {"weight": weight}
if dependencies is not None:
props["dependencies"] = dependencies
self.graph.add_edge(source, dest, **props)
if self.output:
self.output.write("%s\t%s\t%r\n" % (source, dest, props))
def add_conjunction(self, sources, dest, weight):
sources = tuple(sources)
self.conjunctions.add((sources, dest, weight))
for i, source in enumerate(sources):
self.add_edge(source, dest, weight, dependencies=sources)
def ordered_nodes(self):
return sorted(self.graph.nodes())
def update_arrays(self):
n_edges = len(self.edges) + len(self.nodes)
n_nodes = len(self.nodes)
offset = len(self.edges)
mat = sparse.dok_matrix((n_edges, n_nodes))
conjunction_mat = sparse.dok_matrix((n_edges, n_nodes))
vec = np.zeros((n_edges,))
for source, dest in self.graph.edges():
if (source, dest) not in self.edges:
(source, dest) = (dest, source)
edge_num = self.edges.index((source, dest))
weight = self.graph.get_edge_data(source, dest)["weight"]
source_idx = self.nodes.index(source)
mat[edge_num, source_idx] = -1.0
dest_idx = self.nodes.index(dest)
mat[edge_num, dest_idx] = 1.0
vec[edge_num] = weight
# Add edges to ground
for node in self.graph.nodes():
node_num = self.nodes.index(node)
adjusted_node_num = node_num + offset
mat[adjusted_node_num, node_num] = -1.0
vec[adjusted_node_num] = self.ground_weight
# Make matrix of conjunctions, edges -> input nodes
for sources, dest, weight in self.conjunctions:
edge_indices = []
node_indices = []
for source in sources:
if (source, dest) in self.edges:
edge_num = self.edges.index((source, dest))
else:
edge_num = self.edges.index((dest, source))
edge_indices.append(edge_num)
node_indices.append(self.nodes.index(source))
conjunction_mat[edge_indices, node_indices] = 1
# for node_index in node_indices:
# unconnected_edges = [e for e in edge_indices if mat[e, node_index] == 0.0]
self._edge_matrix = mat.tocsr()
self._edge_matrix_transpose = mat.T.tocsr()
self._edge_conductance = vec
self._conjunction_matrix = conjunction_mat.tocsr()
return mat, vec
def make_node_matrix(self):
n_nodes = len(self.nodes)
self._node_matrix = nx.to_scipy_sparse_matrix(self.graph, self.nodes)
def make_node_conjunctions(self):
n_nodes = len(self.nodes)
node_conjunctions = sparse.dok_matrix((n_nodes, n_nodes))
for sources, dest, weight in self.conjunctions:
node_indices = [self.nodes.index(source) for source in sources]
node_conjunctions[self.nodes.index(dest), node_indices] = 1.0
self._node_conjunctions = node_conjunctions.tocsr()
def get_node_matrix(self):
if self._node_matrix is None:
self.make_node_matrix()
return self._node_matrix
def get_node_conjunctions(self):
if self._node_conjunctions is None:
self.make_node_conjunctions()
return self._node_conjunctions
def spreading_activation(self, vec=None, root=None):
if vec is None:
vec = np.ones((len(self.nodes),))
cmat = self.get_node_conjunctions()
nmat = self.get_node_matrix()
for iter in xrange(100):
conj_sums = cmat * vec
conj_par = 1.0 / (cmat * (1.0 / np.maximum(0, vec)))
conj_factor = np.minimum(1.0, conj_par / conj_sums)
newvec = nmat.dot(vec) * conj_factor + vec
if root is not None and newvec[self.nodes.index(root)] < 0.0:
newvec = -newvec
newvec /= np.max(newvec)
print newvec
vec = newvec
return vec
def get_edge_matrix(self):
if self._edge_matrix is None:
self.update_arrays()
return self._edge_matrix
def get_edge_matrix_transpose(self):
if self._edge_matrix is None:
self.update_arrays()
return self._edge_matrix_transpose
def get_conductance(self):
if self._edge_conductance is None:
self.update_arrays()
return self._edge_conductance
def adjusted_conductances(self, equiv_conductances):
assert len(equiv_conductances) == len(self.nodes)
equiv_resistances = 1.0 / np.maximum(0, equiv_conductances)
edge_resistances = 1.0 / self._edge_conductance
combined_resistances = self._conjunction_matrix.dot(equiv_resistances)
new_resistances = edge_resistances + combined_resistances
adjusted_conductances = 1.0 / new_resistances
print adjusted_conductances
return adjusted_conductances
def get_system_matrix(self, conductances):
A_T = self.get_edge_matrix_transpose()
A = self.get_edge_matrix()
G = self.adjusted_conductances(conductances)
return make_product_operator(A_T, make_diag(G), A)
def solve_system(self, known_conductances, current_source):
"""
Get the conductance from root to each node by solving the electrical
system.
"""
current = np.zeros((len(self.nodes),))
current[current_source] = 1.0
system = self.get_system_matrix(known_conductances)
A = self.get_edge_matrix()
# Solve the sparse system of linear equations using cg
new_potentials = sparse_linalg.cg(system, current)[0]
# A = edges by nodes
currents = -A.dot(new_potentials)
potential_differences = new_potentials[current_source] - new_potentials
current_magnitude = np.abs(self.get_edge_matrix_transpose()).dot(currents)
conductance = 1.0 / potential_differences
return conductance
def run_analog(self, root, epsilon=1e-6):
conductance = np.ones((len(self.nodes),))
converged = False
root_index = self.nodes.index(root)
for i in xrange(100):
new_conductance = self.solve_system(conductance, root_index)
diff = np.minimum(conductance, 1000000.0) - np.minimum(new_conductance, 1000000.0)
conductance = new_conductance
print conductance
if np.linalg.norm(diff) < epsilon:
converged = True
break
if not converged:
print "Warning: failed to converge"
return zip(self.nodes, conductance)
class TrustNetwork(object):
def __init__(self, output=None):
self.nodes = OrderedSet()
self._node_matrix = None
self._node_conjunctions = None
self._fast_matrix_up = None
self._fast_matrix_down = None
self._fast_conjunctions = None
@staticmethod
def load(node_file, matrix_up, matrix_down, conjunction_file):
trust = TrustNetwork()
nodes = divisi2.load(node_file)
trust.nodes = OrderedSet(nodes)
trust._fast_matrix_up = divisi2.load(matrix_up)
trust._fast_matrix_down = divisi2.load(matrix_down)
trust._fast_conjunctions = divisi2.load(conjunction_file)
return trust
def add_nodes(self, nodes):
for node in nodes:
self.nodes.add(node)
def scan_edge(self, source, dest):
self.nodes.add(source)
self.nodes.add(dest)
def make_matrices(self):
self._node_matrix = sparse.dok_matrix(
(len(self.nodes), len(self.nodes)))
self._node_conjunctions = sparse.dok_matrix(
(len(self.nodes), len(self.nodes)))
def add_edge(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
#self._node_matrix[source_idx, dest_idx] = weight
self._node_matrix[dest_idx, source_idx] = weight
def add_conjunction(self, sources, dest, weight):
dest_idx = self.nodes.index(dest)
for i, source in enumerate(sources):
self.add_edge(source, dest, weight)
source_idx = self.nodes.index(source)
self._node_conjunctions[dest_idx, source_idx] = 1.0
def add_conjunction_piece(self, source, dest, weight):
source_idx = self.nodes.index(source)
dest_idx = self.nodes.index(dest)
self._node_matrix[dest_idx, source_idx] = weight
self._node_conjunctions[dest_idx, source_idx] = 1.0
def make_fast_matrix(self):
self._fast_matrix = self._node_matrix.tocsr()
for i in xrange(self._node_matrix.shape[0]):
self._node_matrix[0, i] += EPS
self._node_matrix[i, 0] += EPS
abs_matrix = np.abs(self._fast_matrix)
rowsums = 1.0 / (EPS + (abs_matrix).sum(axis=1))
rowsums = np.asarray(rowsums)[:, 0]
rowdiag = make_diag(rowsums)
self._fast_matrix_down = (rowdiag * self._fast_matrix).tocsr()
#self._fast_matrix_up = self._fast_matrix_down.T.tocsr()
colsums = 1.0 / (EPS + (abs_matrix).sum(axis=0))
colsums = np.asarray(colsums)[0, :]
coldiag = make_diag(colsums)
self._fast_matrix_up = (coldiag * self._fast_matrix.T).tocsr()
def make_fast_conjunctions(self):
csr_conjunctions = self._node_conjunctions.tocsr()
n = csr_conjunctions.shape[0]
scale_vec = np.zeros((n, ))
for row in xrange(n):
nnz = csr_conjunctions[row].nnz
if nnz > 0:
scale_vec[row] = 1.0 / nnz
self._fast_conjunctions = make_diag(scale_vec) * csr_conjunctions
def get_matrices(self):
if self._fast_matrix_up is None:
self.make_fast_matrix()
return self._fast_matrix_up, self._fast_matrix_down
def get_conjunctions(self):
if self._fast_conjunctions is None:
self.make_fast_conjunctions()
return self._fast_conjunctions
def corona(self):
cmat = self.get_conjunctions()
mat_up, mat_down = self.get_matrices()
hub = np.ones((mat_up.shape[0], ))
authority = np.ones((mat_up.shape[0], ))
for iter in xrange(100):
vec = authority + hub
vec /= np.max(vec)
root = vec * 0
root[0] = 1.0
conj_sums = cmat * vec
conj_par = 1.0 / (np.maximum(EPS,
cmat * (1.0 / np.maximum(EPS, vec))))
conj_factor = np.minimum(1.0, conj_par / (conj_sums + EPS))
conj_diag = make_diag(conj_factor)
combined = conj_diag * (mat_up + mat_down) + make_diag(
np.ones(len(vec)))
#combined = (mat_up + mat_down) * 0.5
u, sigma, v = sparse_svd(combined, k=4)
activation = np.dot(u, u[0])
#w, v = eigen(combined, k=3, v0=root)
#activation = v[:, np.argmax(w)]
#activation = (activation / (activation[0]+EPS)).real
print activation
print sigma
print conj_factor
print
hub += self._fast_matrix.T * conj_diag * activation
authority += conj_diag * self._fast_matrix * activation
hub /= np.max(hub)
authority /= np.max(authority)
return zip(self.nodes, hub, authority)