#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
# graph_tool -- a general graph manipulation python module
#
# Copyright (C) 2006-2026 Tiago de Paula Peixoto <tiago@skewed.de>
#
# This program is free software; you can redistribute it and/or modify it under
# the terms of the GNU Lesser General Public License as published by the Free
# Software Foundation; either version 3 of the License, or (at your option) any
# later version.
#
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
# details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy
from . util import *
from . blockmodel import *
from . nested_blockmodel import *
from .. decorators import _parallel
[docs]
@_parallel
def minimize_blockmodel_dl(g, state=BlockState, state_args={},
multilevel_mcmc_args={}, refine=True,
epsilon=0.001):
r"""Fit the stochastic block model, by minimizing its description length using an
agglomerative heuristic.
Parameters
----------
g : :class:`~graph_tool.Graph`
The graph.
state : SBM-like state class (optional, default: :class:`~graph_tool.inference.BlockState`)
Type of model that will be used. Must be derived from :class:`~graph_tool.inference.MultilevelMCMCState`.
state_args : ``dict`` (optional, default: ``{}``)
Arguments to be passed to appropriate state constructor (e.g.
:class:`~graph_tool.inference.BlockState`)
multilevel_mcmc_args : ``dict`` (optional, default: ``{}``)
Arguments to be passed to :meth:`~graph_tool.inference.MultilevelMCMCState.multilevel_mcmc_sweep`.
refine : ``bool`` (optional, default: ``True``)
If ``True``, a refinement loop will be run as a final step, controlled
by the relative convergence criterion ``epsilon``.
epsilon : ``float`` (optional, default: ``0.001``)
If ``refine == True``, this value determines the relative convergence
criterion of the refinement step.
Returns
-------
min_state : type given by parameter ``state``
State with minimum description length.
Notes
-----
This function is a convenience wrapper around
:meth:`~graph_tool.inference.MultilevelMCMCState.multilevel_mcmc_sweep`.
See [peixoto-efficient-2014]_ for details on the algorithm.
This algorithm has a complexity of :math:`O(V \ln^2 V)`, where :math:`V` is
the number of nodes in the network.
@parallel@
Examples
--------
.. testsetup:: mdl
gt.seed_rng(43)
np.random.seed(43)
.. doctest:: mdl
>>> g = gt.collection.data["polbooks"]
>>> state = gt.minimize_blockmodel_dl(g)
>>> state.draw(pos=g.vp["pos"], vertex_shape=state.get_blocks(),
... output="polbooks_blocks_mdl.svg")
<...>
.. figure:: polbooks_blocks_mdl.*
:align: center
Block partition of a political books network, which minimizes the
description length of the network according to the degree-corrected
stochastic blockmodel.
.. testsetup:: mdl_overlap
gt.seed_rng(42)
np.random.seed(42)
.. doctest:: mdl_overlap
>>> g = gt.collection.data["polbooks"]
>>> state = gt.minimize_blockmodel_dl(g, state=gt.OverlapBlockState)
>>> state.draw(pos=g.vp["pos"], output="polbooks_overlap_blocks_mdl.svg")
<...>
.. figure:: polbooks_overlap_blocks_mdl.*
:align: center
Overlapping partition of a political books network, which minimizes the
description length of the network according to the overlapping
degree-corrected stochastic blockmodel.
.. doctest:: mdl_pp
>>> g = gt.collection.data["celegansneural"]
>>> state = gt.minimize_blockmodel_dl(g, state=gt.PPBlockState)
>>> state.draw(output="celegans_mdl_pp.pdf")
<...>
.. testcleanup:: mdl_pp
conv_png("celegans_mdl_pp.pdf")
.. figure:: celegans_mdl_pp.png
:align: center
:width: 60%
Assortative partition of the *C. elegans* neural network, which minimizes
the description length of the network according to the degree-corrected
planted-partition blockmodel.
References
----------
.. [peixoto-efficient-2014] Tiago P. Peixoto, "Efficient Monte Carlo and greedy
heuristic for the inference of stochastic block models", Phys. Rev. E 89,
012804 (2014), :doi:`10.1103/PhysRevE.89.012804`, :arxiv:`1310.4378`.
"""
state = state(g, **state_args)
args = dict(niter=1, beta=numpy.inf, force_accept=True)
args.update(multilevel_mcmc_args)
state.multilevel_mcmc_sweep(**args)
if refine:
refine_loop(state, args, epsilon)
return state
[docs]
@_parallel
def minimize_nested_blockmodel_dl(g, state=NestedBlockState,
base_state=BlockState, state_args={},
base_state_args={}, multilevel_mcmc_args={},
simple_init=False, base_factor=10.,
B_min_base=1000, top_factor=2., refine=True,
epsilon=0.001):
r"""Fit the nested stochastic block model, by minimizing its description length
using an agglomerative heuristic.
Parameters
----------
g : :class:`~graph_tool.Graph`
The graph.
state : nested SBM state class (optional, default: :class:`~graph_tool.inference.NestedBlockState`)
Type of next model that will be used.
base_state : base SBM state class (optional, default: :class:`~graph_tool.inference.BlockState`)
Type of model that will be used at the bottom of the hierarchy.
state_args : ``dict`` (optional, default: ``{}``)
Arguments to be passed to appropriate state constructor (e.g.
:class:`~graph_tool.inference.NestedBlockState`)
base_state_args : ``dict`` (optional, default: ``{}``)
Arguments to be passed to appropriate base state constructor (e.g.
:class:`~graph_tool.inference.BlockState`)
multilevel_mcmc_args : ``dict`` (optional, default: ``{}``)
Arguments to be passed to :meth:`~graph_tool.inference.MultilevelMCMCState.multilevel_mcmc_sweep`.
simple_init : ``bool`` (optional, default: ``False``)
If ``True``, a simple initialization scheme will be used, where the
hierarchy shape will be upper bounded by an initial guess based on the
number of nodes and the paramters ``base_factor``, ``top_factor``, and
``B_min_base``. This is meant to be used with ``refine == True`` for an
alternative to the more expensive multilevel minimization algorithm.
base_factor : ``float`` (optional, default: ``10.``)
If ``simple_init == True``, this will determine the minimum number of
groups at the lowest level of the hierarchy as ``N/base_factor``, where
``N`` is the number of vertices at the base level.
B_min_base : ``int`` (optional, default: ``1000``)
If ``simple_init == True``, this will determine the smallest minimum number
of groups at the lowest level during initialization, regardless of the
value of ``base_factor``.
top_factor : ``float`` (optional, default: ``2.``)
If ``simple_init == True``, this will determine the minimum number of
groups at the upper levels of the hierarchy as ``N/top_factor``, where
``N`` is the number of vertices at a particular level.
refine : ``bool`` (optional, default: ``True``)
If ``True``, a refinement loop will be run as a final step, controlled
by the relative convergence criterion ``epsilon``.
epsilon : ``float`` (optional, default: ``0.001``)
If ``refine == True``, this value determines the relative convergence
criterion of the refinement step.
Returns
-------
min_state : type given by parameter ``state``
State with minimum description length.
Notes
-----
This function is a convenience wrapper around
:meth:`~graph_tool.inference.NestedBlockState.multilevel_mcmc_sweep`.
See [peixoto-hierarchical-2014]_ for details on the algorithm.
This algorithm has a complexity of :math:`O(E \ln^2 V)`, where :math:`E` and
:math:`V` are the number of edges and nodes in the network, respectively.
@parallel@
Examples
--------
.. testsetup:: nested_mdl
gt.seed_rng(43)
np.random.seed(43)
.. doctest:: nested_mdl
>>> g = gt.collection.data["power"]
>>> state = gt.minimize_nested_blockmodel_dl(g)
>>> state.draw(output="power_nested_mdl.pdf")
(...)
.. testcleanup:: nested_mdl
conv_png("power_nested_mdl.pdf")
.. figure:: power_nested_mdl.png
:align: center
:width: 60%
Hierarchical Block partition of a power-grid network, which minimizes
the description length of the network according to the nested
(degree-corrected) stochastic blockmodel.
.. doctest:: nested_mdl_overlap
>>> g = gt.collection.data["celegansneural"]
>>> state = gt.minimize_nested_blockmodel_dl(g, base_state=gt.OverlapBlockState)
>>> state.draw(output="celegans_nested_mdl_overlap.pdf")
(...)
.. testcleanup:: nested_mdl_overlap
conv_png("celegans_nested_mdl_overlap.pdf")
.. figure:: celegans_nested_mdl_overlap.png
:align: center
:width: 60%
Overlapping block partition of the *C. elegans* neural network, which
minimizes the description length of the network according to the nested
overlapping degree-corrected stochastic blockmodel.
References
----------
.. [peixoto-hierarchical-2014] Tiago P. Peixoto, "Hierarchical block
structures and high-resolution model selection in large networks ",
Phys. Rev. X 4, 011047 (2014), :doi:`10.1103/PhysRevX.4.011047`,
:arxiv:`1310.4377`.
"""
state = state(g, base_state=base_state,
base_state_args=base_state_args, **state_args)
args = dict(niter=1, beta=numpy.inf)
args.update(multilevel_mcmc_args)
if simple_init:
for l, s in enumerate(state.levels):
if l == 0:
B = int(max(s.get_N() / base_factor, B_min_base))
else:
B = int(s.get_N() / top_factor)
B = max(B, 1)
s.multilevel_mcmc_sweep(**dict(args, B_min=B,
force_accept=True,
bisection=False))
else:
l = 0
while l >= 0:
ret = state.multilevel_mcmc_sweep(ls=[l], **args)
if args.get("verbose", False):
print(l, ret, state)
if abs(ret[0]) < 1e-8:
l -= 1
else:
l = min((l + 1, len(state.levels) - 1))
if refine:
refine_loop(state, args, epsilon)
return state
def refine_loop(state, mcmc_args, epsilon):
eargs = mcmc_args.get("entropy_args", {})
delta = epsilon + 1
while delta > epsilon:
delta = state.multilevel_mcmc_sweep(**dict(mcmc_args, refine=True,
force_accept=False))[0]
delta = abs(delta / state.entropy(**eargs))
