# Source code for graspologic.match.gmp

# Copyright (c) Microsoft Corporation and contributors.

import numpy as np
import math
from scipy.optimize import linear_sum_assignment
from scipy.optimize import minimize_scalar
from sklearn.base import BaseEstimator
from sklearn.utils import check_array
from sklearn.utils import column_or_1d
from .qap import quadratic_assignment

[docs]class GraphMatch(BaseEstimator):
"""
This class solves the Graph Matching Problem and the Quadratic Assignment Problem
(QAP) through an implementation of the Fast Approximate QAP Algorithm (FAQ) (these
two problems are the same up to a sign change) [1].

This algorithm can be thought of as finding an alignment of the vertices of two
graphs which minimizes the number of induced edge disagreements, or, in the case
of weighted graphs, the sum of squared differences of edge weight disagreements.
The option to add seeds (known vertex correspondence between some nodes) is also
available [2].

Parameters
----------

n_init : int, positive (default = 1)
Number of random initializations of the starting permutation matrix that
the FAQ algorithm will undergo. n_init automatically set to 1 if
init_method = 'barycenter'

init : string (default = 'barycenter') or 2d-array
The initial position chosen

If 2d-array, init must be :math:m' x m', where :math:m' = n - m,
and it must be doubly stochastic: each of its rows and columns must
sum to 1.

"barycenter" : the non-informative “flat doubly stochastic matrix,”
:math:J=1 \\times 1^T /n , i.e the barycenter of the feasible region

"rand" : some random point near :math:J, (J+K)/2, where K is some random
doubly stochastic matrix

max_iter : int, positive (default = 30)
Integer specifying the max number of Franke-Wolfe iterations.
FAQ typically converges with modest number of iterations.

shuffle_input : bool (default = True)
Gives users the option to shuffle the nodes of A matrix to avoid results
from inputs that were already matched.

eps : float (default = 0.1)
A positive, threshold stopping criteria such that FW continues to iterate
while Frobenius norm of :math:(P_{i}-P_{i+1}) > \\text{eps}

gmp : bool (default = True)
Gives users the option to solve QAP rather than the Graph Matching Problem
(GMP). This is accomplished through trivial negation of the objective function.

Allows user to specify padding scheme if A and B are not of equal size.
Say that A and B have :math:n_1 and :math:n_2 nodes, respectively, and
:math:n_1 < n_2.

"adopted" : matches A to the best fitting induced subgraph of B. Reduces the
affinity between isolated vertices added to A through padding and low-density
subgraphs of B.

"naive" : matches A to the best fitting subgraph of B.

Attributes
----------

perm_inds_ : array, size (n,) where n is the number of vertices in the fitted graphs.
The indices of the optimal permutation (with the fixed seeds given) on the nodes of B,
to best minimize the objective function :math:f(P) = \\text{trace}(A^T PBP^T ).

score_ : float
The objective function value of for the optimal permutation found.

n_iter_ : int
Number of Frank-Wolfe iterations run. If n_init > 1, :attr:n_iter_ reflects the number of
iterations performed at the initialization returned.

References
----------
.. [1] J.T. Vogelstein, J.M. Conroy, V. Lyzinski, L.J. Podrazik, S.G. Kratzer,
E.T. Harley, D.E. Fishkind, R.J. Vogelstein, and C.E. Priebe, “Fast
approximate quadratic programming for graph matching,” PLOS one, vol. 10,
no. 4, p. e0121002, 2015.

.. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski, C. Priebe,
Seeded graph matching, Pattern Recognit. 87 (2019) 203–215

"""

def __init__(
self,
n_init=1,
init="barycenter",
max_iter=30,
shuffle_input=True,
eps=0.1,
gmp=True,
):
if type(n_init) is int and n_init > 0:
self.n_init = n_init
else:
msg = '"n_init" must be a positive integer'
raise TypeError(msg)
if type(n_init) is int and n_init > 0:
self.n_init = n_init
else:
msg = '"n_init" must be a positive integer'
raise TypeError(msg)
if init == "rand":
self.init = "randomized"
elif init == "barycenter":
self.init = "barycenter"
elif not isinstance(init, str):
self.init = init
else:
msg = 'Invalid "init_method" parameter string'
raise ValueError(msg)
if max_iter > 0 and type(max_iter) is int:
self.max_iter = max_iter
else:
msg = '"max_iter" must be a positive integer'
raise TypeError(msg)
if type(shuffle_input) is bool:
self.shuffle_input = shuffle_input
else:
msg = '"shuffle_input" must be a boolean'
raise TypeError(msg)
if eps > 0 and type(eps) is float:
self.eps = eps
else:
msg = '"eps" must be a positive float'
raise TypeError(msg)
if type(gmp) is bool:
self.gmp = gmp
else:
msg = '"gmp" must be a boolean'
raise TypeError(msg)
msg = 'Invalid "padding" parameter string'
raise ValueError(msg)
else:
msg = '"padding" parameter must be of type string'
raise TypeError(msg)

[docs]    def fit(self, A, B, seeds_A=[], seeds_B=[]):
"""
Fits the model with two assigned adjacency matrices

Parameters
----------
A : 2d-array, square
A square adjacency matrix

B : 2d-array, square
A square adjacency matrix

seeds_A : 1d-array, shape (m , 1) where m <= number of nodes (default = [])
An array where each entry is an index of a node in A.

seeds_B : 1d-array, shape (m , 1) where m <= number of nodes (default = [])
An array where each entry is an index of a node in B The elements of
seeds_A and seeds_B are vertices which are known to be matched, that is,
seeds_A[i] is matched to vertex seeds_B[i].

Returns
-------
self : returns an instance of self
"""
A = check_array(A, copy=True, ensure_2d=True)
B = check_array(B, copy=True, ensure_2d=True)
seeds_A = column_or_1d(seeds_A)
seeds_B = column_or_1d(seeds_B)
partial_match = np.column_stack((seeds_A, seeds_B))

# pads A and B according to section 2.5 of [2]
if A.shape[0] != B.shape[0]:

options = {
"maximize": self.gmp,
"partial_match": partial_match,
"P0": self.init,
"shuffle_input": self.shuffle_input,
"maxiter": self.max_iter,
"tol": self.eps,
}

res = min(
[quadratic_assignment(A, B, options=options) for i in range(self.n_init)],
key=lambda x: x.fun,
)

self.perm_inds_ = res.col_ind  # permutation indices
self.score_ = res.fun  # objective function value
self.n_iter_ = res.nit
return self

[docs]    def fit_predict(self, A, B, seeds_A=[], seeds_B=[]):
"""
Fits the model with two assigned adjacency matrices, returning optimal
permutation indices

Parameters
----------
A : 2d-array, square
A square adjacency matrix

B : 2d-array, square
A square adjacency matrix

seeds_A : 1d-array, shape (m , 1) where m <= number of nodes (default = [])
An array where each entry is an index of a node in A.

seeds_B : 1d-array, shape (m , 1) where m <= number of nodes (default = [])
An array where each entry is an index of a node in B The elements of
seeds_A and seeds_B are vertices which are known to be matched, that is,
seeds_A[i] is matched to vertex seeds_B[i].

Returns
-------
perm_inds_ : 1-d array, some shuffling of [0, n_vert)
The optimal permutation indices to minimize the objective function
"""
self.fit(A, B, seeds_A, seeds_B)
return self.perm_inds_

X_pad = np.zeros((n[1], n[1]))
X_pad[: n[0], : n[0]] = X

A_n = A.shape[0]
B_n = B.shape[0]
n = np.sort([A_n, B_n])
if method == "adopted":
A = 2 * A - np.ones((A_n, A_n))
B = 2 * B - np.ones((B_n, B_n))

if A.shape[0] == n[0]:
A = pad(A, n)
else:
B = pad(B, n)

return A, B