GM+SS using JAgt Seedless Procrustes

# collapse
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.pyplot as plt
import random
import sys
from joblib import Parallel, delayed

from graspy.simulations import sbm_corr

Experiment Summary

Let $(G_1, G_2) \sim \rho-SBM(\vec{n},B)$. (NB: binary, symmetric, hollow.)

$K = 3$.

the marginal SBM is conditional on block sizes $\vec{n}=[n_1,n_2,n_3]$.

$B = [(.20,.01,.01);(.01,.10,.01);(.01,.01,.20)]$. (NB: rank($B$)=3 with evalues $\approx [0.212,0.190,0.098]$.)

with $n = 75$ and $\vec{n}=[n_1,n_2,n_3] = [25,25,25]$

for each $\rho \in \{0.5,0.6,\cdots,0.9,1.0\}$ generate $r$ replicates $(G_1, G_2)$.

For all $r$ replicates, run $GM$, $GM_{SS}$ & $GM_{J.Agt}$ each $t$ times, with each $t$ corresponding to a different random permutation on $G_2$.

Specifically,$G_2' = Q G_2 Q^T,$ where $Q$ is sampled uniformly from the set of $n x n$ permutations matrices.

For each $t$ permutation, run $GM$ & $GM_{SS}$ & $GM_{J.Agt}$ from the barycenter ($\gamma = 0$).

For each $r$, the $t$ permutation with the highest associated objective function value will have it's match ratio recorded

For any $\rho$ value, have $\delta$ denote the average match ratio over the $r$ realizations

Plot $x=\rho$ vs $y$= $\delta$ $\pm$ 2s.e.

This notebook contains figures for $r=50$, $t=10$

NOTE: The max number of FW iterations here is set at 20.

Description of $GM_{ss}$ Procedure

For each $r$, ASE each graph into $d=3$ yielding $\hat{X}_1$ & $\hat{X}_2$

MedianFlip both into the first orthant yielding $\bar{X}_1$ & $\bar{X_2}$

let $Phat = \bar{X}_1 \bar{X}_2^T$ and run $t$ repititions of gm with $G_1,G_2 and Phat$ as the similarity.

Description of $GM_{J.Agt}$ Procedure

For each $r$, ASE each graph into $d=3$ yielding $\hat{X}_1$ & $\hat{X}_2$

With $2^d$ initializations, where $d$ is dimension, use J.Agt's seedless procrustes to find the optimal orthogonal alignment matrix, $Q$.

let $Phat = \hat{X}_1 Q \hat{X}_2^T$ and run $t$ repititions of gm with $G_1,G_2 and Phat$ as the similarity.

# collapse
# load in J.Agt data
# ratios_j = np.genfromtxt('ratios.csv', delimiter = ',')
# ratios_ss_j = np.genfromtxt('ratios_ss.csv', delimiter=',')
# scores_j = np.genfromtxt('scores.csv', delimiter = ',')
# scores_ss_j = np.genfromtxt('scores_ss.csv', delimiter=',')
# rhos = np.arange(5,10.5,0.5) *0.1
# n_p = len(rhos)
# ratios_opt_j = np.genfromtxt('ratios_opt.csv', delimiter = ',')
# ratios_opt_ss_j = np.genfromtxt('ratios_opt_ss.csv', delimiter=',')
# scores_opt_j = np.genfromtxt('scores_opt.csv', delimiter = ',')
# scores_opt_ss_j = np.genfromtxt('scores_opt_ss.csv', delimiter=',')

# collapse
ratios = np.genfromtxt('ratios.csv', delimiter = ',')
ratios_ss = np.genfromtxt('ratios_ss.csv', delimiter=',')
scores = np.genfromtxt('scores.csv', delimiter = ',')
scores_ss = np.genfromtxt('scores_ss.csv', delimiter=',')
ratios_opt = np.genfromtxt('ratios_opt.csv', delimiter = ',')
ratios_opt_ss = np.genfromtxt('ratios_opt_ss.csv', delimiter=',')
scores_opt = np.genfromtxt('scores_opt.csv', delimiter = ',')
scores_opt_ss = np.genfromtxt('scores_opt_ss.csv', delimiter=',')

# collapse
from scipy.stats import sem
import seaborn as sns
error = np.asarray([sem(ratios_j[i,:]) for i in range(n_p)])
average = np.asarray([np.mean(ratios_j[i,:] ) for i in range(n_p)])

error_j = np.asarray([sem(ratios_ss_j[i,:]) for i in range(n_p)])
average_j = np.asarray([np.mean(ratios_ss_j[i,:] ) for i in range(n_p)])

# collapse
error_ss = np.asarray([sem(ratios_ss[i,:]) for i in range(n_p)])
average_ss = np.asarray([np.mean(ratios_ss[i,:] ) for i in range(n_p)])

error2 = np.asarray([sem(ratios[i,:]) for i in range(n_p)])
average2 = np.asarray([np.mean(ratios[i,:] ) for i in range(n_p)])

# collapse
sns.set_context('paper')
sns.set(rc={'figure.figsize':(12,8)})
# plt.errorbar(rhos[odds],average_ss[odds], error_ss[odds],marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM+SS', color='blue')
# plt.errorbar(rhos[odds],average[odds], error[odds],marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM', color='red')
plt.errorbar(rhos,average_j, error_j,marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM+J.Agt', color='green')
plt.errorbar(rhos,average, error,marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM', color='red')
plt.errorbar(rhos,average_ss, error_ss,marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM+SS', color='blue')
plt.xlabel("rho")
plt.ylabel("avergae match ratio")
plt.text(0.5,0.5, 'r=50, t=10')
plt.legend()

<matplotlib.legend.Legend at 0x7f8588c091c0>

Script to run simulations

# collapse
import numpy as np
import matplotlib.pyplot as plt
import random
import sys
from joblib import Parallel, delayed
from .qap_sim import quadratic_assignment_sim
import seaborn as sns
from graspy.match import GraphMatch as GMP
from graspy.simulations import sbm_corr
from .jagt import SeedlessProcrustes
from graspy.embed import AdjacencySpectralEmbed


def run_sim(r, t, n=150, flip='median'):
    def match_ratio(inds, n):
        return np.count_nonzero(inds == np.arange(n)) / n
    def _median_sign_flips(X1, X2):
        X1_medians = np.median(X1, axis=0)
        X2_medians = np.median(X2, axis=0)
        val1 = np.sign(X1_medians).astype(int)
        X1 = np.multiply(val1.reshape(-1, 1).T, X1)
        val2 = np.sign(X2_medians).astype(int)
        X2 = np.multiply(val2.reshape(-1, 1).T, X2)
    
        return X1, X2
    #rhos = 0.1 * np.arange(11)[5:]
    m = r
    rhos = np.arange(5,10.5,0.5) *0.1
    n_p = len(rhos)
    ratios = np.zeros((n_p,m))
    scores = np.zeros((n_p,m))

    ratios_ss = np.zeros((n_p,m))
    scores_ss = np.zeros((n_p,m))

    ratios_opt = np.zeros((n_p,m))
    scores_opt = np.zeros((n_p,m))

    ratios_opt_ss = np.zeros((n_p,m))
    scores_opt_ss = np.zeros((n_p,m))

    n_per_block = int(n/3)
    n_blocks = 3
    block_members = np.array(n_blocks * [n_per_block])
    block_probs = np.array([[0.2, 0.01, 0.01], [0.01, 0.1, 0.01], [0.01, 0.01, 0.2]])
    directed = False
    loops = False
    for k, rho in enumerate(rhos):
        np.random.seed(8888)
        seeds = [np.random.randint(1e8, size=t) for i in range(m)]
        def run_sim(seed):

            A1, A2 = sbm_corr(
                block_members, block_probs, rho, directed=directed, loops=loops
            )
            score = 0
            res_opt = None
            
            score_ss = 0
            res_opt_ss = None

            ase = AdjacencySpectralEmbed(n_components=3, algorithm='truncated')
            Xhat1 = ase.fit_transform(A1)
            Xhat2 = ase.fit_transform(A2)
            if flip=='median':
                xhh1, xhh2 = _median_sign_flips(Xhat1, Xhat2)
                S = xhh1 @ xhh2.T
            elif flip=='jagt':
                sp = SeedlessProcrustes().fit(Xhat1, Xhat2)
                xhh1 = Xhat1@sp.Q
                xhh2 = Xhat2
                S = xhh1 @ xhh2.T
            else:
                S = None
    
            for j in range(t):
                res = quadratic_assignment_sim(A1, A2, True, options={'seed':seed[j]})
                if res['score']>score:
                    res_opt = res
                    score = res['score']
                
                res = quadratic_assignment_sim(A1, A2, True, S, options={'seed':seed[j]})
                if res['score']>score_ss:
                    res_opt_ss = res
                    score_ss = res['score']
                    
            ratio = match_ratio(res_opt['col_ind'], n)
            score = res_opt['score']
            
            ratio_ss = match_ratio(res_opt_ss['col_ind'], n)
            score_ss = res_opt_ss['score']

            res = quadratic_assignment_sim(A1, A2, True, options={'shuffle_input':False})
            ratio_opt = match_ratio(res['col_ind'], n)
            score_opt = res['score']

            res = quadratic_assignment_sim(A1, A2, True, S, options={'shuffle_input':False})
            ratio_opt_ss = match_ratio(res['col_ind'], n)
            score_opt_ss = res['score']


            return ratio, score, ratio_ss, score_ss, ratio_opt, score_opt, ratio_opt_ss, score_opt_ss
        
        result = Parallel(n_jobs=-1, verbose=10)(delayed(run_sim)(seed) for seed in seeds)
        
        ratios[k,:] = [item[0] for item in result]
        scores[k,:] = [item[1] for item in result]
        ratios_ss[k,:] = [item[2] for item in result]
        scores_ss[k,:] = [item[3] for item in result]
        ratios_opt[k,:] = [item[4] for item in result]
        scores_opt[k,:] = [item[5] for item in result]
        ratios_opt_ss[k,:] = [item[6] for item in result]
        scores_opt_ss[k,:] = [item[7] for item in result]
        
        
    np.savetxt('ratios.csv',ratios, delimiter=',')
    np.savetxt('scores.csv',scores, delimiter=',')
    np.savetxt('ratios_ss.csv',ratios_ss, delimiter=',')
    np.savetxt('scores_ss.csv',scores_ss, delimiter=',')
    np.savetxt('ratios_opt.csv',ratios_opt, delimiter=',')
    np.savetxt('scores_opt.csv',scores_opt, delimiter=',')
    np.savetxt('ratios_opt_ss.csv',ratios_opt_ss, delimiter=',')
    np.savetxt('scores_opt_ss.csv',scores_opt_ss, delimiter=',')

    from scipy.stats import sem
    error = [2*sem(ratios[i,:]) for i in range(n_p)]
    average = [np.mean(ratios[i,:] ) for i in range(n_p)]

    error_ss = [2*sem(ratios_ss[i,:]) for i in range(n_p)]
    average_ss = [np.mean(ratios_ss[i,:] ) for i in range(n_p)]
    sns.set_context('paper')
    #sns.set(rc={'figure.figsize':(15,10)})
    txt =f'r={r}, t={t}'
    plt.errorbar(rhos,average_ss, error_ss,marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM+SS')
    plt.errorbar(rhos,average, error,marker='o',capsize=3, elinewidth=1, markeredgewidth=1, label='GM', color='red')
    plt.xlabel("rho")
    plt.ylabel("avergae match ratio")
    plt.text(0.5,0.5,txt)
    plt.legend()
    plt.savefig('figure_matchratio.png', dpi=150, facecolor="w", bbox_inches="tight", pad_inches=0.3)