In ilovato/nevada: Network-Valued Data Analysis

library(reticulate)
py_install(
  packages = "~/Softs/GraphSpace/", 
  envname = "r-reticulate", 
  method = "conda"
)
use_condaenv("r-reticulate")

import os
import sys
#sys.path.append("C:\\Users\\Anna\\OneDrive - Politecnico di Milano\\Windows\\Polimi\\Ricerca\\Regression\\GraphSpace\\")

from core import Graph, GraphSet, Mean, MeanIterative
from distance import euclidean
from matcher import GA, ID
from AlignCompute import mean_aac, gpc_aac, mean_aac_pred, ggr_aac

from core import Graph
from core import GraphSet
from core import Mean
from core import MeanIterative
from matcher import Matcher, alignment, GA, ID, GAS, GAS1
from distance import euclidean, hamming, sqeuclidean

import math
import numpy as np
import pandas as pd
from scipy.sparse import lil_matrix, vstack

1) Binary graphs

Define the graphs:

x1 = {}
x1[0, 0] = [1]
x1[1, 1] = [1]
x1[2, 2] = [1]
x1[3, 3] = [1]
x1[4, 4] = [1]
x1[5, 5] = [1]
x1[0, 1] = [1]
x1[1, 0] = [1]
x1[1, 2] = [1]
x1[2, 1] = [1]
x1[2, 5] = [1]
x1[3, 4] = [1]
x1[4, 3] = [1]
x1[5, 2] = [1]
x2 = {}
x2[0, 0] = [1]
x2[1, 1] = [1]
x2[2, 2] = [1]
x2[3, 3] = [1]
x2[4, 4] = [1]
x2[5, 5] = [1]
x2[0, 1] = [1]
x2[1, 0] = [1]
x2[1, 2] = [1]
x2[2, 1] = [1]
x2[3, 4] = [1]
x2[4, 3] = [1]

Create Graph set:

G = GraphSet(graph_type='directed')
G.add(Graph(x=x1, s=[1,2], adj=None))
G.add(Graph(x=x2, s=[2,3], adj=None))

Compute a distance with euclidean distance without matching the graphs

match=ID(hamming())
match.dis(G.X[0],G.X[1])

2) GRAPHS with Euclidean scalar and vector attributes on both nodes and edges

Define the graphs:

x1 = {}
x1[0, 0] = [0.813, 0.630]
x1[1, 1] = [1.606, 2.488]
x1[2, 2] = [2.300, 0.710]
x1[3, 3] = [0.950, 1.616]
x1[4, 4] = [2.046, 1.560]
x1[5, 5] = [2.959, 2.387]
x1[0, 1] = [1]
x1[1, 0] = [1]
x1[1, 2] = [1]
x1[2, 1] = [1]
x1[2, 5] = [1]
x1[3, 4] = [1]
x1[4, 3] = [1]
x1[5, 2] = [1]
x2 = {}
x2[0, 0] = [0.810, 0.701]
x2[1, 1] = [1.440, 2.437]
x2[2, 2] = [2.358, 0.645]
x2[3, 3] = [0.786, 1.535]
x2[4, 4] = [2.093, 1.591]
x2[5, 5] = [3.3, 2.2]
x2[0, 1] = [1]
x2[1, 0] = [1]
x2[1, 2] = [1]
x2[2, 1] = [1]
x2[3, 4] = [1]
x2[4, 3] = [1]
x3 = {}
x3[0, 0] = [0.71, 0.72]
x3[1, 1] = [1.45532, 2.45648]
x3[2, 2] = [2.21121, 0.757368]
x3[3, 3] = [0.796224, 1.53137]
x3[4, 4] = [2.06496, 1.5699]
x3[5, 5] = [2.75535, 0.194153]
x3[0, 1] = [1]
x3[1, 0] = [1]
x3[0, 5] = [1]
x3[5, 0] = [1]
x3[1, 2] = [1]
x3[2, 1] = [1]
x3[3, 4] = [1]
x3[4, 3] = [1]

Create Graph set:

G = GraphSet(graph_type='directed')
G.add(Graph(x=x1, s=None, adj=None))
G.add(Graph(x=x2, s=None, adj=None))
G.add(Graph(x=x3, s=None, adj=None))

or import a GraphSet

X = GraphSet()
X.read_from_text("Dataset.txt")

Compute the euclidean distance with or without matching between two graphs

Identity matching

match = ID(sqeuclidean())
match.dis(G.X[0], G.X[1])
print(match.f)
# the identity permutation as expected!

Matching Function - GA or GAS:

match = GAS(sqeuclidean())
match.dis(G.X[1], G.X[2])
# to see the matching transformation:
print(match.f)
del match

Compute the mean with the identity matcher

match = ID(sqeuclidean())
mu = Mean(G, match)
MU = mu.mean()
# to see the result:
print(MU.x)

del match, mu, MU

Align All and Compute Mean with GA matcher

match = GA(sqeuclidean())
mu = mean_aac(G, match)
mu.align_and_est()
MU = mu.mean
print(MU.x)

del match, mu, MU

Align All and Compute Mean with GAS matcher

match = GAS(sqeuclidean())
# or equivalently:
# GAS(euclidean())
# GAS('euclidean')
# GAS('euclidean','euclidean')
mu = mean_aac(G, match)
mu.align_and_est()
MU = mu.mean
print(MU.x)

del match, mu, MU

Align All and Compute GPC

n_comp=2
p=gpc_aac(G,GA(sqeuclidean()))
p.align_and_est(n_comp,scale=False,s=[0,10])

To project the data along the i-th GPC you need to: - create the geodesic by interpolation the two points barycenter and p.e_vec.X[i] - save the graphs along the geodesic that correspond to the scores (p.scores[:,i]) For example the first GPC:

n_gpc=0
Vector=p.e_vec.X[n_gpc]
Bar=p.barycenter_net
l=list(np.sort(p.scores[:,n_gpc]))
G_along_GPC=GraphSet()
for i in range(len(l)):
    G_along_GPC.add(p.add(1,Bar,l[i],Vector,range(Vector.n_nodes)))
    print(G_along_GPC.X[i].x)

Align All and Compute GGR regression scalar on graph

G=GraphSet()
G.read_from_text("ErdosReny_100.txt")
# Training and Test set
n_train=10
X_train=G.sublist(list(range(0,n_train)))

# Run GGR:
r=ggr_aac(X_train,GAS(sqeuclidean()),distance=sqeuclidean())
r.align_and_est()

# Proportion of variance explained
r.R2

# Network Coefficient
print(r.network_coef.x)

# Prediction:
Y_test=G.X[1]
x_new=pd.DataFrame(data=[float(Y_test.s)])
r.predict(x_new)

# Conformal Prediction Bands:

Y = GraphSet(graph_type='directed')
for j in range(190):
    x0 = {}
    i0 = np.random.binomial(n=1,p=0.4)
    x0[0,0] = [1]
    x0[1,1] = [1]
    x0[i0,(1-i0)] = [np.random.normal(loc=20, scale=3)]
    Y.add(Graph(x=x0, y=None, adj=None))
for j in range(10):
    x0 = {}
    x0[0,0] = [1]
    x0[1,1] = [1]
    x0[0,1] = [np.random.normal(loc=20, scale=3)]
    x0[1,0] = [np.random.normal(loc=2, scale=0.1)]
    Y.add(Graph(x=x0, y=None, adj=None))

match = GAS()
mu_pred = mean_aac_pred(Y, match)
mu_pred.align_est_and_predRegions()
mu_pred.conformal_matrix