diff --git a/ABCD_properties.ipynb b/ABCD_properties.ipynb new file mode 100644 index 0000000..7498695 --- /dev/null +++ b/ABCD_properties.ipynb @@ -0,0 +1,1360 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "45a8c803", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.stats as stats\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "import os\n", + "from collections import Counter\n", + "import pickle\n", + "import igraph as ig\n", + "import partition_igraph\n", + "from sklearn.metrics import adjusted_rand_score as ARI\n", + "from sklearn.metrics import adjusted_mutual_info_score as AMI\n" + ] + }, + { + "cell_type": "markdown", + "id": "158dc36c", + "metadata": {}, + "source": [ + "# Properties of ABCD\n", + "\n", + "The following experiments were used to generate the Figures and Tables in:\n", + "```\n", + "Bogumił Kamiński, Bartosz Pankratz, Paweł Prałat and François Théberge,\n", + "Modularity of the ABCD Random Graph Model with Community Structure.\n", + "```\n", + "\n", + "Results were obtained with the CLI version of ABCD from: https://github.com/bkamins/ABCDGraphGenerator.jl\n", + "Adjust the path below to your local version of the code.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "98cfae50", + "metadata": {}, + "outputs": [], + "source": [ + "abcd_path = '~/ABCD/utils/'" + ] + }, + { + "cell_type": "markdown", + "id": "afe32f62", + "metadata": {}, + "source": [ + "## Figure 1 - Cumulative degree distribution\n", + "\n", + "With number of nodes: $n$=1,000 and $n$=1,000,000" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "32928926", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "gamma = 2.5\n", + "delta = 5 \n", + "n = 1000\n", + "D = int(np.round(n**0.5))\n", + "\n", + "cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + "os.system(cmd+' >/dev/null 2>&1')\n", + "x = np.array(pd.read_csv('deg.dat',header=None)[0])\n", + "\n", + "C = Counter(x)\n", + "cdf = np.zeros(D+1)\n", + "ctr = 0\n", + "for i in np.arange(D,delta-1,-1):\n", + " ctr += C[i]\n", + " cdf[i] = ctr\n", + "th = [ (k**(1-gamma) - (D+1)**(1-gamma)) / (delta**(1-gamma) - (D+1)**(1-gamma)) for k in np.arange(delta,D+1)]\n", + "\n", + "plt.figure(figsize=(10,7))\n", + "plt.loglog(np.arange(delta,D+1),(cdf[delta:]/n),'b--',label='simulation')\n", + "plt.loglog(np.arange(delta,D+1),th,'r-',label='theory')\n", + "plt.xlabel('K', fontsize=18)\n", + "plt.ylabel('Fraction of nodes with degree >= K', fontsize=16)\n", + "plt.title('n = 1,000',fontsize=18)\n", + "plt.legend(fontsize=16);\n", + "#plt.savefig('degree_1k.pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9ccb3933", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "gamma = 2.5\n", + "delta = 5 \n", + "n = 1000000\n", + "D = int(np.round(n**0.5))\n", + "\n", + "cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + "os.system(cmd+' >/dev/null 2>&1')\n", + "x = np.array(pd.read_csv('deg.dat',header=None)[0])\n", + "\n", + "C = Counter(x)\n", + "cdf = np.zeros(D+1)\n", + "ctr = 0\n", + "for i in np.arange(D,delta-1,-1):\n", + " ctr += C[i]\n", + " cdf[i] = ctr\n", + "th = [ (k**(1-gamma) - (D+1)**(1-gamma)) / (delta**(1-gamma) - (D+1)**(1-gamma)) for k in np.arange(delta,D+1)]\n", + "\n", + "plt.figure(figsize=(10,7))\n", + "plt.loglog(np.arange(delta,D+1),(cdf[delta:]/n),'b--',label='simulation')\n", + "plt.loglog(np.arange(delta,D+1),th,'r-',label='theory')\n", + "plt.xlabel('K', fontsize=18)\n", + "plt.ylabel('Fraction of nodes with degree >= K', fontsize=16)\n", + "plt.title('n = 1,000,000',fontsize=18)\n", + "plt.legend(fontsize=16);\n", + "#plt.savefig('degree_1M.pdf');\n" + ] + }, + { + "cell_type": "markdown", + "id": "8be0cbd1", + "metadata": {}, + "source": [ + "## Figure 2 - Normalized average volume\n", + "\n", + "We generate 100 graphs both with $\\delta$ = 5 and $\\delta$ = 25.\n", + "\n", + "With that many repeats, the code below can take a while to complete (45 min on a Mac Pro),\n", + "so we illustrate the result with 10 repeats below.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "fdebf2b1", + "metadata": {}, + "outputs": [], + "source": [ + "## continuous model\n", + "def qk(k,gamma,delta,D):\n", + " v = (k**(1-gamma) - (k+1)**(1-gamma)) / (delta**(1-gamma) - (D+1)**(1-gamma))\n", + " return v\n", + "## discrete model\n", + "def rk(k,gamma):\n", + " return k**(-gamma)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "82246c55", + "metadata": {}, + "outputs": [], + "source": [ + "REP = 10 ## we used 100 repeats in the paper\n", + "\n", + "gamma = 2.5\n", + "delta = 5\n", + "N = [1000*(2**i) for i in np.arange(16)]\n", + "X = []\n", + "S = []\n", + "d = []\n", + "r = []\n", + "for n in N:\n", + " D = int(np.round(n**0.5))\n", + " z = []\n", + " for i in range(REP):\n", + " cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " x = np.array(pd.read_csv('deg.dat',header=None)[0])\n", + " z.append(sum(x)/n)\n", + " X.append(np.mean(z))\n", + " S.append(np.std(z))\n", + " ## theory\n", + " th = 0\n", + " for k in np.arange(delta,D+1):\n", + " th += (k*qk(k,gamma,delta,D))\n", + " d.append(th)\n", + " ## discrete\n", + " th = 0\n", + " s = 0\n", + " for k in np.arange(delta,D+1):\n", + " x = rk(k,gamma)\n", + " th += (k*x)\n", + " s += x \n", + " r.append(th/s) \n", + "## optional - save a local copy of the results\n", + "#pickle.dump( (X, S, d, r), open( \"./Data/degree_ratio_5.pkl\", \"wb\" ) )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ef59553c", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "## optional - load a local copy of the results \n", + "#X, S, d ,r = pickle.load( open( \"./Data/degree_ratio_5.pkl\", \"rb\" ) )\n", + "\n", + "N = [1000*(2**i) for i in np.arange(16)]\n", + "\n", + "plt.figure(figsize=(10,7))\n", + "\n", + "Y = np.array([i/j for i,j in zip(X,d)])\n", + "err = np.array([i/j for i,j in zip(S,d)])\n", + "plt.semilogx(N, Y, 'r-',label='empirical:continuous model ratio')\n", + "plt.fill_between(N, Y-err, Y+err, color='red', alpha=.2)\n", + "\n", + "Y = [i/j for i,j in zip(X,r)]\n", + "err = np.array([i/j for i,j in zip(S,r)])\n", + "plt.semilogx(N, Y, 'b-',label='empirical:discrete model ratio')\n", + "plt.fill_between(N, Y-err, Y+err, color='blue', alpha=.2)\n", + "\n", + "plt.hlines(y=1,xmin=min(N),xmax=max(N),colors='black',linestyles='dashed')\n", + "plt.title(r\"$\\delta$=5\", fontsize=18)\n", + "plt.xlabel('Number of nodes', fontsize=16)\n", + "plt.ylabel('Normalized volume', fontsize=16)\n", + "plt.ylim((.93,1.03))\n", + "plt.legend();\n", + "#plt.savefig('degree_ratio_5.pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "3f800657", + "metadata": {}, + "outputs": [], + "source": [ + "REP = 10 ## we used 100 repeats in the paper\n", + "\n", + "gamma = 2.5\n", + "delta = 25\n", + "\n", + "N = [1000*(2**i) for i in np.arange(16)]\n", + "X = []\n", + "S = []\n", + "d = []\n", + "r = []\n", + "\n", + "for n in N:\n", + " D = int(np.round(n**0.5))\n", + " z = []\n", + " for i in range(REP):\n", + " cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " x = np.array(pd.read_csv('deg.dat',header=None)[0])\n", + " z.append(sum(x)/n)\n", + " X.append(np.mean(z))\n", + " S.append(np.std(z))\n", + " ## theory\n", + " th = 0\n", + " for k in np.arange(delta,D+1):\n", + " th += (k*qk(k,gamma,delta,D))\n", + " d.append(th)\n", + " ## discrete\n", + " th = 0\n", + " s = 0\n", + " for k in np.arange(delta,D+1):\n", + " x = rk(k,gamma)\n", + " th += (k*x)\n", + " s += x \n", + " r.append(th/s)\n", + " \n", + "## optional - save a local copy of the results\n", + "#pickle.dump( (X, S, d, r), open( \"./Data/degree_ratio_25.pkl\", \"wb\" ) )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "0733fde7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "## optional - load a local copy of the results - uncomment the cell above to (re-)generate\n", + "#X, S, d ,r = pickle.load( open( \"./Data/degree_ratio_25.pkl\", \"rb\" ) )\n", + "N = [1000*(2**i) for i in np.arange(16)]\n", + "\n", + "plt.figure(figsize=(10,7))\n", + "\n", + "Y = np.array([i/j for i,j in zip(X,d)])\n", + "err = np.array([i/j for i,j in zip(S,d)])\n", + "plt.semilogx(N, Y, 'r-',label='empirical:continuous model ratio')\n", + "plt.fill_between(N, Y-err, Y+err, color='red', alpha=.2)\n", + "\n", + "Y = [i/j for i,j in zip(X,r)]\n", + "err = np.array([i/j for i,j in zip(S,r)])\n", + "plt.semilogx(N, Y, 'b-',label='empirical:discrete model ratio')\n", + "plt.fill_between(N, Y-err, Y+err, color='blue', alpha=.2)\n", + "\n", + "plt.hlines(y=1,xmin=min(N),xmax=max(N),colors='black',linestyles='dashed')\n", + "plt.title(r\"$\\delta$=25\", fontsize=18)\n", + "plt.xlabel('Number of nodes', fontsize=16)\n", + "plt.ylabel('Normalized volume', fontsize=16)\n", + "## un-comment to force the same y-range as previous plot\n", + "plt.ylim((.93,1.03))\n", + "plt.legend();\n", + "plt.savefig('degree_ratio_25.pdf');" + ] + }, + { + "cell_type": "markdown", + "id": "62f17847", + "metadata": {}, + "source": [ + "## Figure 3 - Cumulative community size distribution\n", + "\n", + "Again with $n$=1,000 and $n$=1,000,000.\n", + "\n", + "With 30 repeats, the experiment with small graphs of size 1,000 has noticeable variability.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d22f3225", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "beta = 1.5\n", + "s = 50 \n", + "n = 1000\n", + "S = int(np.round(n**0.75))\n", + "\n", + "th = [ (k**(1-beta) - (S+1)**(1-beta)) / (s**(1-beta) - (S+1)**(1-beta)) for k in np.arange(s,S+1)]\n", + "REP = 30\n", + "cdf = np.zeros(S+1)\n", + "\n", + "for rep in range(REP):\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl comm.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " x = np.array(pd.read_csv('comm.dat',header=None)[0])\n", + "\n", + " C = Counter(x)\n", + " nc = len(x) ## NEW \n", + " ctr = 0\n", + " for i in np.arange(S,s-1,-1):\n", + " ctr += C[i]\n", + " cdf[i] += ctr/nc ## NEW\n", + "for i in np.arange(S,s-1,-1): \n", + " cdf[i] /= REP\n", + "\n", + "## plot \n", + "plt.figure(figsize=(10,7))\n", + "plt.loglog(np.arange(s,S+1),th,'r-',label='theory')\n", + "plt.loglog(np.arange(s,S+1),(cdf[s:]),'b--',label='simulation')\n", + "plt.xlabel('K', fontsize=18)\n", + "plt.ylabel('Fraction of communities with size >= K', fontsize=16)\n", + "plt.title('n = 1,000',fontsize=18)\n", + "plt.legend(fontsize=16);\n", + "# plt.savefig('comm_1k.pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "1013df7b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "beta = 1.5\n", + "s = 50 \n", + "n = 1000000\n", + "S = int(np.round(n**0.75))\n", + "\n", + "th = [ (k**(1-beta) - (S+1)**(1-beta)) / (s**(1-beta) - (S+1)**(1-beta)) for k in np.arange(s,S+1)]\n", + "REP = 30\n", + "cdf = np.zeros(S+1)\n", + "\n", + "for rep in range(REP):\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl comm.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " x = np.array(pd.read_csv('comm.dat',header=None)[0])\n", + "\n", + " C = Counter(x)\n", + " nc = len(x) ## NEW \n", + " ctr = 0\n", + " for i in np.arange(S,s-1,-1):\n", + " ctr += C[i]\n", + " cdf[i] += ctr/nc ## NEW\n", + "for i in np.arange(S,s-1,-1): \n", + " cdf[i] /= REP\n", + "\n", + "## plot\n", + "plt.figure(figsize=(10,7))\n", + "plt.loglog(np.arange(s,S+1),th,'r-',label='theory')\n", + "plt.loglog(np.arange(s,S+1),(cdf[s:]),'b--',label='simulation')\n", + "plt.xlabel('K', fontsize=18)\n", + "plt.ylabel('Fraction of communities with size >= K', fontsize=16)\n", + "plt.title('n = 1,000,000',fontsize=18)\n", + "plt.legend(fontsize=16);\n", + "#plt.savefig('comm_1M.pdf');" + ] + }, + { + "cell_type": "markdown", + "id": "87811f22", + "metadata": {}, + "source": [ + "## Figure 4 - Number of communities\n", + "\n", + "We consider 4 combinations of parameters; \n", + "we show the second case below.\n", + "\n", + "* tau=0.75, beta=1.5\n", + "* tau=0.60, beta=1.5\n", + "* tau=0.75, beta=1.25\n", + "* tau=0.75, beta=1.75\n", + "\n", + "Running 100 repeats takes just under 1 hour on a Mac Pro; we ran 100 repeats in the paper;\n", + "below we show results with 10 repeats for speed." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "f1add398", + "metadata": {}, + "outputs": [], + "source": [ + "## adjust the parameters here\n", + "beta = 1.5\n", + "tau = 0.6\n", + "REP = 10 ## we used 100 in the paper\n", + "\n", + "s = 50 \n", + "c = (2-beta)/((beta-1)*s**(beta-1))\n", + "N = [1000*(2**i) for i in np.arange(16)]\n", + "X = []\n", + "Sx = []\n", + "T = []\n", + "\n", + "for n in N:\n", + " S = int(np.round(n**tau))\n", + " z = []\n", + " for i in range(REP):\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl comm.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " x = np.array(pd.read_csv('comm.dat',header=None)[0])\n", + " z.append(len(x))\n", + " X.append(np.mean(z))\n", + " Sx.append(np.std(z))\n", + " ## theory\n", + " th = c*n**(1-tau*(2-beta))\n", + " T.append(th)\n", + "\n", + "## optional - save results in local file\n", + "#pickle.dump( (X, Sx, T), open( \"./tau_60.pkl\", \"wb\" ) )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "2660bcd6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,7))\n", + "Y = np.array([i/j for i,j in zip(X,T)])\n", + "err = np.array([i/j for i,j in zip(Sx,T)])\n", + "plt.semilogx(N, Y, 'r-',label='empirical:theory ratio')\n", + "plt.fill_between(N, Y-err, Y+err, color='red', alpha=.2)\n", + "plt.hlines(y=1,xmin=min(N),xmax=max(N),colors='black',linestyles='dashed')\n", + "plt.title(r\"$\\beta$=1.5, $\\tau$=0.6\", fontsize=18)\n", + "plt.xlabel('Number of nodes', fontsize=16)\n", + "plt.ylabel('Normalized number of communities', fontsize=16)\n", + "plt.legend()\n", + "## adjust y-range to have same as other plot\n", + "plt.ylim((.83,1.22));\n", + "#plt.savefig('comm_ratio_tau_75.pdf');" + ] + }, + { + "cell_type": "markdown", + "id": "09f14f87", + "metadata": {}, + "source": [ + "## Figure 5 - Scaled volumes of communies\n", + "\n", + "30 repeats for $n$=1,000, single one for $n$=1,000,000.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "982bb3e5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "REP = 30\n", + "n = 1000\n", + "\n", + "beta = 1.5\n", + "s = 50 \n", + "tau = 3/4\n", + "gamma = 2.5\n", + "delta = 5\n", + "xi = .2\n", + "D = int(np.round(n**0.5))\n", + "S = int(np.round(n**tau))\n", + "\n", + "d = 0\n", + "t = 0\n", + "for k in np.arange(delta,D+1):\n", + " x = rk(k,gamma)\n", + " d += (k*x)\n", + " t += x \n", + "d = d / t\n", + "x = []\n", + "y = []\n", + "\n", + "for rep in range(REP):\n", + " ## generate graph\n", + " cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl cs.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'graph_sampler.jl net.dat comm.dat deg.dat cs.dat xi '+str(xi)+' false false'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + "\n", + " g = ig.Graph.Read_Ncol('net.dat',directed=False)\n", + " c = np.loadtxt('comm.dat',dtype='uint16',usecols=(1))\n", + " ## ground-truth communities\n", + " gt = [c[int(i['name'])-1]-1 for i in g.vs]\n", + " nc = np.max(gt)+1\n", + " g.vs['comm'] = gt\n", + " g.vs['deg'] = g.degree() \n", + " for i in range(nc):\n", + " j = [v['deg'] for v in g.vs if v['comm']==i] \n", + " x.append(len(j))\n", + " y.append(sum(j)/(d*len(j)))\n", + "\n", + "## plot\n", + "plt.figure(figsize=(10,7))\n", + "plt.plot(x,y,'o')\n", + "plt.xlabel('Size of community',fontsize=14)\n", + "plt.ylabel('Normalized community volume',fontsize=14)\n", + "plt.hlines(y=1,xmin=min(x),xmax=max(x),colors='black',linestyles='dashed')\n", + "plt.title(r\"$n$=1,000\", fontsize=18);\n", + "#plt.savefig('comm_vol_1k.pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "aab54970", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "n = 1000000\n", + "REP = 1\n", + "\n", + "beta = 1.5\n", + "s = 50 \n", + "tau = 3/4\n", + "gamma = 2.5\n", + "delta = 5\n", + "\n", + "xi = .2\n", + "D = int(np.round(n**0.5))\n", + "S = int(np.round(n**tau))\n", + "s = 50\n", + "\n", + "d = 0\n", + "t = 0\n", + "for k in np.arange(delta,D+1):\n", + " x = rk(k,gamma)\n", + " d += (k*x)\n", + " t += x \n", + "d = d / t\n", + "\n", + "x = []\n", + "y = []\n", + "\n", + "for rep in range(REP):\n", + "\n", + " ## generate graph\n", + " cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl cs.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'graph_sampler.jl net.dat comm.dat deg.dat cs.dat xi '+str(xi)+' false false'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + "\n", + " g = ig.Graph.Read_Ncol('net.dat',directed=False)\n", + " c = np.loadtxt('comm.dat',dtype='uint16',usecols=(1))\n", + " ## ground-truth communities\n", + " gt = [c[int(i['name'])-1]-1 for i in g.vs]\n", + " nc = np.max(gt)+1\n", + " g.vs['comm'] = gt\n", + " g.vs['deg'] = g.degree()\n", + " \n", + " for i in range(nc):\n", + " j = [v['deg'] for v in g.vs if v['comm']==i] \n", + " x.append(len(j))\n", + " y.append(sum(j)/(d*len(j)))\n", + " \n", + "## plot\n", + "plt.figure(figsize=(10,7))\n", + "plt.plot(x,y,'o')\n", + "plt.xlabel('Size of community',fontsize=14)\n", + "plt.ylabel('Normalized community volume',fontsize=14)\n", + "plt.hlines(y=1,xmin=min(x),xmax=max(x),colors='black',linestyles='dashed')\n", + "plt.title(r\"$n$=1,000,000\", fontsize=18);\n", + "#plt.savefig('comm_vol_1M.pdf');" + ] + }, + { + "cell_type": "markdown", + "id": "a5ef45d2", + "metadata": {}, + "source": [ + "## Figure 6 - Ground truth modularity with varying $n$\n", + "\n", + "We generated plots for $\\xi$=0.2 (shown below) and $\\xi$=0.7;\n", + "with 30 repeats, the code below takes a few hours to run, so it is commented out and we show a plot using the results saved to a local file." + ] + }, + { + "cell_type": "raw", + "id": "f4bc9cdb", + "metadata": {}, + "source": [ + "REP = 30\n", + "beta = 1.5\n", + "s = 50 \n", + "tau = 3/4\n", + "xi = .2\n", + "delta = 5\n", + "gamma = 2.5\n", + "\n", + "N = [1000*(2**i) for i in np.arange(16)]\n", + "X = []\n", + "Sx = []\n", + "XX = []\n", + "Sxx = []\n", + "\n", + "for n in N:\n", + " print(n)\n", + " S = int(np.round(n**tau))\n", + " D = int(np.round(n**0.5))\n", + " z = []\n", + " zz = []\n", + " for i in range(REP):\n", + " ## generate graph\n", + " cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl cs.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'graph_sampler.jl net.dat comm.dat deg.dat cs.dat xi '+str(xi)+' false false'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + "\n", + " g = ig.Graph.Read_Ncol('net.dat',directed=False)\n", + " c = np.loadtxt('comm.dat',dtype='uint16',usecols=(1))\n", + " ## ground-truth communities\n", + " gt = [c[int(i['name'])-1]-1 for i in g.vs]\n", + " z.append(g.modularity(gt))\n", + " g.vs['comm'] = gt\n", + " zz.append(sum([g.vs[e.tuple[0]]['comm'] == g.vs[e.tuple[1]]['comm'] for e in g.es])/g.ecount())\n", + "\n", + "\n", + " XX.append(np.mean(zz))\n", + " Sxx.append(np.std(zz)) \n", + " X.append(np.mean(z))\n", + " Sx.append(np.std(z))\n", + "\n", + "## optional - save results to local file \n", + "#pickle.dump( (X, Sx, XX, Sxx), open( \"./q_20.pkl\", \"wb\" ) )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "fa157524", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "## optional - load results from local file\n", + "X, Sx, XX, Sxx = pickle.load( open( \"./Data/q_20.pkl\", \"rb\" ) ) # xi = .2\n", + "\n", + "xi = .2\n", + "plt.figure(figsize=(10,7))\n", + "err = np.array([i for i in Sx])\n", + "plt.semilogx(N, X, 'r-',label='ground truth modularity')\n", + "plt.fill_between(N, X-err, X+err, color='red', alpha=.2)\n", + "err = np.array([i for i in Sxx])\n", + "plt.semilogx(N, XX, 'b-',label='edge contribution only')\n", + "plt.fill_between(N, XX-err, XX+err, color='blue', alpha=.2)\n", + "plt.hlines(y=1-xi,xmin=min(N),xmax=max(N),colors='black',linestyles='dashed')\n", + "plt.title(r\"$\\xi$=0.2\", fontsize=18)\n", + "plt.xlabel('Number of nodes', fontsize=16)\n", + "plt.ylabel('Modularity', fontsize=16)\n", + "plt.legend();\n", + "#plt.savefig('q_20.pdf');" + ] + }, + { + "cell_type": "markdown", + "id": "e04da16b", + "metadata": {}, + "source": [ + "## Figure 7&8 and Table 2 - Ground truth and ECG modularity with varying $\\xi$\n", + "\n", + "We generated plots for $n$=1,000 (shown below) and $n$=1,000,000.\n", + "\n", + "With 30 repeats, the code for $n=1,000$ takes about 12 minutes; we show the result for 10 repeats below.\n", + "\n", + "With $n=1,000,000$, this experiment takes several hours; we ran it on several CPUs.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "92132b97", + "metadata": {}, + "outputs": [], + "source": [ + "# n = 1000 or 1000000\n", + "n = 1000 \n", + "REP = 10 ## we used 30 in the paper\n", + "\n", + "beta = 1.5\n", + "s = 50 \n", + "tau = 3/4\n", + "delta = 5\n", + "gamma = 2.5\n", + "\n", + "# init\n", + "q_gt = []\n", + "Sq_gt = []\n", + "ec_gt = []\n", + "Sec_gt = []\n", + "q_ecg = []\n", + "Sq_ecg = []\n", + "ec_ecg = []\n", + "Sec_ecg = []\n", + "sim_ari = []\n", + "sim_ami = []\n", + "\n", + "XI = [.1,.2,.3,.4,.5,.6,.7,.8,.9]\n", + "S = int(np.round(n**tau))\n", + "D = int(np.round(n**0.5))\n", + "\n", + "for xi in XI:\n", + " z_ecg = []\n", + " zz_ecg = []\n", + " z_gt = []\n", + " zz_gt = []\n", + " ari = []\n", + " ami = []\n", + " \n", + " for i in range(REP):\n", + " ## generate graph\n", + " cmd = 'julia '+abcd_path+'deg_sampler.jl deg.dat '+str(gamma)+' '+str(delta)+' '+str(D)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'com_sampler.jl cs.dat '+str(beta)+' '+str(s)+' '+str(S)+' '+str(n)+' 1000'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + " cmd = 'julia '+abcd_path+'graph_sampler.jl net.dat comm.dat deg.dat cs.dat xi '+str(xi)+' false false'\n", + " os.system(cmd+' >/dev/null 2>&1')\n", + "\n", + " g = ig.Graph.Read_Ncol('net.dat',directed=False)\n", + " c = np.loadtxt('comm.dat',dtype='uint16',usecols=(1))\n", + " \n", + " ## ECG\n", + " gt = [c[int(i['name'])-1]-1 for i in g.vs]\n", + " g.vs['gt'] = gt\n", + "\n", + " ecg = g.community_ecg().membership\n", + " g.vs['ecg'] = ecg\n", + " \n", + " ## \n", + " z_ecg.append(g.modularity(ecg))\n", + " zz_ecg.append(sum([g.vs[e.tuple[0]]['ecg'] == g.vs[e.tuple[1]]['ecg'] for e in g.es])/g.ecount())\n", + " z_gt.append(g.modularity(gt))\n", + " zz_gt.append(sum([g.vs[e.tuple[0]]['gt'] == g.vs[e.tuple[1]]['gt'] for e in g.es])/g.ecount())\n", + " ami.append(AMI(g.vs['gt'] ,g.vs['ecg']))\n", + " ari.append(ARI(g.vs['gt'] ,g.vs['ecg']))\n", + "\n", + " q_gt.append(np.mean(z_gt))\n", + " Sq_gt.append(np.std(z_gt))\n", + " ec_gt.append(np.mean(zz_gt))\n", + " Sec_gt.append(np.std(zz_gt))\n", + " q_ecg.append(np.mean(z_ecg))\n", + " Sq_ecg.append(np.std(z_ecg))\n", + " ec_ecg.append(np.mean(zz_ecg))\n", + " Sec_ecg.append(np.std(zz_ecg))\n", + " sim_ari.append(np.mean(ari))\n", + " sim_ami.append(np.mean(ami))\n", + "\n", + "## optional - save results to local file\n", + "#pickle.dump( (q_gt,Sq_gt,ec_gt,Sec_gt,q_ecg,Sq_ecg,ec_ecg,Sec_ecg,sim_ari,sim_ami), \n", + "# open( \"./Data/q_xis_1000_both.pkl\", \"wb\" ) )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "e2d64144", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "## Figure 7 - ground truth\n", + "plt.figure(figsize=(10,7))\n", + "err = np.array([i for i in Sq_gt])\n", + "plt.plot(XI, q_gt, 'r-',label='Ground truth modularity')\n", + "plt.fill_between(XI, q_gt-err, q_gt+err, color='red', alpha=.2)\n", + "err = np.array([i for i in Sec_gt])\n", + "plt.plot(XI, ec_gt, 'b-',label='Edge contribution only')\n", + "plt.fill_between(XI, ec_gt-err, ec_gt+err, color='blue', alpha=.2)\n", + "plt.plot((.1,.9),(.9,.1),'k--',label='theoretical result')\n", + "plt.title(r\"$n$=1,000\", fontsize=18)\n", + "plt.xlabel(r\"$\\xi$\", fontsize=16)\n", + "plt.ylabel('Modularity', fontsize=16)\n", + "plt.legend();\n", + "#plt.savefig('q_xis_1000.pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "7b8fbe95", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "## Figure 8 - ECG\n", + "plt.figure(figsize=(10,7))\n", + "err = np.array([i for i in Sq_ecg])\n", + "plt.plot(XI, q_ecg, 'r-',label='ECG modularity')\n", + "plt.fill_between(XI, q_ecg-err, q_ecg+err, color='red', alpha=.2)\n", + "err = np.array([i for i in Sec_ecg])\n", + "plt.plot(XI, ec_ecg, 'b-',label='Edge contribution only')\n", + "plt.fill_between(XI, ec_ecg-err, ec_ecg+err, color='blue', alpha=.2)\n", + "plt.plot((.1,.9),(.9,.1),'k--',label='theoretical result')\n", + "plt.title(r\"$n$=1,000\", fontsize=18)\n", + "plt.xlabel(r\"$\\xi$\", fontsize=16)\n", + "plt.ylabel('Modularity', fontsize=16)\n", + "plt.legend();\n", + "#plt.savefig('q_xis_1000_ecg.pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "c0e5a180", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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zetCg8PU3WXfA738PH38csoZkrJycHDp16pTsMJJOzUqSsY45Bo49Nqze+vUv8qFJEzjjDPU/iKDkIBnurrtg0ya44i8t4ZFHYPZsuPbaZIclknRKDpLRunSB3/wmjGad1PhYGDkS/vpX+OCDZIcmklRKDpLxfvc7aN8+rKhRdOvtcPDBYSlmkQym5CAZr359uP320KL04FMN4MMPYeDAZIclklRKDiKE/ViOPDLMf1i9xqCoCP7yF3jppWSHJpIUSg4igFlYd+mHH+APfwCKi8PSGuedBytXJjs8kYRLeHIws4FmNt/MFpjZVWWUNzazV8xstpnNNbMRiY5RMlP37qHf4aGHYPrsHPjnP+Gnn+Ccc7Q4n2SchCYHM8sG7geOBroDw8yse4nbRgGfuXtPoB9wu5nlJjJOyVzXXQetWsGFF0LxHt3g1lvh9dfhwQeTHZpIQiW65tAbWODui9x9EzAWOL7EPQ40NDMDGgDfAoWJDVMyVePGoath6lR44glg1Cjo3x9++1v47rtkhyeSMIlODrsAy6LOCyLXot0HdANWAJ8Cl7h7cckHmdlIM5tuZtNXrVpVU/FKBho+HA45JCzW+v0PWfCPf8Abb4QZ1CIZItHJwcq4VrIxdwAwC2gL7AvcZ2aNSr3JfbS793L3Xi1btox3nJLBsrLgvvtg1Sq4/npgl13g0END4VdfJTM0kYRJdHIoANpHnbcj1BCijQBe9GABsBjYM0HxiQCw//5hsvS998KcOZGLTz0FXbvCtGlJjU0kERKdHKYBXc2sU6STeSgwvsQ9S4GjAMysNbAHsCihUYoAN90EjRrBxRdHBisNGgQ77xwW59MMaklzCU0O7l4IXAi8CcwDnnX3uWZ2vpmdH7ntRuBQM/sUmAhc6e6rExmnCEDz5iFBvPtumPJAkybw+OPwxRdhQSaRNKbNfkTKUVQEvXrB6tVhL6D69YHLL4c77oAJE+Doo5MdokiVlbfZj2ZIi5QjOzt0ThcUwM03Ry7edBP07h16rEXSlJKDSAX69AndDLfdBgsWAHl5MHky5OcnOzSRGqPkIFIJt94Kublw6aWRC1lZoZf6ySdh7NhkhiZSI5QcRCqhTZsw5+G11+DVVyMX3WH0aPjVrzT/QdKOkoNIJV10Eey5Z6g9bNhAqD088URIEvn5ofdaJE0oOYhUUm4u3HMPLFwYNgcCoGPHcPGDD+DOO5MZnkhcKTmIxKB/fxg8OAxYWro0cvHMM+HEE8NGEAUFSY1PJF6UHERidMcdoSXpiisiF8zCkt7PPAPt2iU1NpF4UXIQidGuu8LvfhdmTU+cGLnYsiWccEJ4/c03yQpNJG6UHESq4De/gU6dwrpLmzdHFbz9dsge77+ftNhE4kHJQaQK6tUL/c+ffRZmUG91yCGhaSk/H77/PmnxiVSXkoNIFR13HAwcGOY/fP115GKDBmFi3PLlcMklyQxPpFqUHESqyAzuvhvWr4errooqOOigMHLp8cfhhReSFp9IdSg5iFTD7rvDZZeFPDB5clTB1VfDwQfDl18mLTaR6tCS3SLV9OOPsMceYR+gjz4KK7kCoac6JyepsYmUR0t2i9SgBg3Ciq0zZsAjj0QV5OSECREffgiFhUmLT6QqlBxE4mDoUDjssDD/Yc2aqIK33oK+fcPGQCK1iJKDSByYwb33wnffwTXXRBUcdVRY0vXhh5MVmkiVVDo5mNl5Zla/JoMRqc169IBRo8JKGjNnRi7WqQNnnRXW+l6+PJnhicQklprDA8AKM7vfzHrUVEAitdkNN0CzZmF5761jPc4+G4qL4bHHkhmaSExiSQ5dgL8Bg4GZZjbZzM40s7yaCU2k9mnaFG65JfRBP/VU5OJuu8ERR8C4cckMTSQmMQ9lNbM6wInA+UA/4HvgcWC0u8+Ld4CVoaGskkqKi8MUh2XLYP58aNSIsL5369ZQt26ywxPZKq5DWd290N2fc/ejgD2AT4CLgTlm9r6ZDapeuCK1W1ZWWG/p66/hxhsjFzt0CIkhDeYVSWao0mglM2toZhcALwCHATOBPwB1gPFm9sf4hShS+/TuHboa7ror1B6AsGLrXnvB6tXJDE2kUmJKDmbWy8weAlYAtwGzgEPcvZe73+LufYDrgVHxDlSktrn55m37AAFhCvW8efDPfyY1LpHKiGUo68fAVOAI4I9AO3c/092nlrj1baBp/EIUqZ1at4Zjjw0d04WFwD77hEX5Hn5YzUuS8mKpOawAjgW6uvtf3f3bHdw3A+hU7chE0kB+ftgY7q23IhfOPTdsArHdKn0iqSeW5PBXYJKXMbzJzBqY2WEA7r7J3b+KV4Aitdkxx4R5D088EbkwdGhYjEkzpiXFxZIc3gW676Bsj0i5iETJzQ354OWXIxvDNWgQJkIMGZLs0ETKFUtysHLK6gJF1YxFJC3l58OGDfD885ELo0aFKoVICis3OZhZRzM70syOjFzqteU86hgEXA4srcwHmtlAM5tvZgvM7Kod3NPPzGaZ2Vwz007tUqv17h02BdratARhUtz99yctJpGK1Kmg/EzgOsAjx71sX4PwyHkhlRi+ambZwP1Af6AAmGZm4939s6h7mhCW6Rjo7kvNrFWlvxuRFGQGw4eH1VqXLIGOHQlLaVxyCfTpA/vum9T4RMpSUbPSY4Shq0cRksCFkfMtx5HAocDO7v5QJT6vN7DA3Re5+yZgLHB8iXtOA15096UA7v5N5b4VkdR1xhnh65NPRl2oW1cd05Kyyk0O7v6Vu7/v7u8RksGTkfPoY0o5w1pL2gVYFnVeELkWbXegqZm9Z2Yfm1l+JZ8tkrI6doTDDw9NS+6EIUwnnRSyxfr1yQ5PpJRKd0hHEsEP1fy8sjq1Sw6NrQMcAAwCBgDXmNnupR5kNtLMppvZ9FWrVlUzLJGal58PX34Z9pkG4LzzwhCmF15IalwiZamoQ3qRmfWMvF4cOd/RsbASn1cAtI86b0eYXFfynjfc/Sd3Xw18APQs+SB3Hx1ZtqNXy5YtK/HRIsk1ZAjk5UV1TB9+OHTvDosWJTUukbJU1CH9PrA26nV15/xPA7qaWSdgOTCU0McQ7WXgvsjS4LnAQcCd1fxckaRr1AhOOAHGjoU774TcXINZsyAnJ9mhiZRSbnJw9xFRr8+q7oe5e6GZXQi8CWQDj7r7XDM7P1L+gLvPM7M3CEuBFwMPu/uc6n62SCrIzw/JYcKEkCi2JobvvoMmTZIXmEgJldrsx8xygSnAVe7+VkX3J5o2+5HaorAQ2rWDQw+FF1+MXLz6anjoobA7UG5uUuOTzFLtzX4iw047EeYziEgV1akDp50Gr74Ka9ZELh5ySFid79VXkxqbSLRYls94G/hFTQUikiny82HzZnjmmciFgQNhl11C7UEkRcSSHO4FhpnZbWbW18y6mFnn6KOmghRJJz17wt57R+35k50dto17882wrIZICoglObxPGIZ6WeT1F8CXJQ4RqYBZqD1MmQJffBG5ePbZ4es//pG0uESiVTSUNdqIim8Rkco4/XS46qpQe7jxRsIU6uefh379khyZSFCp0UqpTqOVpDYaMCDUHBYuhKyYdnMXiY9qj1YSkfgbPjys0vrvf0ddHDs2LN8qkmSxNCsRWT57GGHnt7wSxe7u58QrMJF0d+KJUL9+WE7jsMMiF6dPh7vvhosuglZarV6Sp9I1BzPbA5gP3Aj8irAw3nDgLMKy20fUQHwiaat+/bDe0nPPRS3Mes45Yabc448nNTaRWJqV/gp8BLQmrK56NFAPOBdYB5wY9+hE0tzw4bB2LYwfH7nQrRv07Rv2eUiD/kCpvWJJDgcSdmjbuOW97l7o7o8S5kDcFefYRNJev35hOY3tthA999zQUz1pUrLCEokpOTQAvnX3YuB7oEVU2XRC8hCRGGRnh03h3nwT/vvfyMWTT4YjjoCioqTGJpktluSwBNg58no+cHJU2bHAd/EJSSSzDB8e8sCYMZELO+0E77wTEoRIksS6tlL/yOs7gBFmNt/M5gKXAI/GOziRTNC9OxxwQImmJYD//Q8+/TQpMYnEMpT1d0BdAHd/1szWA6cCOwF3A1o1TKSK8vPhkktgzpyw7hIAxx4LP/0EM2eGNTdEEiiWPaQ3uvvaqPNX3P0Mdx8c2bJTQytEqmjo0LCc99bF+CB0RsyeDTNmJC0uyVyaIS2SAlq1Cit3P/lkVD/0sGFQr56W8pakKLdZyczeieFZ7u5HVTMekYyVnx/2+3nnHejfn7Bt6Mknw9NPw+23h1lzIglSUc0hizDhrTKHaiEi1fDLX0LjxiWals47D374ASZOTFpckpnKrTm4e78ExSGS8fLy4JRT4Kmn4G9/gwYNgD59YP582H33ZIcnGUZ/7YukkPx8WLcOXnwxcsFMiUGSoqI+h8OAGe7+Y+R1udz9g7hFJpKB+vSBTp1C01J+fuSiezhp1w7+/OekxieZo6J5Du8BBxMW3HsP2NFwVYuUZccrMJFMZBZmTN94IxQUhHyAGWzcGEYtXX891K2b7DAlA1TUrHQE8FnU6yN3cGwpE5FqGj48VBaeeirq4rnnwpo1MG5cssKSDKNtQkVSUJ8+8N13Yca0GVBcDJ07Q9eu8PbbyQ5P0oS2CRWpZfLz4bPPwsoZQNhk+uyz4V//gkWLkhqbZIZKr61kZlnASMJqrO0pe5vQXeMYm0jGOuUUuPjisBjf/vtHLo4YAZs2aTKcJESlm5XM7DbgMmAm8DmwqeQ97j4irtFVkpqVJB0NGQIffADLl0NOTrKjkXRUXrNSLKuyngHc6O7XxScsESlPfj688AK89RYMGhS5WFQEEyaExZgOOiip8Ul6i6XPoQ6geQwiCTJwIDRvXmKfh+LisKTGzTcnLS7JDLEkh+eBATUViIhsLzc3LMz68sth5BIQ2pdGjIDXXoMVK5IZnqS5WJLDZUBXMxttZieZ2ZElj8o8xMwGRnaQW2BmV5Vz34FmVmRmQ2KIUSSt5OeH+W/PPx918eyzQ/PSY48lKyzJALF0SHcBXgT2KVHkRGZIu3u5M6TNLBv4grDdaAEwDRjm7p+Vcd/bwAbgUXd/vuSzoqlDWtKVO3TrFroYPohu1D3iCFi6FL78MgxzFamCeM1z+AfQgrBf9ADCrOgtM6MrO0O6N7DA3Re5+yZgLHB8GfddBLwAfBNDfCJpxyzUHiZNgsWLowrOPTf0PxQUJC02SW+xJIdewCXufq+7v+3u75c8KvGMXYBlUecFkWtbmdkuwInAA+U9yMxGmtl0M5u+atWqGL4NkdrljDPC1yefjLp46qmwcCF06JCUmCT9xZIcllLG3IYYlbVLesl2rbuAK929qIx7t70p7Fvdy917tWzZspphiaSuDh1CK9ITT4RmJiBsOJ2VFSbFrV+f1PgkPcWSHP4EXGlmDarxeQWE2dVbtANKDrnoBYw1syXAEOBvZnZCNT5TpNYbPhwWLIApU6IurloVlm198MGkxSXpK5bkMIDwy3yJmb1iZk+UOB6vxDOmEUY8dTKzXGAoMD76Bnfv5O4d3b0jYfjsBe4+LoY4RdLOSSdBvXolthBt2TJs/vDww1FVCpH4iCU59AWKgR+AvYGflXGUy90LgQuBN4F5wLPuPtfMzjez82OMXSRjNGoEJ54IY8eGoa1bnXsuzJ0LU6cmLTZJT1qyW6SWeOMNOProsKTG4MGRiz/8AG3ahA7qRx5JanxS+2jJbpE08POfw847l1hOo2FDGDo0VCnWrk1abJJ+KtpDugOw0t03R16Xy92Xxi0yEdlOnTpw+ulwzz2wejW0aBEpuOKKMBmiYcOkxifppaKaw2Jgv8jrJZHz8g4RqUHDh8PmzfDMM1EX99wTDjsssmWcSHxUtGT32cDCqNe1v4NCpBbr2RN69AhNS6NGRRV8/TXcdBOMHAn7lFzhRiR25SYHd3886vVjNR6NiFQoPz+0JM2fD3vsEbmYkwOjR4fawz33JDU+SQ9V7pA2s8Zm1svM2sUzIBEp32mnhcnR2815aN48TIb45z81Y1riotzkYGYDzOyWMq7/nrAo3lTgKzN72sxi2VVORKqoTRvo3z/kgeLiqIJzzw0bP7z4YrJCkzRSUc3hfGD36Atm1p+wlMbnwKXAg8CphNVaRSQB8vPDit2TJkVd7NcPOncOM6ZFqqmi5LAf8FqJayMI+ywMiKzQegEhQZxWA/GJSBlOOAEaNCgx5yErCy6+GLp2hcLCZIUmaaKi5NCKbaOVtugP/Nvdv4669holahgiUnN22gmGDIHnnoN166IKLrkkdEzXUSuvVE9FyeEHoP6WEzPrCjQHppS4by1Q7i5wIhJf+flh9Yzx40sUuMNHH4UJESJVVFFy+Jztd2o7njDX4a0S93UC/hvHuESkAocfDu3bl2haAnjnHTjoIHj11aTEJemhouRwJ3CumT1vZvcDNwCfAh+WuO9EYHYNxCciO5CVFXaJe/PNMAduq8MPh7Zt1TEt1VJucojso3ApcCCQT2hOOtmjlnKNzHM4AphQY1GKSJmGDw/DWZ9+OupinTpw9tlhGddly3b4XpHyVDgJzt3vcfdd3b2hux/l7l+WKC9w9ybuPrrmwhSRsnTrBgceWGJCHITkUFwM//hHUuKS2k9LdovUcsOHw6xZ8MknURc7dQoz5TQhTqpIyUGklhs6NLQklao9PPQQTJ6clJik9lNyEKnlWraEY46Bp56CoqKogl13DRtPi1SBkoNIGsjPh5UrYeLEEgXvvRfW+P7mm2SEJbWYkoNIGjj2WGjSpIw5D61awaefltHmJFI+JQeRNFC3Lpx6Krz0Upg1vVX37nDooaH/wbVXl1SekoNImsjPD+sslRqgdN55YWegD0vOXRXZMSUHkTRxyCHQpUsZTUsnnwyNGoXag0glKTmIpAmzMOfh3XdLTIyuXx9uvhkGD05abFL7KDmIpJHhw0PXwlNPlSgYNQqOP77M94iURclBJI107gx9+oSmpVL9z8uXwwMPJCUuqX2UHETSTH4+zJsHH39couDll+HXv4YZM5ISl9QuSg4iaebkk8PQ1lJTG047DfLy1DEtlaLkIJJmmjaF444Ly3hvtxlckyYhczz9NPz0U7LCk1pCyUEkDQ0fDqtXhy0dtnPeebB2LTz/fFLiktpDyUEkDQ0cCC1alNG01LdvmDX9xRdJiUtqj4QnBzMbaGbzzWyBmV1VRvnpZvZJ5PiPmfVMdIwitV1OTuhiGD8e/ve/qAIzmDkTbropabFJ7ZDQ5GBm2cD9wNFAd2CYmXUvcdti4HB37wHcCGiHOZEqGD4cNm6E554rUZCbG74++CA89pjWXJIyJbrm0BtY4O6L3H0TMBbYbmaOu//H3bf8rTMFaJfgGEXSwgEHhG1Ey1yQ1T0swjRiBAwZEjooRKIkOjnsAkRP7C+IXNuRc4DXyyows5FmNt3Mpq9atSqOIYqkB7Mw5+Hf/4aFC8sonDAB/vIXeOUV2GefMnqvJZMlOjlYGdfKrNOa2RGE5HBlWeXuPtrde7l7r5YtW8YxRJH0cfrpIQ88+WQZhdnZ8NvfwrRp0Lw5DBoECxYkPEZJTYlODgVA+6jzdsCKkjeZWQ/gYeB4d1+ToNhE0k779nDEEaFpaYddCz17wvTpMG4c7LZbuLZyZaJClBSV6OQwDehqZp3MLBcYCoyPvsHMOgAvAsPdXePtRKopPz80K02eXM5NeXnwy1+G1//+N3TsCDfeCIWFiQhRUlBCk4O7FwIXAm8C84Bn3X2umZ1vZudHbrsWaA78zcxmmdn0RMYokm4GD4addipjn4cd2WsvOOkkuPZaOOywMjosJBOYp8Ewtl69evn06cohIjtyxhnw2muhtSgvr5JvGjMmLNRXWAj33QdnnVWTIUoSmNnH7t6rrDLNkBbJAPn58N13IUFU2rBh8Omn0Ls3rFHXX6apk+wARKTmHXUUtGkTmpZOOimGN7ZvD//617bz8ePDKKdBg+Ieo6QW1RxEMkB2dhjWOmECxDwtKCsrHO5w111w7LFw/vla2TXNKTmIZIj8/NB98MwzVXyAGbz+OvzmNzB6NOy7L0ydGs8QJYUoOYhkiH32Cb/PKz1qqSx168Ktt8I778CmTWFP0jlz4hWipBAlB5EMMnx4mBD9+efVfFC/fvDJJ3DvvbD33uGampnSipKDSAY57bTQfVDmYnyxatw4DHWFsGn1rrvCAw9oldc0oeQgkkF23hkGDAjJobg4jg9u3Bj23z8ki1/+Er7+Oo4Pl2RQchDJMPn5sGxZGHgUt9Ux2rYNq7refTdMnBg6OMaNi9PDJRmUHEQyzPHHw89+BpdfHnYMHTs2TrWIrCy4+GL4+OMwP+L99+PwUEkWJQeRDFOvXvi9PW5cWEpj2DDYb78wvy0u3QXdu8OUKXDLLeF86lT4z3/i8GBJJCUHkQxkFmoQs2bB00/D+vXh/OCDw4ToaieJ3Nww7BXgD38IVZWrr4bNm6sbuiSIkoNIBsvKCjWHzz6Dhx8OC/P17x/2gPjwwzh9yIsvwplnwk03wSGHxGEcrSSCkoOIUKcOnHMOfPkl3HNP+P3dt29YQmnmzGo+vFEjePRReOEFWLIktGFV+6FS05QcRGSrunXhoovCFg633BI2CNp/fzj55DCVoVoGDw6rvF52GfToEa4VFVU7ZqkZSg4iUkr9+nDllbB4cdjz5403wkToM8+ERYuq8eA2bULzUnZ2mAux116hRiEpR8lBRHaocWO44YaQJC67DJ59FvbYI8x1W768mg9ftw4aNoQhQ8JGQmvXxiNkiRMlBxGpUIsW8Ne/huamkSPhkUdgt93CXImYlwDfonPnMMT1mmvClO0ePWDSpLjGLVWn5CAilda2Ldx/P8yfD0OHhlnWnTuH3+/ffVeFB+bkwB//GIZG1akTHg5hxdcXXoAVK+IYvcRCe0iLSJV9/jlcd11obmrSBH7729Ch3aBBFR72449hPY8mTcLEuYMPDtc7dAhDYA85JGxj165dHL+DzKY9pEWkRuy5Z9g8aObMMPT197+HLl3CEksbNsT4sAYNQmKAMNx1yhS480446KBQs7j0UliwIJRPnhwy0UsvaZG/GqKag4jEzeTJYUL0u++GP/CvvTb0NefkxOHhBQXQsmUYb/vAA3DJJaH5CaBjx1Cz+NvftiUYqZBqDiKSEIccEjaJmzgxJIeRI6FbN3jqqThMaWjXbtuSHOefH0Y3TZ4Md9wBBx4Is2eHCXcQhlb97GeqXVSDkoOIxN2RR4aBSK+8EuZMnHEG9OwZfk/HrbGibt3QL/F//xc6PebODeuBQEgkmzeHHvPBg8P8in79tr138WKt81QBJQcRqRFmcOyxoT9i7Njwu3jwYOjdG958s4Y3jLvsstBnsXZt6K+47TY48cRQ5h46SBo3hsMPh6uugpdfrsaY3PSkPgcRSYjCwjCd4YYb4KuvQqvPTTeFrwlVXAzPPReapP7zn5C9CgvDMKt77gmvH3oo1Er22ScMsU1T5fU5KDmISEJt3BhWgP3Tn0JXwIAB4XWvMn9FJcD69WGDombNwl4Us2aF0VIQ2sQOPDB0ppx1Fuy+e5jZ/eOPYWZgVu1ufFGHtIikjLp1YdSoMNv61lth2rTw+3fw4NBtkHD16oVmpu7dw3nPnmH12DFj4OyzQyLYMj0cwoYXrVuHb6R9+zDU9oQTtq1MuGQJvPZaqJF8/XWtXVxQNQcRSaq1a8N0httvhx9+CL93W7TYdjRvXv55w4ahf6NGbdwYPiQ3NySJCRPC7O2VK8OxYkXoFO/WLczyvvDCbe/Nzg7f1KRJYTr5u++Grfjatg0d5W3ahNc775zwmoialUQk5a1ZA6NHh4FEq1eH89Wrt73e0R/gOTkVJ5CS1xo0qMGE8u238MUX2yeOlStDBmzUCG68MUwAKen770P5vfeGHvvoxNGmDRx3XAjaPW7Bp1RyMLOBwN1ANvCwu99Sotwi5ccA64Cz3H1Gec9UchBJb8XF4XdndMIomUBKXluzJry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xigtecgamiari
00.10.8037560.8037561.0000001.000000
10.20.7124900.7123920.9997010.999663
20.30.6236550.6234090.9985430.998586
30.40.5269940.5235960.9732880.971992
40.50.4445320.4166060.6976920.647980
50.60.3546750.3098860.2084490.123891
60.70.2632950.2816140.0744780.024235
70.80.1758090.2820670.0317310.009415
80.90.0876450.2799590.0127210.003412
\n", + "
" + ], + "text/plain": [ + " xi gt ecg ami ari\n", + "0 0.1 0.803756 0.803756 1.000000 1.000000\n", + "1 0.2 0.712490 0.712392 0.999701 0.999663\n", + "2 0.3 0.623655 0.623409 0.998543 0.998586\n", + "3 0.4 0.526994 0.523596 0.973288 0.971992\n", + "4 0.5 0.444532 0.416606 0.697692 0.647980\n", + "5 0.6 0.354675 0.309886 0.208449 0.123891\n", + "6 0.7 0.263295 0.281614 0.074478 0.024235\n", + "7 0.8 0.175809 0.282067 0.031731 0.009415\n", + "8 0.9 0.087645 0.279959 0.012721 0.003412" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## Table 2\n", + "df = pd.DataFrame(np.array([XI,q_gt,q_ecg,sim_ami,sim_ari]).transpose(),columns=['xi','gt','ecg','ami','ari'])\n", + "df" + ] + }, + { + "cell_type": "markdown", + "id": "10153170", + "metadata": {}, + "source": [ + "## Results for (19), (20)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "f79b27c5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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deltabestab
0500.00340377
1600.00709078
2700.01075088
3800.015538711
4900.019448811
51000.021706812
61100.023731813
71200.025561814
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" + ], + "text/plain": [ + " delta best a b\n", + "0 50 0.003403 7 7\n", + "1 60 0.007090 7 8\n", + "2 70 0.010750 8 8\n", + "3 80 0.015538 7 11\n", + "4 90 0.019448 8 11\n", + "5 100 0.021706 8 12\n", + "6 110 0.023731 8 13\n", + "7 120 0.025561 8 14" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D[D['delta']<=120]" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [conda env:graphmining]", + "language": "python", + "name": "conda-env-graphmining-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}