0-Spectral-Background.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NzkdmHfHBSwa"
   },
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ellisalicante/GraphRewiring-Tutorial/blob/main/0-Spectral-Background.ipynb).\n",
    "\n",
    "# Introduction to Spectral Theory: Graph Laplacian and its eigenfunctions, Dirichlet energies, Heat Kernels and Commute Times\n",
    "***Tutorial on Graph Rewiring: From Theory to Applications in Fairness***\n",
    "\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ellisalicante/GraphRewiring-Tutorial/blob/main/0-Spectral-Background.ipynb).\n",
    "\n",
    "Francisco Escolano, ELLIS Alicante UNIT "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "COLLAB_ENV = False\n",
    "if COLLAB_ENV:\n",
    "    !pip install 'scipy>=1.8'\n",
    "    !pip install mycolorpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nRbn5mNmBoI6"
   },
   "source": [
    "## The Graph Laplacian and its Eigenfunctions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "\n",
    "from scipy.linalg import fractional_matrix_power\n",
    "from scipy.spatial.distance import pdist\n",
    "from scipy.spatial.distance import squareform\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as matplotlib\n",
    "import matplotlib.cm as cm\n",
    "from mycolorpy import colorlist as mcp\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some utils for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the k-th Laplacian Eigenvalue on the Graph\n",
    "def plot_eigenvector_over_graph(G,evecs,k, seed=63):\n",
    "  # Extract eigenvector from the evecs matrix and transform into dim (n,)\n",
    "  u = np.array(np.real(evecs[:,k]))\n",
    "  u = np.squeeze(np.transpose(u))\n",
    "  v = u + 100 #avoid negatives for plotting colors properly\n",
    "  # Create the color map \n",
    "  vColor =mcp.gen_color_normalized(cmap=\"seismic\",data_arr=v)\n",
    "  pos = nx.spring_layout(G,seed=seed)  # Seed layout for reproducibility\n",
    "  # Draw the graph\n",
    "  fig, ax = plt.subplots(figsize=(5,5))\n",
    "  nx.draw(G, pos, node_color=vColor, node_size=300, cmap=plt.cm.Blues, ax=ax)\n",
    "\n",
    "  sm = plt.cm.ScalarMappable(cmap=\"seismic\", norm=plt.Normalize(vmin=u.min(), vmax=u.max()))\n",
    "  sm.set_array([])\n",
    "  cbar = plt.colorbar(sm)\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Create a synthetic graph using given probabilities**\n",
    "\n",
    "Have you ever wondered hot the eigenfunctions change when you change the topology of the graph?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "8b_GlfkdLtQ5",
    "outputId": "c3653791-8f4b-46cb-db78-f82b21236c9c"
   },
   "outputs": [],
   "source": [
    "# Create Synthetic graph\n",
    "sizes = [10, 10]\n",
    "gap_prob = 0.05\n",
    "probs = [[0.75, gap_prob], [gap_prob, 0.75]]\n",
    "G = nx.stochastic_block_model(sizes, probs, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#nodes_in_coms = 10\n",
    "#nodes_in_bottleneck = 2\n",
    "#G = nx.barbell_graph(nodes_in_coms,nodes_in_bottleneck)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "- Number of edges: 64\n"
     ]
    }
   ],
   "source": [
    "A = nx.adjacency_matrix(G)\n",
    "L = nx.laplacian_matrix(G)\n",
    "#L = nx.normalized_laplacian_matrix(G)\n",
    "print(f\"\"\"- Number of edges: {G.size()}\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Finding Eigenvalues and Eigenvectors**\n",
    "\n",
    "$$\\mathbf{AX}=\\mathbf{A\\Lambda}$$\n",
    "where $\\textrm{diag}(\\Lambda) = [\\lambda_1(A),\\dots,\\lambda_n(A)]$ an 0's elsewhere.\n",
    "\n",
    "We find Eigenvectors and Eigenvalues. Then we order them so $0=\\lambda^\\downarrow_1(A)\\leq\\lambda^\\downarrow_2(A)\\leq\\dots\\leq\\lambda^\\downarrow_n(A)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "- Shape eigenvalues: (20,) [n]\n",
      "- Shape eigenvectors:(20, 20) [n,n]\n"
     ]
    }
   ],
   "source": [
    "e, evecs = np.linalg.eig(L.todense())\n",
    "print(f'''- Shape eigenvalues: {e.shape} [n]\n",
    "- Shape eigenvectors:{evecs.shape} [n,n]''')\n",
    "\n",
    "# Sort them (both e's and evecs's) ascending\n",
    "idx =e.argsort()\n",
    "e = e[idx]\n",
    "evecs = evecs[:,idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot value of eigenvectors on the graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_printed_evecs = G.number_of_nodes()\n",
    "n_printed_evecs = 5\n",
    "for k in range(n_printed_evecs):\n",
    "  plot_eigenvector_over_graph(G,evecs,k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 267
    },
    "id": "PHskjD9AAtMk",
    "outputId": "f8469981-a81c-4505-ad8a-5a36582b1c6e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_eigenvalues(input_list):  \n",
    "  x = range(len(input_list))\n",
    "  y = np.asarray(input_list)\n",
    "  plt.plot(x,y, 'r')\n",
    "  # show the plot\n",
    "  plt.show()\n",
    "plot_eigenvalues(list(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KZbjI2laB2JC"
   },
   "source": [
    "## 2. The Dirichlet Integral for Semi-Supervised Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the labels of uB and uD on the Graph\n",
    "def plot_Dirichlet_labels_over_graph(G,idxB,idxD,uB,uD):\n",
    "  u = np.zeros(G.number_of_nodes())\n",
    "  # Store the values in uB and then uD\n",
    "  for i in range(uB.shape[0]):\n",
    "    u[idxB[i]]=uB[i]*100\n",
    "    print(u[idxB[i]])\n",
    "  for j in range(uD.shape[1]):\n",
    "    u[idxD[j]]=uD[0,j]*100\n",
    "  print('u is',u)\n",
    "  print('uD[0,:]', uD[0,:])\n",
    "  # Create the color map \n",
    "  vColor =mcp.gen_color_normalized(cmap=\"seismic\",data_arr=u)\n",
    "  pos = nx.spring_layout(G,seed=63)\n",
    "  # Draw the graph\n",
    "  nx.draw(G, pos, node_color=vColor, node_size=800, cmap=plt.cm.Blues)\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "SHWU3_9qliCD",
    "outputId": "2335c7f5-c87e-4bc1-a1e3-50cf4a47b250"
   },
   "outputs": [],
   "source": [
    "# Dirichlet Integral and Random Walker\n",
    "idxAll = set(range(G.number_of_nodes()))\n",
    "idxB = set([0, 19])\n",
    "idxD = set([x for x in idxAll if x not in idxB])\n",
    "print(idxAll)\n",
    "\n",
    "idxB = np.array(list(idxB))\n",
    "idxD = np.array(list(idxD))\n",
    "print(idxB)\n",
    "print(idxD)\n",
    "Ldense = L.todense()\n",
    "print(Ldense)\n",
    "LdenseD = Ldense[idxD,:]\n",
    "LdenseD = LdenseD[:,idxD]\n",
    "print(LdenseD)\n",
    "\n",
    "print(idxD.shape[0])\n",
    "print(idxB.shape[0])\n",
    "print(np.zeros((2,2)))\n",
    "Bdense = np.zeros((idxB.shape[0],idxD.shape[0]))\n",
    "print(Ldense.shape)\n",
    "Bdense = Ldense[idxB,:]\n",
    "Bdense = Bdense[:,idxD]\n",
    "print(Bdense)\n",
    "\n",
    "Inv = np.matmul(np.linalg.inv(LdenseD),-np.transpose(Bdense))\n",
    "print(\"inv\",Inv)\n",
    "uB = np.array([1,0])\n",
    "uD = np.matmul(Inv,np.transpose(uB))\n",
    "print(uD)\n",
    "print(uD.shape)\n",
    "plot_Dirichlet_labels_over_graph(G,idxB,idxD,uB,uD)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "esJ69JSLB9xW"
   },
   "source": [
    "## 3. Heat Kernels and Graph Diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "4Cv_l7mVilzK",
    "outputId": "e16a2f0a-d3e8-4d70-8b43-5529b546637b"
   },
   "outputs": [],
   "source": [
    "# Heat Kernels\n",
    "def heat_kernel(G,e, evecs,beta):\n",
    "  n = G.number_of_nodes()\n",
    "  H = np.zeros((n,n))\n",
    "  Phi = evecs\n",
    "  Lambda = np.diag(np.exp(-beta*e))\n",
    "  H = np.matmul(Phi,Lambda)\n",
    "  H = np.matmul(H,np.transpose(Phi))\n",
    "  return H\n",
    "\n",
    "# Plot the beta-th Heat Kernel on the Graph\n",
    "def plot_beta_heat_kernel_over_graph(G,e,evecs,beta):\n",
    "  # Extract the heat kernel\n",
    "  H = heat_kernel(G,e,evecs,beta)\n",
    "  # From the heat kernel extract the colors of the edges\n",
    "  E = G.edges()\n",
    "  u = np.zeros(G.number_of_edges())\n",
    "  k = 0 \n",
    "  for e in E: \n",
    "    i = e[0]\n",
    "    j = e[1]\n",
    "    u[k] = H[i,j]*100 \n",
    "    k = k + 1\n",
    "  # And also those of the nodes\n",
    "  V = G.nodes()\n",
    "  n = np.zeros(G.number_of_nodes())\n",
    "  l = 0\n",
    "  for v in V: \n",
    "    n[l] = H[l,l]*100\n",
    "    l = l + 1    \n",
    "  # Create the color maps \n",
    "  eColor =mcp.gen_color_normalized(cmap=\"seismic\",data_arr=u)\n",
    "  nColor =mcp.gen_color_normalized(cmap=\"seismic\",data_arr=n)\n",
    "  pos = nx.spring_layout(G,seed=63)\n",
    "  options = {\n",
    "    \"node_color\": nColor, #\"#A0CBE2\",\n",
    "    \"edge_color\": eColor,\n",
    "    \"width\": 4,\n",
    "    \"edge_cmap\": plt.cm.Blues,\n",
    "    \"with_labels\": False,\n",
    "  }\n",
    "  # Draw the graph\n",
    "  nx.draw(G, pos, **options)\n",
    "  plt.show()\n",
    "\"\"\"\n",
    "H1 = heat_kernel(G,e,evecs,beta=1)\n",
    "print(H1.shape)\n",
    "plt.imshow(H1*(A.todense()), alpha=0.8, cmap=\"seismic\")\n",
    "print(A.todense())\n",
    "#plt.imshow(np.diag(e), alpha=0.8, cmap=\"seismic\") \n",
    "\"\"\"\n",
    "\n",
    "# Plot the beta-th Heat Kernel on the Graph\n",
    "def plot_beta_heat_kernel_trace(G,e,evecs,node, color):\n",
    "  HKS_list = []\n",
    "  betar = 0.001\n",
    "  beta = 0\n",
    "  for k in range(1000):\n",
    "     H = heat_kernel(G,e,evecs,beta)\n",
    "     HKS_list.append(H[node,node])\n",
    "     beta = beta + betar\n",
    "  x = range(len(HKS_list))\n",
    "  y = np.asarray(HKS_list)\n",
    "  plt.plot(x,y, color)\n",
    "  # show the plot\n",
    "  plt.show()\n",
    "\n",
    "\n",
    "plot_beta_heat_kernel_over_graph(G,e,evecs,beta=0.01)\n",
    "plot_beta_heat_kernel_over_graph(G,e,evecs,beta=0.1)\n",
    "plot_beta_heat_kernel_over_graph(G,e,evecs,beta=0.5)\n",
    "plot_beta_heat_kernel_over_graph(G,e,evecs,beta=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "WuyY6Adg81dK",
    "outputId": "c64bb6a3-527c-4686-a46d-77166dfebdc3"
   },
   "outputs": [],
   "source": [
    "# Plot HKS: a node inside a community looses slowly its heat\n",
    "plot_beta_heat_kernel_trace(G,e,evecs,node=1,color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "8XJ3m6rM-eAb",
    "outputId": "d1c837c1-47a6-4296-e24c-f32c6dd76de8"
   },
   "outputs": [],
   "source": [
    "# Plot HKS: a node in between communities looses its heat faster\n",
    "plot_beta_heat_kernel_trace(G,e,evecs,node=10, color='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "H3Tm1c8jCNq5"
   },
   "source": [
    "## 4. Commute Times and their Embedding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "qbsYP0pa1-Nw",
    "outputId": "67989355-dd2c-4e7e-b648-8629e07468a2"
   },
   "outputs": [],
   "source": [
    "# Commute Times Embedding\n",
    "def graph_vol(G):\n",
    "  A = nx.adjacency_matrix(G)\n",
    "  D = A.sum(axis=1)\n",
    "  D = D.squeeze()\n",
    "  d = np.zeros(G.number_of_nodes())\n",
    "  for i in range(G.number_of_nodes()):\n",
    "    d[i] = D[0,i]\n",
    "  vol = d.sum()\n",
    "  return vol\n",
    "\n",
    "def commute_times_embedding(G,e, evecs):\n",
    "  n = G.number_of_nodes()\n",
    "  vol = graph_vol(G)\n",
    "  A = nx.adjacency_matrix(G)\n",
    "  D = A.sum(axis=1)\n",
    "  Phi = evecs\n",
    "  Lambda = np.diag(e)\n",
    "  Lambda = fractional_matrix_power(Lambda, -0.5)\n",
    "  Lambda[0,0] = 0\n",
    "  CTE = np.sqrt(vol)*np.matmul(Lambda,np.transpose(Phi))\n",
    "  # Embedding is in the columns\n",
    "  return CTE\n",
    "\n",
    "# Plot the CT distance on the Graph\n",
    "def plot_commute_times_over_graph(G,e,evecs):\n",
    "  # Extract the embedding\n",
    "  CTE = commute_times_embedding(G,e, evecs)\n",
    "  # Embedding is in the columns and we move it to the rows\n",
    "  CT = pdist(np.transpose(CTE), 'euclidean')\n",
    "  CT = squareform(CT)\n",
    "  # From the commute times extract the colors of the edges\n",
    "  E = G.edges()\n",
    "  u = np.zeros(G.number_of_edges())\n",
    "  k = 0 \n",
    "  for e in E: \n",
    "    i = e[0]\n",
    "    j = e[1]\n",
    "    u[k] = CT[i,j]*100 \n",
    "    k = k + 1   \n",
    "  # Create the color map\n",
    "  eColor =mcp.gen_color_normalized(cmap=\"seismic\",data_arr=u)\n",
    "  pos = nx.spring_layout(G,seed=63)\n",
    "  options = {\n",
    "    \"node_color\": \"#A0CBE2\",\n",
    "    \"edge_color\": eColor,\n",
    "    \"width\": 4,\n",
    "    \"edge_cmap\": plt.cm.Blues,\n",
    "    \"with_labels\": False,\n",
    "  }\n",
    "  # Draw the graph\n",
    "  nx.draw(G, pos, **options)\n",
    "  plt.show()\n",
    "\n",
    "plot_commute_times_over_graph(G,e,evecs)\n",
    "\n",
    "CTE = commute_times_embedding(G,e, evecs)\n",
    "CT = pdist(np.transpose(CTE), 'euclidean')\n",
    "CT = squareform(CT)\n",
    "plt.imshow(CT, alpha=0.8, cmap=\"seismic\")\n",
    "#plt.imshow(CTE[:3,:], alpha=0.8, cmap=\"seismic\")\n",
    "print(CTE[:3,:])\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "xs1 = CTE[0,:10] \n",
    "ys1 = CTE[1,:10]\n",
    "zs1 = CTE[2,:10]\n",
    "ax.scatter(xs1,ys1,zs1, marker=\"x\", c=\"red\")\n",
    "xs2 = CTE[0,11:20] \n",
    "ys2 = CTE[1,11:20]\n",
    "zs2 = CTE[2,11:20]\n",
    "ax.scatter(xs2,ys2,zs2, marker=\"o\", c=\"blue\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "H6xN_F7Cew3J",
    "outputId": "448c7b30-2386-4c3e-c5cd-bd60b0a57482"
   },
   "outputs": [],
   "source": [
    "# Commute Times as an optimzation problem \n",
    "NL = nx.normalized_laplacian_matrix(G)\n",
    "NLdense = NL.todense()\n",
    "plt.imshow(NLdense, alpha=0.8, cmap=\"seismic\")\n",
    "# Finding eigen values and eigen vectors\n",
    "eNL, evecsNL = np.linalg.eig(NLdense)\n",
    "# Sort them (both e's and evecs's) ascending\n",
    "idx =eNL.argsort()\n",
    "eNL = eNL[idx]\n",
    "evecsNL = evecsNL[:,idx]\n",
    "print(eNL.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "bpRB7atwJ9Zi",
    "outputId": "6f2ae219-dad2-428b-d358-a43497121bda"
   },
   "outputs": [],
   "source": [
    "# Let Z be the CT Embedding\n",
    "# Initialize (first row with Zeros)\n",
    "n = nx.number_of_nodes(G)\n",
    "Z = np.zeros((1,3))\n",
    "# Deterministic initialization\n",
    "Z = np.concatenate((Z,np.ones((n-1,3))),axis = 0)\n",
    "# Random initialization\n",
    "Z = np.random.rand(n,3)\n",
    "plt.imshow(Z, alpha=0.8, cmap=\"seismic\")\n",
    "\n",
    "def optimizing_commute_times_cost_function(Z,NLdense, lambdaReg):\n",
    "  return np.trace(np.matmul(np.matmul(np.transpose(Z),NLdense),Z)) + lambdaReg*np.linalg.norm(np.matmul(np.transpose(Z),Z)-np.eye(Z.shape[1])) #+ lambdaReg*np.linalg.norm(np.matmul(Z,np.transpose(Z))-np.eye(Z.shape[0]))\n",
    "\n",
    "mu = 0.01\n",
    "lambdaReg =0.1\n",
    "cost_list=[]\n",
    "embedding_list = []\n",
    "embedding_list.append(Z)\n",
    "maxiter = 1000\n",
    "for i in range(maxiter):\n",
    "  grad = 2*np.matmul(NLdense,Z) + lambdaReg*4*np.matmul(Z,np.matmul(np.transpose(Z),Z)-np.eye(Z.shape[1]))  #+ lambdaReg*4*np.matmul(np.transpose(Z),np.matmul(Z,np.transpose(Z))-np.eye(Z.shape[0]))\n",
    "  Z = Z - mu*grad\n",
    "  cost_list.append(optimizing_commute_times_cost_function(Z,NLdense,lambdaReg))\n",
    "  embedding_list.append(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "Ic7G5fYtvc99",
    "outputId": "cf01c1d0-cdc6-4f0c-8502-a486d2634788"
   },
   "outputs": [],
   "source": [
    "plt.imshow(Z, alpha=0.8, cmap=\"seismic\")\n",
    "#plot_commute_times_over_graph(G,eNL,evecsNL)\n",
    "print('regularization cost', np.linalg.norm(np.eye(Z.shape[1])-np.matmul(np.transpose(Z),Z)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "OzT457JMS-90",
    "outputId": "7d13efd5-67c3-4ba1-ea8d-7086198b6946"
   },
   "outputs": [],
   "source": [
    "# plot the function\n",
    "x = range(maxiter)\n",
    "y = np.asarray(cost_list)\n",
    "plt.plot(x,y, 'r')\n",
    "\n",
    "# show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 837
    },
    "id": "NCyqqwnlPgNY",
    "outputId": "ab9c4cb8-1125-4e95-fb02-22300d291056"
   },
   "outputs": [],
   "source": [
    "CTZ = pdist(Z, 'euclidean')\n",
    "CTZ = squareform(CTZ)\n",
    "plt.imshow(CTZ, alpha=0.8, cmap=\"seismic\")\n",
    "\n",
    "def plot_optimized_commute_time_embedding(Z):\n",
    "  from mpl_toolkits.mplot3d import Axes3D\n",
    "  fig = plt.figure(figsize=(5,5))\n",
    "  ax = fig.add_subplot(111, projection='3d')\n",
    "  xs1 = Z[:10, 0] \n",
    "  ys1 = Z[:10, 1]\n",
    "  zs1 = Z[:10, 2]\n",
    "  ax.scatter(xs1,ys1,zs1, marker=\"x\", c=\"red\")\n",
    "  xs2 = Z[11:20, 0] \n",
    "  ys2 = Z[11:20, 1]\n",
    "  zs2 = Z[11:20, 2]\n",
    "  ax.scatter(xs2,ys2,zs2, marker=\"o\", c=\"blue\")\n",
    "  plt.show()\n",
    "\n",
    "# After First iteration\n",
    "plot_optimized_commute_time_embedding(embedding_list[0])\n",
    "# Finally...\n",
    "plot_optimized_commute_time_embedding(Z) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 319
    },
    "id": "52hbxINZszkf",
    "outputId": "76729153-33e4-413c-fbb4-3162a780cef1"
   },
   "outputs": [],
   "source": [
    "# Plot the optimized CT distance on the Graph\n",
    "def plot_optimized_commute_times_over_graph(G,Z):\n",
    "  # Embedding is given by Z\n",
    "  # Embedding is in the columns and we move it to the rows\n",
    "  CT = pdist(Z, 'euclidean')\n",
    "  CT = squareform(CT)\n",
    "  # From the commute times extract the colors of the edges\n",
    "  E = G.edges()\n",
    "  u = np.zeros(G.number_of_edges())\n",
    "  k = 0 \n",
    "  for e in E: \n",
    "    i = e[0]\n",
    "    j = e[1]\n",
    "    u[k] = CT[i,j]*100 \n",
    "    k = k + 1   \n",
    "  # Create the color map\n",
    "  eColor =mcp.gen_color_normalized(cmap=\"seismic\",data_arr=u)\n",
    "  pos = nx.spring_layout(G,seed=63)\n",
    "  options = {\n",
    "    \"node_color\": \"#A0CBE2\",\n",
    "    \"edge_color\": eColor,\n",
    "    \"width\": 4,\n",
    "    \"edge_cmap\": plt.cm.Blues,\n",
    "    \"with_labels\": False,\n",
    "  }\n",
    "  # Draw the graph\n",
    "  nx.draw(G, pos, **options)\n",
    "  plt.show()\n",
    "\n",
    "plot_optimized_commute_times_over_graph(G,Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "Wgw4UF5HVk40",
    "outputId": "847e0e5b-7df2-478f-8614-9db673e3f606"
   },
   "outputs": [],
   "source": [
    "# Commute Times as a NullSpace\n",
    "NLpinv = np.linalg.pinv(NLdense) \n",
    "CTpinv = np.zeros((n,n))\n",
    "for i in range(n):\n",
    "  for j in range(n):\n",
    "    CTpinv[i,j] = graph_vol(G)*(NLpinv[i,i] + NLpinv[j,j] - 2*NLpinv[i,j])\n",
    "plt.imshow(CTpinv, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RviGnk-hCpkL"
   },
   "source": [
    "## 5. Graph Debiasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 508
    },
    "id": "CZgrG7yHiUUt",
    "outputId": "4e061377-1c6b-454f-8033-9330a150c3ce"
   },
   "outputs": [],
   "source": [
    "# Debiasing if necessary\n",
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "def find_errors(CT): \n",
    "  n = int(CT.shape[0]/2)\n",
    "  CTZ = np.copy(CT)\n",
    "\n",
    "  # Fill diagonal with +Inf\n",
    "  for i in range(2*n):\n",
    "    CTZ[i,i] = 9999\n",
    "  \n",
    "  y_true = np.concatenate((np.ones((1,n)),np.zeros((1,n))),axis = 1)\n",
    "  y_pred = np.zeros((1,2*n))\n",
    "  for i in range(2*n):\n",
    "    ithrow = CTZ[i,:]\n",
    "    nearest_idx = np.unravel_index(np.argmin(ithrow, axis=None),shape=ithrow.shape)[0]\n",
    "    if i < n:\n",
    "      if nearest_idx < n:\n",
    "        y_pred[0,i] = 1\n",
    "      else: \n",
    "        y_pred[0,i] = 0\n",
    "    else:\n",
    "      if nearest_idx >= n:\n",
    "        y_pred[0,i] = 0\n",
    "      else: \n",
    "        y_pred[0,i] = 1\n",
    "  return confusion_matrix(y_true[0], y_pred[0])\n",
    "\n",
    "print(find_errors(CTZ))\n",
    "print(find_errors(CTpinv))\n",
    "print(find_errors(CT))\n",
    "HK = heat_kernel(G,e,evecs,beta=0.01)\n",
    "print(find_errors(HK))\n",
    "print(HK[0,:])\n",
    "plt.imshow(HK, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 386
    },
    "id": "nqEqxbFsqR-_",
    "outputId": "d4f27048-ebae-4ea6-8297-280675065ea2"
   },
   "outputs": [],
   "source": [
    "# Optimization Example: Rewiring wrt algebraic conectivity (on unnormalized Laplacian)\n",
    "\n",
    "# Need to recompute e, evecs of unnormalized L during optimization. Over Graph argument\n",
    "def unnormalized_laplacian_eigenvectors(G):\n",
    "  n = G.number_of_nodes()\n",
    "  Ldense = nx.laplacian_matrix(G).todense()\n",
    "  # Finding eigen values and eigen vectors\n",
    "  eL, evecsL = np.linalg.eig(Ldense)\n",
    "  # Sort them (both e's and evecs's) ascending\n",
    "  idx =eL.argsort()\n",
    "  eL = eL[idx]\n",
    "  evecsL = evecsL[:,idx]\n",
    "  return eL, evecsL\n",
    "\n",
    "def derivative_of_lambda2_wrt_adjacency(G): \n",
    "  n = G.number_of_nodes()\n",
    "  eL, evecsL =  unnormalized_laplacian_eigenvectors(G)\n",
    "  # Fiedler's value and vector\n",
    "  lambda2 = eL[1]\n",
    "  u2 = evecsL[:,1]\n",
    "  # Construct the derivative matrix \n",
    "  u2u2T = np.matmul(u2,np.transpose(u2))\n",
    "  #print(u2u2T[2,:])\n",
    "  dl2 = np.matmul(np.diag(np.diag(u2u2T)),np.ones((n,n))) - u2u2T\n",
    "  # Symmetrize and subtract the diag since it is an undirected graph\n",
    "  #dl2 = dl2 + np.transpose(dl2) - np.diag(np.diag(dl2))\n",
    "  return dl2\n",
    "\n",
    "# Structure of the derivative: low values intra-class, higher values inter-class\n",
    "# The derivative is governed by the Fiedler vector:\n",
    "# u2u2T: each row is partitioned into positive and negative entries according to the clustering\n",
    "# diag(u2u2T)*1nn: puts positive correlations in each row.\n",
    "# diag(u2u2T)*1nn - u2u2T subtracts from positive correlations.\n",
    "# dl2(i,j): is the deviation of the Fiedler vector info from the self-correlation. \n",
    "#          I.e. mis-classified nodes (low value of Fiedler entry will have large deviation)\n",
    " \n",
    "dl2 = derivative_of_lambda2_wrt_adjacency(G)\n",
    "print(np.diag(dl2))\n",
    "print(dl2[2,:])\n",
    "plt.imshow(dl2, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "id": "8T5_ryW1z_nH",
    "outputId": "a9a939e4-3708-4043-81da-dda1e49e6398"
   },
   "outputs": [],
   "source": [
    "A = nx.adjacency_matrix(G).todense()\n",
    "print(A.shape)\n",
    "plt.imshow(A, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 404
    },
    "id": "VFxpzEkg3xMG",
    "outputId": "c7b4b2f4-aaa2-4649-8eda-412337cc2395"
   },
   "outputs": [],
   "source": [
    "# If we apply derivatives without recalculating eigensystem we ACTUALLY DENSIFY the graph!\n",
    "# We enlarge intra-class edges (fill the gaps)\n",
    "# But inter-class edges are still active\n",
    "mu = 0.1\n",
    "lambdaReg =0.1\n",
    "maxiter = 1000\n",
    "Ac = np.copy(A)\n",
    "print(A.shape)\n",
    "print(Ac[0,2])\n",
    "for k in range(maxiter):\n",
    "  dl2 = derivative_of_lambda2_wrt_adjacency(G)\n",
    "  Ac  = Ac - mu*dl2\n",
    "plt.imshow(Ac, alpha=0.8, cmap=\"seismic\")\n",
    "print(Ac[3,:])\n",
    "print(A[3,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 369
    },
    "id": "sVegImV39eYE",
    "outputId": "19c94dfc-6a09-4981-f44f-703a80f3b6b3"
   },
   "outputs": [],
   "source": [
    "# If we apply derivatives WITH recalculating eigensystem....\n",
    "import copy \n",
    "\n",
    "mu = 0.01\n",
    "lambdaReg =20.0\n",
    "maxiter = 100\n",
    "inneriter = 10\n",
    "Ac = np.copy(A)\n",
    "print(A.shape)\n",
    "dl2c = np.copy(dl2)\n",
    "print(Ac[0,2])\n",
    "Gc = copy.deepcopy(G)\n",
    "\n",
    "cost_list=[]\n",
    "lambda2_list = []\n",
    "fiedler_list = []\n",
    "\n",
    "def optimizing_lambda2_cost_function(A,Apred, lambda2):\n",
    "  return np.linalg.norm(A-Apred) + lambdaReg*(lambda2**2)\n",
    "\n",
    "def plot_input_list(input_list):  \n",
    "  x = range(maxiter)\n",
    "  y = np.asarray(input_list)\n",
    "  plt.plot(x,y, 'r')\n",
    "  # show the plot\n",
    "  plt.show()\n",
    "\n",
    "for k in range(maxiter):\n",
    "  # Recalculate eigengap \n",
    "  eL, evecsL =  unnormalized_laplacian_eigenvectors(Gc)\n",
    "  lambda2 = eL[1]\n",
    "\n",
    "  # Compute dJ wrt A \n",
    "  # Inner loop to densify\n",
    "  for l in range(inneriter):\n",
    "   dl2c = derivative_of_lambda2_wrt_adjacency(Gc) \n",
    "   Ac  = Ac - mu*dl2c\n",
    "\n",
    "  partialJ = 2*(Ac - A) + lambdaReg*2*lambda2*dl2c\n",
    "  dJ = partialJ + np.transpose(partialJ) - np.diag(np.diag(partialJ))\n",
    "\n",
    "  # Update adjacency\n",
    "  Ac  = Ac - mu*dJ\n",
    "  # Clipping: negatives to 0, positives to 1 \n",
    "  Ac = np.clip(Ac,0,1)\n",
    "\n",
    "  # Graph from adjacency matrix \n",
    "  Gc = nx.convert_matrix.from_numpy_matrix(Ac)\n",
    "\n",
    "  # Update cost_list\n",
    "  cost_list.append(optimizing_lambda2_cost_function(A, Ac, lambda2))\n",
    "  lambda2_list.append(lambda2)\n",
    "  fiedler_list.append(evecsL[:,1])\n",
    "  \n",
    "\n",
    "plt.imshow(Ac, alpha=0.8, cmap=\"seismic\")\n",
    "print(Ac[0,2])\n",
    "\n",
    "\n",
    "print(optimizing_lambda2_cost_function(A,Ac, lambda2))\n",
    "print(np.max(abs(Ac-A)))\n",
    "print(np.min(abs(Ac-A)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "POi9s_SlHWMc",
    "outputId": "d2e3846b-f4b1-49b7-f1e4-4b96772164e4"
   },
   "outputs": [],
   "source": [
    "plot_input_list(cost_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "4PwuOfcgQVA7",
    "outputId": "99e304a6-dc42-41bb-f44f-9077b070d145"
   },
   "outputs": [],
   "source": [
    "plot_input_list(lambda2_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "aWQxkTiHRQA8",
    "outputId": "7a8bcaf5-4eac-4c31-f1c7-9e27d26b1c81"
   },
   "outputs": [],
   "source": [
    "print(fiedler_list[0])\n",
    "print(fiedler_list[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "t3fy_BYMBfF1",
    "outputId": "94fe3ded-a40d-4d99-a73b-cbd6b6e7d46e"
   },
   "outputs": [],
   "source": [
    "plt.imshow(A, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "mgo7ZUbUoEzK",
    "outputId": "0a24be2b-f82e-41b8-a671-d5e0b7c57e9d"
   },
   "outputs": [],
   "source": [
    "plt.imshow(Ac, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BdjopSz3xP3a",
    "outputId": "a8b08794-56d1-432d-ce56-7fe36ff6d0ca"
   },
   "outputs": [],
   "source": [
    "print(Ac[3,:])\n",
    "print(A[3,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "H8Oof2SvV1vj"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7pquqNTyNhAx",
    "outputId": "d85e9edf-1d5e-4303-de02-9915ef693300"
   },
   "outputs": [],
   "source": [
    "print(Gc.edges)\n",
    "print(G.edges)\n",
    "print(nx.adjacency_matrix(Gc))\n",
    "print(nx.adjacency_matrix(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YbC-YsGkC4Yl"
   },
   "source": [
    "## 6. Convolutions in GNNs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "HJ04rBguiauO",
    "outputId": "e5f04af3-e0ac-4b3e-ba4c-8cb6a1672dd8"
   },
   "outputs": [],
   "source": [
    "# Spatial convolution (Kipf & Welling)\n",
    "n = nx.number_of_nodes(G)\n",
    "\n",
    "# Get features from learned CT\n",
    "X = Z\n",
    "\n",
    "def select_k_indexes_and_set_zeros_in_features(X,k):\n",
    "  sel = np.random.randint(2, size=n)\n",
    "  Xcorrupted = X.copy()\n",
    "  for i in range(n):\n",
    "    if sel[i]==1: \n",
    "      Xcorrupted[i,0] = 0; \n",
    "      Xcorrupted[i,1] = 0; \n",
    "      Xcorrupted[i,2] = 0;\n",
    "  return Xcorrupted\n",
    "\n",
    "Xcorrupted = select_k_indexes_and_set_zeros_in_features(X,5)\n",
    "\n",
    "# Compute the Ahat adjacency (normalized Atilde: A with self similarity)\n",
    "def compute_ahat_adjacency(G): \n",
    "  A = nx.adjacency_matrix(G).todense()\n",
    "  I = np.eye(n)\n",
    "  Atilde = A + I # Self similarity added \n",
    "  d = np.sum(Atilde,axis=1) # Degrees\n",
    "  d = np.squeeze(d)\n",
    "  Dtilde = np.zeros((n,n))\n",
    "  for i in range(n):\n",
    "   Dtilde[i,i] = d[0,i]\n",
    "  Dtilde = fractional_matrix_power(Dtilde, -0.5)\n",
    "  Ahat = np.matmul(Dtilde,np.matmul(Atilde,Dtilde))\n",
    "  return Ahat\n",
    "\n",
    "Ahat = compute_ahat_adjacency(G)\n",
    "plt.imshow(Ahat, alpha=0.8, cmap=\"seismic\")\n",
    "\n",
    "# A vanilla result of X diffusion on G \n",
    "fvanilla = np.matmul(Ahat,np.matmul(Ahat,Xcorrupted))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "YRVgxO5tnPUG",
    "outputId": "100fd17a-fc7d-49fb-cd8f-d73c524ab2d9"
   },
   "outputs": [],
   "source": [
    "plt.imshow(Z, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "VJgWmw5-n5d0",
    "outputId": "4a782959-d5ef-4c0c-9421-848fce63c9ed"
   },
   "outputs": [],
   "source": [
    "plt.imshow(Xcorrupted, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "OWSG8AU-sVB9",
    "outputId": "421c91a2-07a2-43ca-cab3-b93f5085bb24"
   },
   "outputs": [],
   "source": [
    "plt.imshow(fvanilla, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "N9HYZQyHv1JR",
    "outputId": "63423f00-b115-4495-e406-5c6203ec09b4"
   },
   "outputs": [],
   "source": [
    "# Add to vanilla two weight matrices\n",
    "W1 = np.random.rand(3,3)\n",
    "W2 = np.random.rand(3,3)\n",
    "X1 = np.matmul(np.matmul(Ahat,Xcorrupted),W1)\n",
    "fweighted = np.matmul(np.matmul(A,X1),W2)\n",
    "\n",
    "plt.imshow(fweighted, alpha=0.8, cmap=\"seismic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 612
    },
    "id": "TVsoc9lSU2cC",
    "outputId": "7760c52a-e507-463b-a0b0-9b5f2777bc58"
   },
   "outputs": [],
   "source": [
    "# Graph Fourier Transform for X \n",
    "Xhat = np.matmul(np.transpose(evecsNL),X)\n",
    "plt.imshow(Xhat, alpha=0.8, cmap=\"seismic\")\n",
    "print(Xhat)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "LcE0J1ljYKFf",
    "outputId": "ac108fc8-693e-4429-b27c-e3b53934180f"
   },
   "outputs": [],
   "source": [
    "# Reconstruct Normalized Laplacian \n",
    "Lrecon = np.matmul(np.matmul(evecsNL,np.diag(e)),np.transpose(evecsNL))\n",
    "plt.imshow(Lrecon, alpha=0.8, cmap=\"seismic\")"
   ]
  }
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