{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "wanted-celebration",
   "metadata": {},
   "source": [
    "# Implementing PageRank from scratch\n",
    "\n",
    "*This notebook follows a similar approach as [the slides](http://web.stanford.edu/class/cs246/slides/09-pagerank.pdf) and [book](http://infolab.stanford.edu/~ullman/mmds/ch5.pdf) of the course \"Mining Massive Data Sets\" from Jure Leskovec. I attempt to follow closely his notation.*\n",
    "\n",
    "In this notebook I will implement from scratch the PageRank algorithm that the founders of Google proposed (Bringing Order to the Web, 1998) to rank (order) the results of our google searches. Google was not the first search engine, but it was the first at utilising both the content of the webpage and the importance of the webpage in the huge graph containing all the webpages.\n",
    "\n",
    "How can one define importance of a webpage or equivalently the importance of a node in a graph? In the PageRank algorithm the importance of a webpage depends on how many other webpages link to that webpage. Also, if an important webpage links to you, then you are considered important too. While all these might sound abstract we can define importance of webpage (node) $j$ as:\n",
    "$$\n",
    "r_j = \\sum_{i \\rightarrow j} \\dfrac{r_i}{d_i}\n",
    "$$\n",
    "where $d_i$ is the out-degree of node $i$ and $i \\rightarrow j$ includes all the nodes $i$ that point to node $j$.\n",
    "\n",
    "Some takeaways from the above equation:\n",
    "* Your importance depends on the importance of your incoming links, which gives a recursive flavour to our definition\n",
    "* You divide equally your importance (vote) to all the nodes you point to\n",
    "* The more important you are the more important your outgoing votes are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "respected-story",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "resident-lexington",
   "metadata": {},
   "source": [
    "## Ideal Internet Graph\n",
    "\n",
    "We will start by having an ideal internet graph that does not contain any dead-ends or spider traps (more on that later) to get the basic and super elegant idea of PageRank. We will then gradually lift these assumptions and build the full PageRank algorithm that could be used on any graph of any size efficiently.\n",
    "\n",
    "![PageRank](img/ideal_graph.png)\n",
    "\n",
    "*Note:* The above matrix is called stochastic since all of its columns sum to 1. It can also be called transition matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ultimate-sandwich",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A simple ideal stochastic ajacency matrix\n",
    "M = np.array([\n",
    "    [0.5, 0.5, 0],\n",
    "    [0.5, 0, 1],\n",
    "    [0, 0.5, 0]\n",
    "])\n",
    "\n",
    "# A prior starting distribution\n",
    "r_start = np.array([0.2, 0.6, 0.2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "manufactured-reflection",
   "metadata": {},
   "source": [
    "We want to solve the equation $r = Mr$. This looks similar to the equation $Ax = λx$ which we solve in order to find the eigenvectors of $A$. So, $r$ is the eigenvector of $M$ with eigenvalue 1. We can easily find this eigenvector through the power iteration where $r^{(t+1)} = Mr^{(t)}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "elect-blocking",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.39920254 0.40208778 0.19870968]\n"
     ]
    }
   ],
   "source": [
    "max_iterations = 20\n",
    "r_old = r_start\n",
    "history = [r_start]\n",
    "\n",
    "for _ in range(max_iterations):\n",
    "    # Find the new r\n",
    "    r_new = M @ r_old\n",
    "    \n",
    "    # Save the history of updates\n",
    "    history.append(r_new)\n",
    "    \n",
    "    # Update r_old\n",
    "    r_old = r_new\n",
    "    \n",
    "print(r_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "split-optics",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "history = np.array(history)\n",
    "def plot_history(history):\n",
    "    fig = plt.figure(figsize=(10, 5))\n",
    "\n",
    "    plt.plot(np.arange(len(history)), history[:, 0], label=\"Node A\", color=\"tab:orange\", alpha=0.7, linewidth=2, marker='o')\n",
    "    plt.plot(np.arange(len(history)), history[:, 1], label=\"Node B\", color=\"tab:blue\", alpha=0.7, linewidth=2, marker='o')\n",
    "    plt.plot(np.arange(len(history)), history[:, 2], label=\"Node C\", color=\"tab:purple\", alpha=0.7, linewidth=2, marker='o')\n",
    "\n",
    "    plt.legend(prop={'size': 13}, markerscale=2.5)\n",
    "    plt.xlabel(\"Iteration\")\n",
    "    plt.ylabel(\"Importance\")\n",
    "    plt.grid()\n",
    "    plt.title(\"Convergence of the rank vector r using power iteration\", fontsize=14)\n",
    "    plt.show()\n",
    "    \n",
    "plot_history(history)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "positive-forty",
   "metadata": {},
   "source": [
    "Our algorithm converges and it seems like nodes A and B are equally important with an importance of 0.4 and node C does not seem important with an importance of 0.2. This intuitevely makes sense since node C has only one incoming link when compared to A and B that have two."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sufficient-accreditation",
   "metadata": {},
   "source": [
    "## Dead-ends and spider traps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "different-biography",
   "metadata": {},
   "source": [
    "The super simple and small example above is also ideal. This means that in order for a unique r (stationary distribution) to exist the graph satisfied two requirements:\n",
    "* No dead ends\n",
    "* No spider traps, for example $a \\rightarrow b \\leftrightharpoons c$ has a trap since if we go from a to b we can never go back to a again.\n",
    "\n",
    "Intuitevely the problem with the spider traps makes sense, since what we are actually doing is letting a surfer infinetely surf on our nodes and at each time $t$ we ask on which node the surfer currently is. By collecting an infinite number of answers we form the stationary distribution $r$. So, if our surfer gets trapped (which is certain since the surfer performs infinite steps), it will never visit again the rest of the graph.\n",
    "\n",
    "Let's first create **a dead-end** on our previosly ideal graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "shared-darwin",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A not so stochastic ajacency matrix due to a dead end\n",
    "M = np.array([\n",
    "    [0.5, 0.5, 0],\n",
    "    [0.5, 0, 0],\n",
    "    [0, 0.5, 0]\n",
    "])\n",
    "\n",
    "# A prior starting distribution\n",
    "r_start = np.array([0.2, 0.6, 0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "sharing-angle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_iterations = 20\n",
    "r_old = r_start\n",
    "history = [r_start]\n",
    "\n",
    "for _ in range(max_iterations):\n",
    "    # Find the new r\n",
    "    r_new = M @ r_old\n",
    "    \n",
    "    # Save the history of updates\n",
    "    history.append(r_new)\n",
    "    \n",
    "    # Update r_old\n",
    "    r_old = r_new\n",
    "    \n",
    "plot_history(np.array(history))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "infinite-memorial",
   "metadata": {},
   "source": [
    "We notice that all the nodes converge to an improtance of 0. Our surfer has nowhere to go when it reaches the dead-end at node C, so she \"vanishes\". This means that the total importance of the graph leaks out.\n",
    "\n",
    "Now we create **a spider trap**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ignored-hollywood",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A stochastic ajacency matrix with a spider trap\n",
    "M = np.array([\n",
    "    [0.5, 0, 0],\n",
    "    [0.5, 0, 1],\n",
    "    [0, 1, 0]\n",
    "])\n",
    "\n",
    "# A prior starting distribution\n",
    "r_start = np.array([0.2, 0.6, 0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "complete-sugar",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_iterations = 20\n",
    "r_old = r_start\n",
    "history = [r_start]\n",
    "\n",
    "for _ in range(max_iterations):\n",
    "    # Find the new r\n",
    "    r_new = M @ r_old\n",
    "    \n",
    "    # Save the history of updates\n",
    "    history.append(r_new)\n",
    "    \n",
    "    # Update r_old\n",
    "    r_old = r_new\n",
    "    \n",
    "plot_history(np.array(history))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "frozen-linux",
   "metadata": {},
   "source": [
    "We created a spider trap between node B and C. As a result the surfer is trapped on that neighborhood which absrobs all the importance. After infinite steps she will never visit again node A and also the importance of node B and C will constantly oscillate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mathematical-pottery",
   "metadata": {},
   "source": [
    "These two problems presented above occur on many webpages and force us to patch our above implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "opened-routine",
   "metadata": {},
   "source": [
    "## Fixing the dead ends and traps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "distinct-price",
   "metadata": {},
   "source": [
    "First, we will solve the problem of spider-traps and the solution of dead-ends will come naturally. The PageRank paper suggests that our surfer can now teleport on any node with a probability of $1 - β$ where $β$ is a user defined variable (usually around 0.8 - 0.9). This means that if our surfer gets trapped, after some steps it will manage to teleport and possibly escape the trap.\n",
    "\n",
    "Similarly, in the case of dead-ends the surfer will always teleport at its next step. This means that our previously stochastic adjacency matrix remains stochastic since its dead-end column now sums to 1.\n",
    "\n",
    "Our new rule for calcualting the importance of a single node $j$ becomes:\n",
    "$$\n",
    "r_j = \\sum_{i \\rightarrow j} β \\dfrac{r_i}{d_i} + (1-β)\\dfrac{1}{N}\n",
    "$$\n",
    "and as a result of the power iteration method, $r=Mr$ becomes $r=Ar$ where $A$ is given by:\n",
    "$$\n",
    "A = βM + (1-b)\\left( \\frac{1}{N} \\right) _{NxN}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "silent-namibia",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A stochastic ajacency matrix with a spider trap\n",
    "M = np.array([\n",
    "    [0.5, 0, 0],\n",
    "    [0.5, 0, 1],\n",
    "    [0, 1, 0]\n",
    "])\n",
    "\n",
    "# A prior starting distribution\n",
    "r_start = np.array([0.2, 0.6, 0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "drawn-magazine",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta = 0.75  # This means that the probability of teleporting is high (approximately 1 teleport every 4 steps). Normally beta is around 0.85\n",
    "N = np.full((len(M), len(M)), 1 / len(M))\n",
    "\n",
    "max_iterations = 20\n",
    "r_old = r_start\n",
    "history = [r_start]\n",
    "\n",
    "for _ in range(max_iterations):\n",
    "    # Find the new r\n",
    "    A = beta * M + (1 - beta) * N\n",
    "    r_new = A @ r_old\n",
    "    \n",
    "    # Save the history of updates\n",
    "    history.append(r_new)\n",
    "    \n",
    "    # Update r_old\n",
    "    r_old = r_new\n",
    "    \n",
    "plot_history(np.array(history))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compact-infection",
   "metadata": {},
   "source": [
    "We succesfully dealt with the spider trap and we can see that our power iteration method converged giving the final importance to our nodes. In the case of google page ranking, this means that in the list of search results we would first present webpage B then C and finally A.\n",
    "\n",
    "I do not present the results of dealing with the dead ends but you can imagine that we manually add on each dead end node an outgoing edge to all the nodes of our graph."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "correct-wallet",
   "metadata": {},
   "source": [
    "## Surfing and Markov Chains\n",
    "\n",
    "In case you are familiar with the theory behind Markov chains you can find a direct comparison between them and PageRank. Briefly, a Markov chain describes an event that depends only on the exact previous event. For example, if our surfer went to webpages A->B->C the next webpage depends only on webpage C. The probability of going from C to another webpage is given to us from the tranisition matrix $M$, which we have presented above as the stochastic adjacency matrix.\n",
    "\n",
    "In our case we have made one strong assumption, that the probability of surfing from webpage A to any outgoing link is equal to $\\dfrac{1}{d_A}$ where $d_A$ is the number of outgoing links. This means that our surfer randomly selects one of the possible outgoing links.\n",
    "\n",
    "Finally, the principal eigenvector that we find above using the power iteration method is called **stationary vector** and is **unique** for a given matrix $M$ if that matrix follows some rules such as:\n",
    "* Each column sums to 1 (stochastic)\n",
    "* No spider traps\n",
    "* No dead-ends\n",
    "\n",
    "I believe that this gives a more sound (and definetely simplified) approach as to why we must deal with dead-ends and spider traps."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sophisticated-carrier",
   "metadata": {},
   "source": [
    "## Scaling issues\n",
    "\n",
    "You might suspect that the whole internet does not include only 3 webpages A, B, C. Actually, the estimated number of webpages is around 1.7 billion. Our algorithm needs to keep on each iteration a vector for `r_new`, a vector of `r_old` and the adjacency matrix M or A. `r_new` and `r_old` contain 1.7 billion float entries each which results to $2 * 1.7 * 10^9 * 4$ bytes = 13.6GB which I believe can easily fit the memory of the Google machines. Our main problem however is the size of M, A. They both have the same size $NxN$ where N is the number of total webpages. This means that in order to fit one of these matrices we need $(1.7 * 10^9)^2*4$ bytes ~  14*10^6TB. Well that seems pretty big and probably not even google would be able to store that matrix.\n",
    "\n",
    "Some good and some bad news. The good news are that the matrix M (the ideal one) is sparse and can be stored and loaded efficiently. Assuming that there are on average 10 outgoing links per page this means we need $1.7 * 10^9 * 4 * 10$ bytes ~ 68GB so in total we need $r_{old} + r_{new} + M = 81.6GB$. Yay, this soudns reasonable enough and we can store it easily on a single Google machine. However, the bad new are that the matrix M can be used only in the ideal scenario that the graph of all the webpages does not include any spider traps or dead-ends as we showed above.\n",
    "\n",
    "In the more realistic scenario there are many dead-ends and spider traps, so we must use the matrix A instead of matrix M. Well, matrix A is not sparse at all and actually has almost no 0 values. This means that we actually need 14million TB to perform the power iteration. Fortunately, there is a way to get back to using the sparse matrix M which can also include traps and dead-ends. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "democratic-cemetery",
   "metadata": {},
   "source": [
    "## Fixing our issues, again\n",
    "\n",
    "Assuming no dead end, we could rerwite our power iteration rule $r = \\left(βM + (1-b)\\left( \\frac{1}{N} \\right)_{NxN}\\right)r$ to $r = βMr + \\left( \\frac{1 - b}{N} \\right)_{N}$. Instead of adding an NxN full matrix to M, we instead add an N sized vector to the final result. With the above rewrite we have avoided using the dense matrix A. \n",
    "\n",
    "Now, we must also deal with the dead-ends. As you remember in the case of dead-ends there was a leak of importance. We can quantify the total leak (from both the dead-ends and the random teleportations) as $1 - S$ where $S = \\sum_jr_j'$ and $r_j'$ is the importance of node j without caring about possible teloportation that ended up on node j.\n",
    "\n",
    "![PageRank](img/pagerank_full.png)\n",
    "\n",
    "*[Image from Yure's Leskovec slides](http://web.stanford.edu/class/cs246/slides/09-pagerank.pdf)*\n",
    "\n",
    "I had two main difficulties understanding the above algorithm. First, what is the S? Second, where did the 1 - b go? In the case that we did not have any dead-ends S == 1 - b and the equation takes the form we presented above. In the case of dead ends S is b - dead end leaks, so the numerator becomes 1 - b + dead_end_leaks and we have accounted for both spider-traps and dead ends while using the sparse matrix M.\n",
    "\n",
    "Below, we show the implementation of the final version of our PageRank algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "overall-latex",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A stochastic adjacency matrix with a spider trap\n",
    "M = np.array([\n",
    "    [0.5, 0, 0],\n",
    "    [0.5, 0, 1],\n",
    "    [0, 1, 0]\n",
    "])\n",
    "\n",
    "# A prior starting distribution\n",
    "r_start = np.array([1/3, 1/3, 1/3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "knowing-score",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta = 0.75\n",
    "N = np.full((len(M), len(M)), 1 / len(M))\n",
    "\n",
    "max_iterations = 20\n",
    "r_old = r_start\n",
    "history = [r_start]\n",
    "\n",
    "for _ in range(max_iterations):\n",
    "    # Find the new r'\n",
    "    r_prime = beta * M @ r_old  # We only use matrix M and avoid calculating the dense matrix A\n",
    "    \n",
    "    # Calculate the residual (leak) from dead ends and random teleports\n",
    "    leak = 1 - np.sum(r_prime)\n",
    "    \n",
    "    # Calcualte r_new\n",
    "    r_new = r_prime + (1 / len(r_prime)) * leak\n",
    "    \n",
    "    # Save the history of updates\n",
    "    history.append(r_new)\n",
    "    \n",
    "    # Update r_old\n",
    "    r_old = r_new\n",
    "    \n",
    "plot_history(np.array(history))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "instant-syndicate",
   "metadata": {},
   "source": [
    "We got the exact same results as in the case above while we avoided using the dense matrix A. We have successfully created a method that will be able to rank the importance of pages regardless of the graph size and relatively fast. Approximately, even for the biggest graphs (many billions of nodes) the power iteration method converges at ~50 iterations.\n",
    "\n",
    "$$\n",
    "The \\hspace{1mm} End!\n",
    "$$"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:TextClassificationAndDeduplication]",
   "language": "python",
   "name": "conda-env-TextClassificationAndDeduplication-py"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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 },
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}