Practice extra 10 - Graph-based Recommenders basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recommender Systems 2024/25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Practice 7 – Graph-based Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "vscode": {
     "languageId": "plaintext"
    }
   },
   "source": [
    "## Graph-based Recommenders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is a Graph?\n",
    "\n",
    "In layman terms, a graph is a set of **interconnected entities**. Each entity is represented by a *node*, while the connections are called *edges*. Thus, mathematically speaking, a graph $G \\in \\mathbb{R}^{n\\times n}$ can be represented as two sets, $N$ (nodes) and $E$ (edges).$$G = (N,E) \\\\ N = \\{x_i | i \\in [1, |N|]_{\\mathbb{N}}\\} \\\\ E = \\{\\{x_i, x_j\\} | x_i,x_j \\in N\\}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graph Notation\n",
    "\n",
    "#### Graph Chart\n",
    "\n",
    "Nodes are usually represented graphically as circles, with lines (=edges) connecting one another"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: plotly in /opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages (5.22.0)\n",
      "Requirement already satisfied: tenacity>=6.2.0 in /opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages (from plotly) (8.2.2)\n",
      "Requirement already satisfied: packaging in /opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages (from plotly) (23.2)\n"
     ]
    }
   ],
   "source": [
    "!pip install plotly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "G = nx.Graph()\n",
    "G.add_nodes_from([1,2,3,4,5])\n",
    "G.add_edges_from([(1,2),(1,3),(1,5),(2,4),(3,5)])\n",
    "\n",
    "nx.draw(G, with_labels=True, node_color=\"green\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hoverinfo": "none",
         "line": {
          "color": "gray",
          "width": 1
         },
         "mode": "lines",
         "type": "scatter",
         "x": [
          0.16991911651442762,
          -0.4601688018675636,
          null,
          0.16991911651442762,
          0.4984679961495893,
          null,
          0.16991911651442762,
          0.7917816892035467,
          null,
          -0.4601688018675636,
          -1,
          null,
          0.4984679961495893,
          0.7917816892035467,
          null
         ],
         "y": [
          0.12482395520255483,
          -0.33815869156792977,
          null,
          0.12482395520255483,
          0.6736007964751934,
          null,
          0.12482395520255483,
          0.2744935426173893,
          null,
          -0.33815869156792977,
          -0.7347596027272076,
          null,
          0.6736007964751934,
          0.2744935426173893,
          null
         ]
        },
        {
         "marker": {
          "color": "blue",
          "size": 25
         },
         "mode": "markers+text",
         "text": [
          "1",
          "2",
          "3",
          "4",
          "5"
         ],
         "textposition": "top center",
         "type": "scatter",
         "x": [
          0.16991911651442762,
          -0.4601688018675636,
          0.4984679961495893,
          -1,
          0.7917816892035467
         ],
         "y": [
          0.12482395520255483,
          -0.33815869156792977,
          0.6736007964751934,
          -0.7347596027272076,
          0.2744935426173893
         ]
        }
       ],
       "layout": {
        "hovermode": "closest",
        "showlegend": false,
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
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        "title": {
         "text": "Example Graph"
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   "source": [
    "# Draw a more beautiful, interactive graph\n",
    "\n",
    "def setup_plotly_graph(G : nx.Graph):\n",
    "    pos = nx.spring_layout(G)\n",
    "    edge_x, edge_y = [], []\n",
    "    for edge in G.edges():\n",
    "        x0, y0 = pos[edge[0]]\n",
    "        x1, y1 = pos[edge[1]]\n",
    "        edge_x += [x0, x1, None]\n",
    "        edge_y += [y0, y1, None]\n",
    "\n",
    "    node_x, node_y = zip(*pos.values())\n",
    "\n",
    "    return edge_x, edge_y, node_x, node_y\n",
    "\n",
    "def draw_plotly(G : nx.Graph):\n",
    "    edge_x, edge_y, node_x, node_y = setup_plotly_graph(G)\n",
    "\n",
    "    edge_trace = go.Scatter(x=edge_x, y=edge_y,\n",
    "                            line=dict(width=1, color='gray'),\n",
    "                            hoverinfo='none',\n",
    "                            mode='lines')\n",
    "    node_trace = go.Scatter(x=node_x, y=node_y,\n",
    "                            mode='markers+text',\n",
    "                            marker=dict(size=25, color='blue'),\n",
    "                            text=list(G.nodes),\n",
    "                            textposition=\"top center\")\n",
    "\n",
    "    fig = go.Figure(data=[edge_trace, node_trace],\n",
    "                    layout=go.Layout(title=\"Example Graph\",\n",
    "                                    showlegend=False,\n",
    "                                    hovermode='closest'))\n",
    "    \n",
    "    return fig\n",
    "\n",
    "fig = draw_plotly(G)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Adjacency Lists\n",
    "\n",
    "For each node in the graph, its adjacency list contains all nodes it is connected to. Pros: easily readable, cons: redundant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: [2, 3, 5]\n",
      "2: [1, 4]\n",
      "3: [1, 5]\n",
      "4: [2]\n",
      "5: [1, 3]\n"
     ]
    }
   ],
   "source": [
    "for k,v in G.adj.items():\n",
    "    print(\"{}: {}\".format(k, list(v.keys())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adjacency Matrices\n",
    "\n",
    "##### Node-2-Edge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A node-2-edge adjacency matrix $A$ has shape equal to $|N|\\times|E|$: each row represents a node within the graph, while each column represents an edge. The element $a_{i,j}$ will be set to 1 (or to edge $j$'s weight) if edge $j$ touches node $i$. Thus, only 2 elements per column (the nodes that are connected by edge $j$) will be greater than zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, 0, 0],\n",
       "       [1, 0, 0, 1, 0],\n",
       "       [0, 1, 0, 0, 1],\n",
       "       [0, 0, 0, 1, 0],\n",
       "       [0, 0, 1, 0, 1]], dtype=int32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def node_to_edge_adjacency_matrix(G : nx.Graph):\n",
    "    # Get the list of nodes and edges\n",
    "    nodes = list(G.nodes)\n",
    "    edges = [(x[0] - 1,x[1] - 1) for x in list(G.edges)]\n",
    "\n",
    "    # Initialize the node-to-edge adjacency matrix\n",
    "    n = len(nodes)\n",
    "    m = len(edges)\n",
    "    matrix = np.zeros((n, m), dtype=np.int32)\n",
    "\n",
    "    # Populate the matrix\n",
    "    for edge_index, (u, v) in enumerate(edges):\n",
    "        matrix[u, edge_index] = 1\n",
    "        matrix[v, edge_index] = 1\n",
    "\n",
    "    return matrix\n",
    "\n",
    "node_to_edge_adjacency_matrix(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Node-2-Node"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A node-2-node adjacency matrix $B$ has shape equal to $|N|\\times |N|$: each row represents a node, as well as each column. Thus, $b_{i,j}$ will be greater than zero if node $i$ is connected to node $j$ by means of edge $(i,j)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 0, 1],\n",
       "       [1, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 0, 1],\n",
       "       [0, 1, 0, 0, 0],\n",
       "       [1, 0, 1, 0, 0]], dtype=int32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = nx.to_numpy_array(G, dtype=np.int32)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For our purposes, the most convenient form of graph representation are n2n adjacency matrices."
   ]
  },
  {
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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graphs in Recommendation\n",
    "- Nodes: users, items\n",
    "- Edges: interactions\n",
    "\n",
    "The graph representation of a recommendation scenario is inherently *bipartite*.\n",
    "\n",
    "> **Bipartite Graph**: a graph $G$ is bipartite if its set of nodes $N$ can be divided into two **disjoint** sets of nodes, $N_1$ and $N_2$, such that for every edge $e$ in $G$, $e$ connects a node belonging to $N_1$ to a node in $N_2$ or vice versa, thus there is no inter-set connections among nodes within $N_1$ nor $N_2$.\n",
    "\n",
    "In our case, class $N_1$ is defined by the *user nodes*, and class $N_2$ by *item nodes*, since the edges define user-item interactions.\n",
    "\n",
    "Consequently, the graph's adjacency matrix will **contain the URM**.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "> **Path**: a sequence of $m + 1$ nodes $n_0 \\rightarrow n_1 \\rightarrow n_2 \\rightarrow ... \\rightarrow n_m$ such that $\\forall i = 1, ..., m, (n_{i-1}, n_{i}) \\in E$.\n",
    "\n",
    "I.e., a *path* is a sequence of connected nodes within a graph. A path will have a starting node $A$ and a destination node $B$. In the context of recommendation, we can think of paths as **collaborative signals**!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import numpy as np\n",
    "import scipy.sparse as sps\n",
    "from sklearn.preprocessing import normalize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Illustrative Example\n",
    "Let's create a graph $G$ with 2 users, 3 items and the following adjacency matrix: $$\\begin{bmatrix}0 & 0 & 1 & 0 & 1 \\\\ 0 & 0 & 1 & 1 & 0 \\\\ 1 & 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & 0 \\\\ 1 & 0 & 0 & 0 & 0\\end{bmatrix}.$$\n",
    "\n",
    "It corresponds to the following schema:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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         "text": "Example Graph"
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   ],
   "source": [
    "G = nx.from_dict_of_dicts({\n",
    "    0 : {2 : {}, 4 : {}},\n",
    "    1 : {2 : {}, 3 : {}},\n",
    "    2 : {0 : {}, 1 : {}},\n",
    "    3 : {1 : {}},\n",
    "    4 : {0 : {}}\n",
    "})\n",
    "\n",
    "draw_plotly(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 1, 0, 1],\n",
       "       [0, 0, 1, 1, 0],\n",
       "       [1, 1, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0],\n",
       "       [1, 0, 0, 0, 0]], dtype=int32)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = nx.to_numpy_array(G, dtype=np.int32)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute a random walk, we need to compute the node-to-node *transition probability matrix* $P$. Then, we simply select a node and create a starting state $\\Pi^{(0)}$, which is nothing more than a one-hot-encoding vector identifying the selected starting node, and we multiply it by $P$, obtaining state $\\Pi^{(1)}$. This represents a step in our random walk: if we want to take more steps, we simply take $\\Pi^{(n)}$ and multiply it by $P$ again and again, following what is known as a *Markov chain*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transition probability function\n",
    "def transition(g : np.ndarray, n0 : int, hops : int):\n",
    "    # initial state\n",
    "    state = np.zeros(g.shape[1], dtype=np.float32)\n",
    "    state[n0] = 1\n",
    "\n",
    "    # compute transition probability matrix (can be done once)\n",
    "    transition_probability_matrix = np.array([x / x.sum().astype(np.float32) for x in g], dtype=np.float32)\n",
    "    # print(transition_probability_matrix)\n",
    "\n",
    "    j = 0\n",
    "    print(\"Hop: 0, state: {}\".format(state))\n",
    "    while j != hops:\n",
    "        state = state.dot(transition_probability_matrix)\n",
    "        print(\"Hop: {}, state: {}\".format(j+1, state))\n",
    "        j += 1\n",
    "    return state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hop: 0, state: [1. 0. 0. 0. 0.]\n",
      "Hop: 1, state: [0.  0.  0.5 0.  0.5]\n",
      "Hop: 2, state: [0.75 0.25 0.   0.   0.  ]\n",
      "Hop: 3, state: [0.    0.    0.5   0.125 0.375]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.   , 0.   , 0.5  , 0.125, 0.375], dtype=float32)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transition(g=a, n0=0, hops=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Steady State"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we continue walking for long enough, we will reach a *periodic steady state*: our walk will find an equilibrium, and start jumping from the same subset of users to the same subset of item every time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hop: 0, state: [1. 0. 0. 0. 0.]\n",
      "Hop: 1, state: [0.  0.  0.5 0.  0.5]\n",
      "Hop: 2, state: [0.75 0.25 0.   0.   0.  ]\n",
      "Hop: 3, state: [0.    0.    0.5   0.125 0.375]\n",
      "Hop: 4, state: [0.625 0.375 0.    0.    0.   ]\n",
      "Hop: 5, state: [0.     0.     0.5    0.1875 0.3125]\n",
      "Hop: 6, state: [0.5625 0.4375 0.     0.     0.    ]\n",
      "Hop: 7, state: [0.      0.      0.5     0.21875 0.28125]\n",
      "Hop: 8, state: [0.53125 0.46875 0.      0.      0.     ]\n",
      "Hop: 9, state: [0.       0.       0.5      0.234375 0.265625]\n",
      "Hop: 10, state: [0.515625 0.484375 0.       0.       0.      ]\n",
      "Hop: 11, state: [0.        0.        0.5       0.2421875 0.2578125]\n",
      "Hop: 12, state: [0.5078125 0.4921875 0.        0.        0.       ]\n",
      "Hop: 13, state: [0.         0.         0.5        0.24609375 0.25390625]\n",
      "Hop: 14, state: [0.50390625 0.49609375 0.         0.         0.        ]\n",
      "Hop: 15, state: [0.         0.         0.5        0.24804688 0.25195312]\n",
      "Hop: 16, state: [0.5019531  0.49804688 0.         0.         0.        ]\n",
      "Hop: 17, state: [0.         0.         0.5        0.24902344 0.25097656]\n",
      "Hop: 18, state: [0.50097656 0.49902344 0.         0.         0.        ]\n",
      "Hop: 19, state: [0.         0.         0.5        0.24951172 0.25048828]\n",
      "Hop: 20, state: [0.5004883  0.49951172 0.         0.         0.        ]\n",
      "Hop: 21, state: [0.         0.         0.5        0.24975586 0.25024414]\n",
      "Hop: 22, state: [0.50024414 0.49975586 0.         0.         0.        ]\n",
      "Hop: 23, state: [0.         0.         0.5        0.24987793 0.25012207]\n",
      "Hop: 24, state: [0.5001221  0.49987793 0.         0.         0.        ]\n",
      "Hop: 25, state: [0.         0.         0.5        0.24993896 0.25006104]\n",
      "Hop: 26, state: [0.50006104 0.49993896 0.         0.         0.        ]\n",
      "Hop: 27, state: [0.         0.         0.5        0.24996948 0.25003052]\n",
      "Hop: 28, state: [0.5000305  0.49996948 0.         0.         0.        ]\n",
      "Hop: 29, state: [0.         0.         0.5        0.24998474 0.25001526]\n",
      "Hop: 30, state: [0.50001526 0.49998474 0.         0.         0.        ]\n",
      "Hop: 31, state: [0.         0.         0.5        0.24999237 0.25000763]\n",
      "Hop: 32, state: [0.5000076  0.49999237 0.         0.         0.        ]\n",
      "Hop: 33, state: [0.         0.         0.5        0.24999619 0.2500038 ]\n",
      "Hop: 34, state: [0.5000038 0.4999962 0.        0.        0.       ]\n",
      "Hop: 35, state: [0.        0.        0.5       0.2499981 0.2500019]\n",
      "Hop: 36, state: [0.5000019 0.4999981 0.        0.        0.       ]\n",
      "Hop: 37, state: [0.         0.         0.5        0.24999905 0.25000095]\n",
      "Hop: 38, state: [0.50000095 0.49999905 0.         0.         0.        ]\n",
      "Hop: 39, state: [0.         0.         0.5        0.24999952 0.25000048]\n",
      "Hop: 40, state: [0.5000005  0.49999952 0.         0.         0.        ]\n",
      "Hop: 41, state: [0.         0.         0.5        0.24999976 0.25000024]\n",
      "Hop: 42, state: [0.50000024 0.49999976 0.         0.         0.        ]\n",
      "Hop: 43, state: [0.         0.         0.5        0.24999988 0.25000012]\n",
      "Hop: 44, state: [0.5000001  0.49999988 0.         0.         0.        ]\n",
      "Hop: 45, state: [0.         0.         0.5        0.24999994 0.25000006]\n",
      "Hop: 46, state: [0.50000006 0.49999994 0.         0.         0.        ]\n",
      "Hop: 47, state: [0.         0.         0.5        0.24999997 0.25000003]\n",
      "Hop: 48, state: [0.5        0.49999997 0.         0.         0.        ]\n",
      "Hop: 49, state: [0.         0.         0.5        0.24999999 0.25      ]\n",
      "Hop: 50, state: [0.5 0.5 0.  0.  0. ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.5, 0.5, 0. , 0. , 0. ], dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transition(g=a, n0=0, hops=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $P^3$, $P^3_\\alpha$, $RP^3_\\beta$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading the dataset and splitting it in the usual way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Movielens10M: Verifying data consistency...\n",
      "Movielens10M: Verifying data consistency... Passed!\n",
      "DataReader: current dataset is: Movielens10M\n",
      "\tNumber of items: 10681\n",
      "\tNumber of users: 69878\n",
      "\tNumber of interactions in URM_all: 10000054\n",
      "\tValue range in URM_all: 0.50-5.00\n",
      "\tInteraction density: 1.34E-02\n",
      "\tInteractions per user:\n",
      "\t\t Min: 2.00E+01\n",
      "\t\t Avg: 1.43E+02\n",
      "\t\t Max: 7.36E+03\n",
      "\tInteractions per item:\n",
      "\t\t Min: 0.00E+00\n",
      "\t\t Avg: 9.36E+02\n",
      "\t\t Max: 3.49E+04\n",
      "\tGini Index: 0.57\n",
      "\n",
      "\tICM name: ICM_tags, Value range: 1.00 / 69.00, Num features: 10106, feature occurrences: 106820, density 9.90E-04\n",
      "\tICM name: ICM_genres, Value range: 1.00 / 1.00, Num features: 20, feature occurrences: 21564, density 1.01E-01\n",
      "\tICM name: ICM_all, Value range: 1.00 / 69.00, Num features: 10126, feature occurrences: 128384, density 1.19E-03\n",
      "\tICM name: ICM_year, Value range: 1.92E+03 / 2.01E+03, Num features: 1, feature occurrences: 10681, density 1.00E+00\n",
      "\n",
      "\n",
      "Warning: 70 (0.10 %) of 69878 users have no sampled items\n",
      "Warning: 227 (0.32 %) of 69878 users have no sampled items\n"
     ]
    }
   ],
   "source": [
    "from Data_manager.split_functions.split_train_validation_random_holdout import split_train_in_two_percentage_global_sample\n",
    "from Data_manager.Movielens.Movielens10MReader import Movielens10MReader\n",
    "\n",
    "data_reader = Movielens10MReader()\n",
    "data_loaded = data_reader.load_data()\n",
    "\n",
    "URM_all = data_loaded.get_URM_all()\n",
    "\n",
    "URM_train_val, URM_test = split_train_in_two_percentage_global_sample(URM_all, 0.8)\n",
    "URM_train, URM_val = split_train_in_two_percentage_global_sample(URM_train_val, 0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our transition function would pretty much still work to build a random-walk based recommender. PROBLEM: this is not an illustrative example. We are dealing with tens of millions of interactions within a matrix that is immensely sparse! Computing it in full as we have done before would kill the program due to memory issues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def transition_matrix(g : np.ndarray, hops : int):\n",
    "    # initial state\n",
    "    state = np.diag(np.ones(g.shape))\n",
    "\n",
    "    # compute transition probability matrix (can be done once)\n",
    "    transition_probability_matrix = np.array([x / x.sum().astype(np.float32) for x in g], dtype=np.float32) # -> this is equivalent to a column-wise l1 normalization\n",
    "    # print(transition_probability_matrix)\n",
    "\n",
    "    j = 0\n",
    "    print(\"Hop: 0, state: {}\".format(state))\n",
    "    while j != hops:\n",
    "        state = state.dot(transition_probability_matrix)\n",
    "        print(\"Hop: {}, state: {}\".format(j+1, state))\n",
    "        j += 1\n",
    "    return state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To save RAM, we will compute the matrix multiplications in gradual blocks, and store each block in one data structure that will be built up incrementally. Introducing the `Incremental_Similarity_Builder`, a structure built for this exact purpose you can find in the framework:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Incremental_Similarity_Builder:\n",
    "    \n",
    "    def __init__(self, matrix_size_0, matrix_size_1, initial_data_block = 10000000, additional_data_block = 10000000, dtype = np.float32):\n",
    "\n",
    "        self._matrix_size = [matrix_size_0, matrix_size_1]\n",
    "        self._initial_data_block = initial_data_block\n",
    "        self._additional_data_block = additional_data_block\n",
    "        self._next_cell_pointer = 0\n",
    "\n",
    "        self._dtype_data = dtype\n",
    "        self._dtype_coordinates = np.uint32\n",
    "        self._max_value_of_coordinate_dtype = np.iinfo(self._dtype_coordinates).max\n",
    "\n",
    "        self._row_array = np.zeros(self._initial_data_block, dtype=self._dtype_coordinates)\n",
    "        self._col_array = np.zeros(self._initial_data_block, dtype=self._dtype_coordinates)\n",
    "        self._data_array = np.zeros(self._initial_data_block, dtype=self._dtype_data)\n",
    "\n",
    "\n",
    "    def add_data_lists(self, row_list_to_add, col_list_to_add, data_list_to_add):\n",
    "\n",
    "        for data_point_index in range(len(row_list_to_add)):\n",
    "\n",
    "            if self._next_cell_pointer == len(self._row_array):\n",
    "                self._row_array = np.concatenate((self._row_array, np.zeros(self._additional_data_block, dtype=self._dtype_coordinates)))\n",
    "                self._col_array = np.concatenate((self._col_array, np.zeros(self._additional_data_block, dtype=self._dtype_coordinates)))\n",
    "                self._data_array = np.concatenate((self._data_array, np.zeros(self._additional_data_block, dtype=self._dtype_data)))\n",
    "\n",
    "            self._row_array[self._next_cell_pointer] = row_list_to_add[data_point_index]\n",
    "            self._col_array[self._next_cell_pointer] = col_list_to_add[data_point_index]\n",
    "            self._data_array[self._next_cell_pointer] = data_list_to_add[data_point_index]\n",
    "\n",
    "            self._next_cell_pointer += 1\n",
    "\n",
    "    def get_SparseMatrix(self):\n",
    "\n",
    "        shape = (self._matrix_size[0], self._matrix_size[1])\n",
    "\n",
    "        sparseMatrix = sps.csr_matrix((self._data_array[:self._next_cell_pointer],\n",
    "                                       (self._row_array[:self._next_cell_pointer], self._col_array[:self._next_cell_pointer])),\n",
    "                                      shape=shape,\n",
    "                                      dtype=self._dtype_data)\n",
    "\n",
    "        sparseMatrix.eliminate_zeros()\n",
    "\n",
    "        return sparseMatrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the help of `Incremental_Similarity_Builder` we can now build the block-based matrix multiplication. To additionally increase sparsity in order to save memory, we can select the top-K greatest values for each row using `similarityMatrixTopK`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Recommenders.Recommender_utils import similarityMatrixTopK\n",
    "\n",
    "def block_mul(matrix_1, matrix_2, block_dim : int = 200, topK = 100, normalize_sim : bool = False, degree = None):\n",
    "\n",
    "    similarity_builder = Incremental_Similarity_Builder(matrix_1.shape[0], matrix_2.shape[1], initial_data_block=matrix_2.shape[1]*topK, dtype = np.float32)\n",
    "\n",
    "    for current_block_start_row in range(0, matrix_1.shape[0], block_dim):\n",
    "\n",
    "        if current_block_start_row + block_dim > matrix_1.shape[0]:\n",
    "            block_dim = matrix_1.shape[0] - current_block_start_row\n",
    "\n",
    "        similarity_block = matrix_1[current_block_start_row:current_block_start_row + block_dim, :] * matrix_2\n",
    "        similarity_block = similarity_block.toarray()\n",
    "\n",
    "        for row_in_block in range(block_dim):\n",
    "            row_data = similarity_block[row_in_block, :]\n",
    "            if degree is not None : row_data = np.multiply(row_data, degree)\n",
    "            if current_block_start_row + row_in_block < matrix_2.shape[1]:\n",
    "                row_data[current_block_start_row + row_in_block] = 0 # <-- elements on diagonal are set to 0, prevent obvious solution\n",
    "\n",
    "            relevant_items_partition = np.argpartition(-row_data, topK-1, axis=0)[:topK]\n",
    "            row_data = row_data[relevant_items_partition]\n",
    "\n",
    "            # Incrementally build sparse matrix, do not add zeros\n",
    "            if np.any(row_data == 0.0):\n",
    "                non_zero_mask = row_data != 0.0\n",
    "                relevant_items_partition = relevant_items_partition[non_zero_mask]\n",
    "                row_data = row_data[non_zero_mask]\n",
    "\n",
    "            similarity_builder.add_data_lists(row_list_to_add=np.ones(len(row_data), dtype = np.int32) * (current_block_start_row + row_in_block),\n",
    "                                            col_list_to_add=relevant_items_partition,\n",
    "                                            data_list_to_add=row_data)\n",
    "\n",
    "    W_sparse = similarity_builder.get_SparseMatrix()\n",
    "\n",
    "    if normalize_sim:\n",
    "        W_sparse = normalize(W_sparse, norm='l1', axis=1)\n",
    "\n",
    "    if topK and W_sparse.get_shape()[0] == W_sparse.get_shape()[1]:\n",
    "        W_sparse = similarityMatrixTopK(W_sparse, k=topK)\n",
    "\n",
    "    return W_sparse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a functional block-based matrix multiplication, we can re-build the transition function. To increase efficiency even more, we can exploit the sparsity of the transition probability matrix:$$\\begin{bmatrix}0 & P_{ui} \\\\ P_{iu} & 0\\end{bmatrix}.$$ Remember that $P_{ui}$ is nothing more than the column-wise L1 normalization of $URM$, and $P_{iu}$ is the analogous normalization of $URM^T$. After 3 random walk steps, the state matrix looks like this: $$\\begin{bmatrix}0 & P_{ui}\\cdot P_{iu}\\cdot P_{ui} \\\\ P_{iu} \\cdot P_{ui} \\cdot P_{iu} & 0\\end{bmatrix}.$$\n",
    "Since the only random walk meta-path we care about is $U \\rightarrow I \\rightarrow U \\rightarrow I$, we can compute the top-right portion of the matrix and ignore the rest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We don't need to compute the full matrix, we just need Pui and Piu which we can compute from the URM\n",
    "def transition_matrix_blocks(URM, hops : int, alpha : float = 1., beta : float = 1., topK : int = 100, extract_similarity : bool = False, normalize_sim : bool = False):\n",
    "\n",
    "    # compute Pui (column-wise l1 norm)\n",
    "    P_ui = normalize(URM, norm='l1', axis=1)\n",
    "\n",
    "    # compute Piu (column-wise l1 norm over TRANSPOSED URM)\n",
    "    t_URM = URM.transpose(copy=True)\n",
    "    t_URM.data = np.ones(t_URM.data.size, np.float32) # <- we binarize: weights, if present, are already in P_ui\n",
    "\n",
    "    if beta != 1. : # RP3beta\n",
    "\n",
    "        t_URM_sum = np.array(t_URM.sum(axis=1)).ravel()\n",
    "        degree = np.zeros(URM.shape[1])\n",
    "\n",
    "        non_zero_mask = (t_URM_sum!=0.0)\n",
    "        degree[non_zero_mask] = np.power(t_URM_sum[non_zero_mask], -beta)\n",
    "    else : degree = None\n",
    "\n",
    "    P_iu = normalize(t_URM, norm='l1', axis=1) # <- axis is still 1, because transposition was performed beforehand\n",
    "    del(t_URM) # <- save memory\n",
    "\n",
    "    if alpha != 1. : # P3alpha\n",
    "        P_ui = P_ui.power(alpha)\n",
    "        P_iu = P_iu.power(alpha)\n",
    "\n",
    "    j = 1\n",
    "    state = P_ui \n",
    "    deg = None\n",
    "\n",
    "    # equivalence to similarity item-based model: extracting sim matrix could be useful for hybrids\n",
    "    sim_matrix = P_iu if extract_similarity else None\n",
    "    \n",
    "    while j < hops:\n",
    "        if j == hops - 1: deg = degree\n",
    "        if j % 2 != 0:\n",
    "            state = block_mul(state, P_iu, topK=topK, normalize_sim=normalize_sim, degree=deg) # state * P_iu\n",
    "            if extract_similarity and (j > 1 and j < hops - 1) :\n",
    "                sim_matrix = block_mul(sim_matrix, P_iu, topK=topK, normalize_sim=normalize_sim, degree=deg) # sim_matrix * P_iu\n",
    "        else:\n",
    "            state = block_mul(state, P_ui, topK=topK, normalize_sim=normalize_sim, degree=deg) # state * P_ui\n",
    "            if extract_similarity and (j >= 1 and j < hops - 1) :\n",
    "                sim_matrix = block_mul(sim_matrix, P_ui, topK=topK, normalize_sim=normalize_sim, degree=deg) # sim_matrix * P_ui\n",
    "        j += 1\n",
    "\n",
    "    return state, sim_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the hyperparameters $\\alpha$ and $\\beta$ act within the function: we can set those to some value in order to compute $P^3_\\alpha$ and/or $RP^3_\\beta$. The `extract_similarity` flag allows us to extract also a similarity matrix we could use to build hybrids. In fact, graph-based methods can be thought of as similarity-based methods: in the case of a 3-step random walk, the matrix $P_{iu} \\cdot P_{ui}$ works as a similarity matrix, which we can multiply to any user profile to obtain recommendation predictions.\n",
    "\n",
    "Notice that creating a similarity matrix in the way we show in this notebook is inefficient in terms of memory, as it creates an additional hefty matrix which we would essentially use to compute the same predictions: for this reason, the `Recommenders.GraphBased` classes within the framework cut the ambiguities short and *only* compute the similarity matrix.\n",
    "\n",
    "Finally, let's put everything together in a `Recommender` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Optional\n",
    "from Recommenders.BaseRecommender import BaseRecommender\n",
    "\n",
    "class P3Recommender(BaseRecommender):\n",
    "    def __init__(self, URM, topK : int = 100, normalize_sim : bool = False):\n",
    "        super().__init__(URM)\n",
    "        self.topK = topK\n",
    "        self.normalize_sim = normalize_sim\n",
    "\n",
    "    def fit(self):\n",
    "        self.three_step_walk, _ = transition_matrix_blocks(self.URM_train,\n",
    "                                                           3,\n",
    "                                                           topK=self.topK,\n",
    "                                                           normalize_sim=self.normalize_sim,\n",
    "                                                           extract_similarity=False)\n",
    "\n",
    "    def recommend(self, user_id, remove_seen : bool = True, at : Optional[int] = None):\n",
    "        Pi_0 = np.zeros(self.URM_train.shape[0], dtype=np.int32)\n",
    "        Pi_0[user_id] = 1\n",
    "        Pi_0 = sps.csr_matrix(Pi_0)\n",
    "\n",
    "        ranking = Pi_0.dot(self.three_step_walk).toarray().ravel()\n",
    "\n",
    "        if remove_seen:\n",
    "            user_profile_start = self.URM_train.indptr[user_id]\n",
    "            user_profile_end = self.URM_train.indptr[user_id+1]\n",
    "            \n",
    "            seen_items = self.URM_train.indices[user_profile_start:user_profile_end]\n",
    "            \n",
    "            ranking[seen_items] = -np.inf\n",
    "            \n",
    "        ranking = np.flip(np.argsort(ranking))\n",
    "        return ranking[:at]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "class P3alphaRecommender(BaseRecommender):\n",
    "    def __init__(self, URM, alpha, topK : int = 100, normalize_sim : bool = False, extract_similarity=False):\n",
    "        super().__init__(URM)\n",
    "        self.alpha = alpha\n",
    "        self.topK = topK\n",
    "        self.normalize_sim = normalize_sim\n",
    "        self.extract_similarity = extract_similarity\n",
    "\n",
    "    def fit(self):\n",
    "        self.three_step_walk, self.sim_matrix = transition_matrix_blocks(self.URM_train,\n",
    "                                                                         3,\n",
    "                                                                         self.alpha,\n",
    "                                                                         topK=self.topK,\n",
    "                                                                         extract_similarity=self.extract_similarity,\n",
    "                                                                         normalize_sim=self.normalize_sim) # <- only change wrt P3 is the alpha exponent\n",
    "\n",
    "    def recommend(self, user_id, remove_seen : bool = True, at : Optional[int] = None):\n",
    "        Pi_0 = np.zeros(self.URM_train.shape[0], dtype=np.int32)\n",
    "        Pi_0[user_id] = 1\n",
    "        Pi_0 = sps.csr_matrix(Pi_0)\n",
    "\n",
    "        ranking = Pi_0.dot(self.three_step_walk).toarray().ravel()\n",
    "\n",
    "        if remove_seen:\n",
    "            user_profile_start = self.URM_train.indptr[user_id]\n",
    "            user_profile_end = self.URM_train.indptr[user_id+1]\n",
    "            \n",
    "            seen_items = self.URM_train.indices[user_profile_start:user_profile_end]\n",
    "            \n",
    "            ranking[seen_items] = -np.inf\n",
    "            \n",
    "        ranking = np.flip(np.argsort(ranking))\n",
    "        return ranking[:at]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RP3betaRecommender(BaseRecommender):\n",
    "    def __init__(self, URM, alpha, beta, topK : int = 100, normalize_sim : bool = False):\n",
    "        super().__init__(URM)\n",
    "        self.alpha = alpha\n",
    "        self.beta = beta\n",
    "        self.topK = topK\n",
    "        self.normalize_sim = normalize_sim\n",
    "\n",
    "    def fit(self):\n",
    "        self.three_step_walk, _ = transition_matrix_blocks(self.URM_train,\n",
    "                                                           3,\n",
    "                                                           self.alpha,\n",
    "                                                           self.beta,\n",
    "                                                           topK=self.topK,\n",
    "                                                           normalize_sim=self.normalize_sim,\n",
    "                                                           extract_similarity=False) # <- only change wrt P3alpha is beta\n",
    "\n",
    "    def recommend(self, user_id, remove_seen : bool = True, at : Optional[int] = None):\n",
    "        Pi_0 = np.zeros(self.URM_train.shape[0], dtype=np.int32)\n",
    "        Pi_0[user_id] = 1\n",
    "        Pi_0 = sps.csr_matrix(Pi_0)\n",
    "\n",
    "        ranking = Pi_0.dot(self.three_step_walk).toarray().ravel()\n",
    "\n",
    "        if remove_seen:\n",
    "            user_profile_start = self.URM_train.indptr[user_id]\n",
    "            user_profile_end = self.URM_train.indptr[user_id+1]\n",
    "            \n",
    "            seen_items = self.URM_train.indices[user_profile_start:user_profile_end]\n",
    "            \n",
    "            ranking[seen_items] = -np.inf\n",
    "            \n",
    "        ranking = np.flip(np.argsort(ranking))\n",
    "        return ranking[:at]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to evaluate the models, we implement some metrics, as seen in Practice 02."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def precision(recommended_items, relevant_items):\n",
    "    \n",
    "    is_relevant = np.in1d(recommended_items, relevant_items, assume_unique=True)\n",
    "    \n",
    "    precision_score = np.sum(is_relevant, dtype=np.float32) / len(is_relevant)\n",
    "    \n",
    "    return precision_score\n",
    "\n",
    "def recall(recommended_items, relevant_items):\n",
    "    \n",
    "    is_relevant = np.in1d(recommended_items, relevant_items, assume_unique=True)\n",
    "    \n",
    "    recall_score = np.sum(is_relevant, dtype=np.float32) / relevant_items.shape[0]\n",
    "    \n",
    "    return recall_score\n",
    "\n",
    "def AP(recommended_items, relevant_items):\n",
    "   \n",
    "    is_relevant = np.in1d(recommended_items, relevant_items, assume_unique=True)\n",
    "    \n",
    "    # Cumulative sum: precision at 1, at 2, at 3 ...\n",
    "    p_at_k = is_relevant * np.cumsum(is_relevant, dtype=np.float32) / (1 + np.arange(is_relevant.shape[0]))\n",
    "    \n",
    "    ap_score = np.sum(p_at_k) / np.min([relevant_items.shape[0], is_relevant.shape[0]])\n",
    "\n",
    "    return ap_score\n",
    "\n",
    "def evaluate_recommender(URM_test : sps.csr_matrix, recommender : BaseRecommender, cutoff : int = 10):\n",
    "    \n",
    "    cumulative_precision = 0.0\n",
    "    cumulative_recall = 0.0\n",
    "    cumulative_AP = 0.0\n",
    "    \n",
    "    num_eval = 0\n",
    "\n",
    "    for user_id in range(URM_test.shape[0]):\n",
    "\n",
    "        relevant_items = URM_test.indices[URM_test.indptr[user_id]:URM_test.indptr[user_id+1]]\n",
    "        \n",
    "        if len(relevant_items)>0:\n",
    "            \n",
    "            recommended_items = recommender.recommend(user_id, at=cutoff)\n",
    "            num_eval+=1\n",
    "\n",
    "            cumulative_precision += precision(recommended_items, relevant_items)\n",
    "            cumulative_recall += recall(recommended_items, relevant_items)\n",
    "            cumulative_AP += AP(recommended_items, relevant_items)\n",
    "            \n",
    "    cumulative_precision /= num_eval\n",
    "    cumulative_recall /= num_eval\n",
    "    MAP = cumulative_AP / num_eval\n",
    "    \n",
    "    print(\"Recommender results are: Precision = {:.4f}, Recall = {:.4f}, MAP = {:.4f}\".format(\n",
    "        cumulative_precision, cumulative_recall, MAP)) \n",
    "    \n",
    "    return MAP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now all the material necessary to fit and evaluate our classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender_Base_Class: URM Detected 33 ( 0.3%) items with no interactions.\n",
      "Recommender_Base_Class: URM Detected 33 ( 0.3%) items with no interactions.\n",
      "Recommender_Base_Class: URM Detected 33 ( 0.3%) items with no interactions.\n",
      "Recommender results are: Precision = 0.1460, Recall = 0.1225, MAP = 0.0976\n",
      "P3 trained in 2.88 min\n",
      "Recommender results are: Precision = 0.1869, Recall = 0.1282, MAP = 0.1263\n",
      "P3alpha trained in 2.85 min\n",
      "Recommender results are: Precision = 0.0701, Recall = 0.0642, MAP = 0.0399\n",
      "RP3beta trained in 2.81 min\n"
     ]
    }
   ],
   "source": [
    "# PRAXIS WHEN USING THE COURSE'S FRAMEWORK: USE EvaluatorHoldout FOR EVALUATIONS\n",
    "# from Evaluation.Evaluator import EvaluatorHoldout\n",
    "# evaluator_test = EvaluatorHoldout(URM_test, cutoff_list=[10])\n",
    "from Utils.seconds_to_biggest_unit import seconds_to_biggest_unit\n",
    "\n",
    "models = {\n",
    "    'P3' : P3Recommender(URM_train_val),\n",
    "    'P3alpha' : P3alphaRecommender(URM_train_val, alpha=0.5, extract_similarity=True),\n",
    "    'RP3beta' : RP3betaRecommender(URM_train_val, alpha=0.5, beta=0.3)\n",
    "}\n",
    "\n",
    "for model_name, model_obj in models.items():\n",
    "    time_start = time.time()\n",
    "    model_obj.fit()\n",
    "    time_end_value, time_unit = seconds_to_biggest_unit(time.time() - time_start)\n",
    "    # PRAXIS WHEN USING THE COURSE'S FRAMEWORK: result_df, _ = evaluator_test.evaluateRecommender(model_obj)\n",
    "    _ = evaluate_recommender(URM_test, model_obj)\n",
    "    print(\"{} trained in {:.2f} {}\".format(model_name, time_end_value, time_unit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using `optuna`, we can run some hyperparameter optimization trials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 15:34:57,555] A new study created in memory with name: no-name-1da03be1-3b57-48ad-83e7-adfe3df75985\n",
      "[I 2024-12-05 15:34:57,555] A new study created in memory with name: no-name-c24d9cd2-2044-4e6f-83b5-ec1c5e180a55\n"
     ]
    }
   ],
   "source": [
    "# Create and launch optuna study for each recommender. Optimize for MAP@10.\n",
    "import pandas as pd\n",
    "\n",
    "import optuna\n",
    "\n",
    "def objective_function_P3alpha(optuna_trial):\n",
    "    recommender_instance = P3alphaRecommender(URM_train,\n",
    "                                              alpha=optuna_trial.suggest_float(\"alpha\", 0.01, 0.99),\n",
    "                                              topK=optuna_trial.suggest_int(\"topK\", 5, 150),\n",
    "                                              normalize_sim=optuna_trial.suggest_int(\"normalize_sim\", 0, 1))\n",
    "\n",
    "    recommender_instance.fit()\n",
    "\n",
    "    evaluation = evaluate_recommender(URM_val, recommender_instance)\n",
    "    return evaluation\n",
    "\n",
    "def objective_function_RP3beta(optuna_trial):\n",
    "    recommender_instance = RP3betaRecommender(URM_train,\n",
    "                                              alpha=optuna_trial.suggest_float(\"alpha\", 0.01, 0.99),\n",
    "                                              beta=optuna_trial.suggest_float(\"beta\", 0.01, 0.99),\n",
    "                                              topK=optuna_trial.suggest_int(\"topK\", 5, 150),\n",
    "                                              normalize_sim=optuna_trial.suggest_int(\"normalize_sim\", 0, 1))\n",
    "    \n",
    "    recommender_instance.fit()\n",
    "    \n",
    "    evaluation = evaluate_recommender(URM_val, recommender_instance)\n",
    "    return evaluation\n",
    "\n",
    "class SaveResults(object):\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.results_df = pd.DataFrame(columns = [\"result\"])\n",
    "    \n",
    "    def __call__(self, optuna_study, optuna_trial):\n",
    "        hyperparam_dict = optuna_trial.params.copy()\n",
    "        hyperparam_dict[\"result\"] = optuna_trial.values[0]\n",
    "        \n",
    "        self.results_df = pd.concat([self.results_df, pd.DataFrame([hyperparam_dict])], ignore_index=True)\n",
    "\n",
    "optuna_study_P3alpha = optuna.create_study(direction=\"maximize\")\n",
    "optuna_study_RP3beta = optuna.create_study(direction=\"maximize\")\n",
    "save_results_P3alpha = SaveResults()\n",
    "save_results_RP3beta = SaveResults()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender_Base_Class: URM Detected 63 ( 0.6%) items with no interactions.\n"
     ]
    }
   ],
   "source": [
    "optuna_study_P3alpha.optimize(objective_function_P3alpha,\n",
    "                              callbacks=[save_results_P3alpha],\n",
    "                              n_trials=5)\n",
    "\n",
    "P3alpha_optimal = P3alphaRecommender(URM_train_val,\n",
    "                                     alpha=optuna_study_P3alpha.best_trial.params['alpha'],\n",
    "                                     topK=optuna_study_P3alpha.best_trial.params['topK'],\n",
    "                                     normalize_sim=optuna_study_P3alpha.best_trial.params['normalize_sim'])\n",
    "P3alpha_optimal.fit()\n",
    "_ = evaluate_recommender(URM_test, P3alpha_optimal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:17:18,825] Trial 0 finished with value: 0.0007832848526214606 and parameters: {'alpha': 0.13816576352217333, 'beta': 0.7675199258210855, 'topK': 74, 'normalize_sim': 0}. Best is trial 0 with value: 0.0007832848526214606.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0023, Recall = 0.0026, MAP = 0.0008\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/pp/q0kl1bl507q_7gsf1tczbrg80000gn/T/ipykernel_36348/1586423476.py:38: FutureWarning:\n",
      "\n",
      "The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "\n",
      "[I 2024-12-05 11:22:20,438] Trial 1 finished with value: 0.011508608619804454 and parameters: {'alpha': 0.15830414583349872, 'beta': 0.34858823902629654, 'topK': 57, 'normalize_sim': 0}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0212, Recall = 0.0286, MAP = 0.0115\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:30:24,973] Trial 2 finished with value: 0.00697170031549431 and parameters: {'alpha': 0.606117578606874, 'beta': 0.5900084759332745, 'topK': 136, 'normalize_sim': 1}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0131, Recall = 0.0199, MAP = 0.0070\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:36:33,305] Trial 3 finished with value: 0.0004824428943243249 and parameters: {'alpha': 0.06605006757828416, 'beta': 0.9410833280888563, 'topK': 99, 'normalize_sim': 1}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0017, Recall = 0.0007, MAP = 0.0005\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:41:39,812] Trial 4 finished with value: 0.004936541207895078 and parameters: {'alpha': 0.8060329781280261, 'beta': 0.6542546332371698, 'topK': 64, 'normalize_sim': 0}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0110, Recall = 0.0143, MAP = 0.0049\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:46:27,976] Trial 5 finished with value: 0.0010867754159389238 and parameters: {'alpha': 0.3317446611261399, 'beta': 0.7087016501008411, 'topK': 66, 'normalize_sim': 1}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0033, Recall = 0.0029, MAP = 0.0011\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:49:37,849] Trial 6 finished with value: 0.0010287106722887886 and parameters: {'alpha': 0.13398871960676667, 'beta': 0.7339761601892191, 'topK': 20, 'normalize_sim': 0}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0027, Recall = 0.0029, MAP = 0.0010\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:55:55,292] Trial 7 finished with value: 0.0038113592712490673 and parameters: {'alpha': 0.08170106716394615, 'beta': 0.5109778981140413, 'topK': 103, 'normalize_sim': 1}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0079, Recall = 0.0117, MAP = 0.0038\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 11:58:55,676] Trial 8 finished with value: 0.0027386509046307818 and parameters: {'alpha': 0.5839069631159212, 'beta': 0.406539203723294, 'topK': 17, 'normalize_sim': 1}. Best is trial 1 with value: 0.011508608619804454.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0052, Recall = 0.0070, MAP = 0.0027\n",
      "Recommender_Base_Class: URM Detected 72 ( 0.7%) items with no interactions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[I 2024-12-05 12:08:05,341] Trial 9 finished with value: 0.04475421056481944 and parameters: {'alpha': 0.8410532210931146, 'beta': 0.20883840392024278, 'topK': 146, 'normalize_sim': 1}. Best is trial 9 with value: 0.04475421056481944.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.0754, Recall = 0.0923, MAP = 0.0448\n",
      "Recommender_Base_Class: URM Detected 31 ( 0.3%) items with no interactions.\n",
      "Recommender results are: Precision = 0.1015, Recall = 0.1020, MAP = 0.0621\n"
     ]
    }
   ],
   "source": [
    "optuna_study_RP3beta.optimize(objective_function_RP3beta,\n",
    "                              callbacks=[save_results_RP3beta],\n",
    "                              n_trials=5)\n",
    "\n",
    "RP3beta_optimal = RP3betaRecommender(URM_train_val,\n",
    "                                     alpha=optuna_study_RP3beta.best_trial.params['alpha'],\n",
    "                                     beta=optuna_study_RP3beta.best_trial.params['beta'],\n",
    "                                     topK=optuna_study_RP3beta.best_trial.params['topK'],\n",
    "                                     normalize_sim=optuna_study_RP3beta.best_trial.params['normalize_sim'])\n",
    "\n",
    "RP3beta_optimal.fit()\n",
    "_ = evaluate_recommender(URM_test, RP3beta_optimal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following cell, we show how to correctly import, fit and evaluate a `Recommenders.GraphBased` model straight from the framework."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RP3betaRecommender: URM Detected 31 ( 0.3%) items with no interactions.\n",
      "RP3betaRecommender: Similarity column 10681 (100.0%), 1681.39 column/sec. Elapsed time 6.35 sec\n",
      "EvaluatorHoldout: Ignoring 81 ( 0.1%) Users that have less than 1 test interactions\n",
      "EvaluatorHoldout: Processed 69797 (100.0%) in 11.56 sec. Users per second: 6037\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECISION</th>\n",
       "      <th>PRECISION_RECALL_MIN_DEN</th>\n",
       "      <th>RECALL</th>\n",
       "      <th>MAP</th>\n",
       "      <th>MAP_MIN_DEN</th>\n",
       "      <th>MRR</th>\n",
       "      <th>NDCG</th>\n",
       "      <th>F1</th>\n",
       "      <th>HIT_RATE</th>\n",
       "      <th>ARHR_ALL_HITS</th>\n",
       "      <th>...</th>\n",
       "      <th>COVERAGE_USER</th>\n",
       "      <th>COVERAGE_USER_HIT</th>\n",
       "      <th>USERS_IN_GT</th>\n",
       "      <th>DIVERSITY_GINI</th>\n",
       "      <th>SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_DIVERSITY_HERFINDAHL</th>\n",
       "      <th>RATIO_DIVERSITY_GINI</th>\n",
       "      <th>RATIO_SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_AVERAGE_POPULARITY</th>\n",
       "      <th>RATIO_NOVELTY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.276798</td>\n",
       "      <td>0.319192</td>\n",
       "      <td>0.181803</td>\n",
       "      <td>0.19267</td>\n",
       "      <td>0.215998</td>\n",
       "      <td>0.576656</td>\n",
       "      <td>0.27116</td>\n",
       "      <td>0.219462</td>\n",
       "      <td>0.82366</td>\n",
       "      <td>1.013639</td>\n",
       "      <td>...</td>\n",
       "      <td>0.998841</td>\n",
       "      <td>0.822705</td>\n",
       "      <td>0.998841</td>\n",
       "      <td>0.008337</td>\n",
       "      <td>6.650779</td>\n",
       "      <td>0.982606</td>\n",
       "      <td>0.042818</td>\n",
       "      <td>0.587265</td>\n",
       "      <td>2.222096</td>\n",
       "      <td>0.069</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECISION PRECISION_RECALL_MIN_DEN    RECALL      MAP MAP_MIN_DEN  \\\n",
       "cutoff                                                                     \n",
       "10      0.276798                 0.319192  0.181803  0.19267    0.215998   \n",
       "\n",
       "             MRR     NDCG        F1 HIT_RATE ARHR_ALL_HITS  ... COVERAGE_USER  \\\n",
       "cutoff                                                      ...                 \n",
       "10      0.576656  0.27116  0.219462  0.82366      1.013639  ...      0.998841   \n",
       "\n",
       "       COVERAGE_USER_HIT USERS_IN_GT DIVERSITY_GINI SHANNON_ENTROPY  \\\n",
       "cutoff                                                                \n",
       "10              0.822705    0.998841       0.008337        6.650779   \n",
       "\n",
       "       RATIO_DIVERSITY_HERFINDAHL RATIO_DIVERSITY_GINI RATIO_SHANNON_ENTROPY  \\\n",
       "cutoff                                                                         \n",
       "10                       0.982606             0.042818              0.587265   \n",
       "\n",
       "       RATIO_AVERAGE_POPULARITY RATIO_NOVELTY  \n",
       "cutoff                                         \n",
       "10                     2.222096         0.069  \n",
       "\n",
       "[1 rows x 27 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from Recommenders.GraphBased.RP3betaRecommender import RP3betaRecommender\n",
    "from Evaluation.Evaluator import EvaluatorHoldout\n",
    "\n",
    "recommender_fw = RP3betaRecommender(URM_train_val)\n",
    "recommender_fw.fit(alpha=0.5, beta=0.3, topK=RP3beta_optimal.topK, normalize_similarity=RP3beta_optimal.normalize_sim)\n",
    "\n",
    "evaluator_test = EvaluatorHoldout(URM_test, [10])\n",
    "\n",
    "# evaluate_recommender(URM_test, recommender_try)\n",
    "result_fw_df, _ = evaluator_test.evaluateRecommender(recommender_fw)\n",
    "result_fw_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now compare $P^3$, $P^3_\\alpha$ and $RP^3_\\beta$. Plotting each model's recommendation frequencies, we can have an idea of how much their predictions differ. Also, we can assess each model in terms of recommendation *diversity*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_rec_frequencies(list_recommenders, URM_all, TopPop_order : bool = False):\n",
    "\n",
    "    x_tick = np.arange(URM_all.shape[1])\n",
    "    counters = [np.zeros(URM_all.shape[1]) for i in range(len(list_recommenders))]\n",
    "\n",
    "    for user_id in range(URM_all.shape[0]):\n",
    "\n",
    "        for i in range(len(list_recommenders)):\n",
    "            recs = list_recommenders[i].recommend(user_id, at=10)\n",
    "            counters[i][recs] += 1\n",
    "        \n",
    "    if TopPop_order:\n",
    "        item_popularity = np.ediff1d(URM_all.tocsc().indptr)\n",
    "        sorted_items = np.argsort(item_popularity)\n",
    "        sorted_items = np.flip(sorted_items, axis=0)\n",
    "    else:\n",
    "        sorted_items = np.argsort(-counters[0])\n",
    "        \n",
    "    for j in range(len(counters)):    \n",
    "        plt.plot(x_tick, counters[j][sorted_items], label = \"Model {}\".format(j))\n",
    "    if TopPop_order : plt.plot(x_tick, item_popularity[sorted_items], label = \"TopPop\")\n",
    "\n",
    "    plt.ylabel('Number of recommendations')\n",
    "    plt.xlabel('Items')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'P3alpha_optimal' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[24], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m plot_rec_frequencies([models[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mP3\u001b[39m\u001b[38;5;124m'\u001b[39m], \u001b[43mP3alpha_optimal\u001b[49m, RP3beta_optimal], URM_all)\n",
      "\u001b[0;31mNameError\u001b[0m: name 'P3alpha_optimal' is not defined"
     ]
    }
   ],
   "source": [
    "plot_rec_frequencies([models['P3'], P3alpha_optimal, RP3beta_optimal], URM_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P^3$ provides recommendations that are noticeably less diverse than the other models. See how short and skewed its \"short head\" is?\n",
    "\n",
    "### $P^5$, $P^7$\n",
    "\n",
    "The random walk we perform has not necessarily got to be 3 steps long: any odd number of steps will work (3, 5, 7...), with varying degrees of success. We can build a `Recommender` class that takes this into account, using the same structure as the previous `P3Recommender`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# P5/P7 e come cambiano le raccomandazioni/similarity density (se la RAM regge) --> se non regge, applicare KNN come da framework (similarityMatrixTopK)\n",
    "class PXRecommender(BaseRecommender):\n",
    "    def __init__(self, URM, hops : int):\n",
    "        self.URM = URM\n",
    "        self.hops = hops\n",
    "        if hops % 2 == 0:\n",
    "            raise ValueError(\"Number of hops must be odd.\")\n",
    "\n",
    "    def fit(self):\n",
    "        self.n_step_walk, _ = transition_matrix_blocks(self.URM, self.hops, extract_similarity=False)\n",
    "\n",
    "    def recommend(self, user_id, remove_seen : bool = True, at : Optional[int] = None):\n",
    "        Pi_0 = np.zeros(self.URM.shape[0], dtype=np.int32)\n",
    "        Pi_0[user_id] = 1\n",
    "        Pi_0 = sps.csr_matrix(Pi_0)\n",
    "\n",
    "        ranking = Pi_0.dot(self.n_step_walk).toarray().ravel()\n",
    "\n",
    "        if remove_seen:\n",
    "            user_profile_start = self.URM.indptr[user_id]\n",
    "            user_profile_end = self.URM.indptr[user_id+1]\n",
    "            \n",
    "            seen_items = self.URM.indices[user_profile_start:user_profile_end]\n",
    "            \n",
    "            ranking[seen_items] = -np.inf\n",
    "            \n",
    "        ranking = np.flip(np.argsort(ranking))\n",
    "        return ranking[:at]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now train, test and compare three graph-based models that differ in the number of steps they make in their random walks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommender results are: Precision = 0.1471, Recall = 0.1231, MAP = 0.0986\n",
      "P3 trained in 2.88 min\n",
      "Recommender results are: Precision = 0.1100, Recall = 0.0793, MAP = 0.0650\n",
      "P5 trained in 5.54 min\n",
      "Recommender results are: Precision = 0.1033, Recall = 0.0743, MAP = 0.0602\n",
      "P7 trained in 8.01 min\n"
     ]
    }
   ],
   "source": [
    "# Compute recommendations on test set with P3, P5 and P7\n",
    "models = {\n",
    "    'P3' : PXRecommender(URM_train_val, hops=3),\n",
    "    'P5' : PXRecommender(URM_train_val, hops=5),\n",
    "    'P7' : PXRecommender(URM_train_val, hops=7)\n",
    "}\n",
    "\n",
    "for model_name, model_obj in models.items():\n",
    "    time_start = time.time()\n",
    "    model_obj.fit()\n",
    "    time_end_value, time_unit = seconds_to_biggest_unit(time.time() - time_start)\n",
    "    # PRAXIS WHEN USING THE COURSE'S FRAMEWORK: result_df, _ = evaluator_test.evaluateRecommender(model_obj)\n",
    "    _ = evaluate_recommender(URM_test, model_obj)\n",
    "    print(\"{} trained in {:.2f} {}\".format(model_name, time_end_value, time_unit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the more steps we take, the worse the model performs, both in terms of MAP and of training time. This is not by chance: obviously, we need to perform more computations; also, the more steps a random walk is composed of, the more we *smoothe* interaction signals (i.e., the recommender we obtain becomes more and more prone to **Popularity bias**)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[26], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Popularity plot\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mplot_rec_frequencies\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43my\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43m_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mmodels\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mitems\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mURM_all\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mTopPop_order\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[0;32mIn[23], line 11\u001b[0m, in \u001b[0;36mplot_rec_frequencies\u001b[0;34m(list_recommenders, URM_all, TopPop_order)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m user_id \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(URM_all\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m]):\n\u001b[1;32m     10\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28mlen\u001b[39m(list_recommenders)):\n\u001b[0;32m---> 11\u001b[0m         recs \u001b[38;5;241m=\u001b[39m \u001b[43mlist_recommenders\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrecommend\u001b[49m\u001b[43m(\u001b[49m\u001b[43muser_id\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mat\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     12\u001b[0m         counters[i][recs] \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m     14\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m TopPop_order:\n",
      "Cell \u001b[0;32mIn[18], line 22\u001b[0m, in \u001b[0;36mP3Recommender.recommend\u001b[0;34m(self, user_id, remove_seen, at)\u001b[0m\n\u001b[1;32m     19\u001b[0m Pi_0[user_id] \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m     20\u001b[0m Pi_0 \u001b[38;5;241m=\u001b[39m sps\u001b[38;5;241m.\u001b[39mcsr_matrix(Pi_0)\n\u001b[0;32m---> 22\u001b[0m ranking \u001b[38;5;241m=\u001b[39m \u001b[43mPi_0\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdot\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mthree_step_walk\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mtoarray()\u001b[38;5;241m.\u001b[39mravel()\n\u001b[1;32m     24\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m remove_seen:\n\u001b[1;32m     25\u001b[0m     user_profile_start \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mURM_train\u001b[38;5;241m.\u001b[39mindptr[user_id]\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages/scipy/sparse/_base.py:474\u001b[0m, in \u001b[0;36m_spbase.dot\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    472\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m \u001b[38;5;241m*\u001b[39m other\n\u001b[1;32m    473\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 474\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m@\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mother\u001b[49m\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages/scipy/sparse/_base.py:695\u001b[0m, in \u001b[0;36m_spbase.__matmul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    692\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m isscalarlike(other):\n\u001b[1;32m    693\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mScalar operands are not allowed, \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    694\u001b[0m                      \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124muse \u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m*\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m instead\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m--> 695\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_matmul_dispatch\u001b[49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages/scipy/sparse/_base.py:606\u001b[0m, in \u001b[0;36m_spbase._matmul_dispatch\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    604\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m other\u001b[38;5;241m.\u001b[39mndim \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m    605\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mCannot yet multiply a 1d sparse array\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m--> 606\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_matmul_sparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    608\u001b[0m \u001b[38;5;66;03m# If it's a list or whatever, treat it like an array\u001b[39;00m\n\u001b[1;32m    609\u001b[0m other_a \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39masanyarray(other)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/RSFramework/lib/python3.9/site-packages/scipy/sparse/_compressed.py:535\u001b[0m, in \u001b[0;36m_cs_matrix._matmul_sparse\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    532\u001b[0m data \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mempty(nnz, dtype\u001b[38;5;241m=\u001b[39mupcast(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mdtype, other\u001b[38;5;241m.\u001b[39mdtype))\n\u001b[1;32m    534\u001b[0m fn \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(_sparsetools, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mformat \u001b[38;5;241m+\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m_matmat\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m--> 535\u001b[0m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[43mM\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mN\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43masarray\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mindptr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43midx_dtype\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    536\u001b[0m \u001b[43m   \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43masarray\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mindices\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43midx_dtype\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    537\u001b[0m \u001b[43m   \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    538\u001b[0m \u001b[43m   \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43masarray\u001b[49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mindptr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43midx_dtype\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    539\u001b[0m \u001b[43m   \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43masarray\u001b[49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mindices\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43midx_dtype\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    540\u001b[0m \u001b[43m   \u001b[49m\u001b[43mother\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    541\u001b[0m \u001b[43m   \u001b[49m\u001b[43mindptr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mindices\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    543\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__class__\u001b[39m((data, indices, indptr), shape\u001b[38;5;241m=\u001b[39m(M, N))\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Popularity plot\n",
    "plot_rec_frequencies([y for _, y in models.items()], URM_all, TopPop_order=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even so, it is easy to make hybrids of graph-based models using different steps, as they have the same model structure."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding Content Metadata to the Mix\n",
    "\n",
    "*Tripartite graph*: in this case, we don't only have to deal with users and items. Content-based attributes are inserted into the graph as a third class of nodes, creating an adjacency matrix that looks like this:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Notice how attributes are only connected to items. A case for user-related attributes can also be explored, but it is out of the scope of this practice session.\n",
    "\n",
    "#### How do Random Walks change?\n",
    "\n",
    "Now, we are not only interested in the $U \\rightarrow I \\rightarrow U \\rightarrow I$ meta-path, as we can structure random walks that also follow the $U \\rightarrow I \\rightarrow A \\rightarrow I$ meta-path. We will need to handle this case as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ICM_genres = data_loaded.get_loaded_ICM_dict()[\"ICM_genres\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RP3betaRecommender: URM Detected 31 ( 0.3%) items with no interactions.\n",
      "RP3betaRecommender: Similarity column 10681 (100.0%), 1696.29 column/sec. Elapsed time 6.30 sec\n",
      "RP3betaRecommender: Similarity column 10681 (100.0%), 7347.02 column/sec. Elapsed time 1.45 sec\n",
      "ItemKNNCustomSimilarityRecommender: URM Detected 31 ( 0.3%) items with no interactions.\n",
      "EvaluatorHoldout: Ignoring 81 ( 0.1%) Users that have less than 1 test interactions\n",
      "EvaluatorHoldout: Processed 69797 (100.0%) in 15.19 sec. Users per second: 4594\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECISION</th>\n",
       "      <th>PRECISION_RECALL_MIN_DEN</th>\n",
       "      <th>RECALL</th>\n",
       "      <th>MAP</th>\n",
       "      <th>MAP_MIN_DEN</th>\n",
       "      <th>MRR</th>\n",
       "      <th>NDCG</th>\n",
       "      <th>F1</th>\n",
       "      <th>HIT_RATE</th>\n",
       "      <th>ARHR_ALL_HITS</th>\n",
       "      <th>...</th>\n",
       "      <th>COVERAGE_USER</th>\n",
       "      <th>COVERAGE_USER_HIT</th>\n",
       "      <th>USERS_IN_GT</th>\n",
       "      <th>DIVERSITY_GINI</th>\n",
       "      <th>SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_DIVERSITY_HERFINDAHL</th>\n",
       "      <th>RATIO_DIVERSITY_GINI</th>\n",
       "      <th>RATIO_SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_AVERAGE_POPULARITY</th>\n",
       "      <th>RATIO_NOVELTY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.302258</td>\n",
       "      <td>0.345797</td>\n",
       "      <td>0.191316</td>\n",
       "      <td>0.217371</td>\n",
       "      <td>0.24167</td>\n",
       "      <td>0.603101</td>\n",
       "      <td>0.292025</td>\n",
       "      <td>0.234318</td>\n",
       "      <td>0.838847</td>\n",
       "      <td>1.096253</td>\n",
       "      <td>...</td>\n",
       "      <td>0.998841</td>\n",
       "      <td>0.837875</td>\n",
       "      <td>0.998841</td>\n",
       "      <td>0.01167</td>\n",
       "      <td>7.081081</td>\n",
       "      <td>0.986881</td>\n",
       "      <td>0.059933</td>\n",
       "      <td>0.625261</td>\n",
       "      <td>2.079951</td>\n",
       "      <td>0.070043</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECISION PRECISION_RECALL_MIN_DEN    RECALL       MAP MAP_MIN_DEN  \\\n",
       "cutoff                                                                      \n",
       "10      0.302258                 0.345797  0.191316  0.217371     0.24167   \n",
       "\n",
       "             MRR      NDCG        F1  HIT_RATE ARHR_ALL_HITS  ...  \\\n",
       "cutoff                                                        ...   \n",
       "10      0.603101  0.292025  0.234318  0.838847      1.096253  ...   \n",
       "\n",
       "       COVERAGE_USER COVERAGE_USER_HIT USERS_IN_GT DIVERSITY_GINI  \\\n",
       "cutoff                                                              \n",
       "10          0.998841          0.837875    0.998841        0.01167   \n",
       "\n",
       "       SHANNON_ENTROPY RATIO_DIVERSITY_HERFINDAHL RATIO_DIVERSITY_GINI  \\\n",
       "cutoff                                                                   \n",
       "10            7.081081                   0.986881             0.059933   \n",
       "\n",
       "       RATIO_SHANNON_ENTROPY RATIO_AVERAGE_POPULARITY RATIO_NOVELTY  \n",
       "cutoff                                                               \n",
       "10                  0.625261                 2.079951      0.070043  \n",
       "\n",
       "[1 rows x 27 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from Recommenders.GraphBased.RP3betaRecommender import RP3betaRecommender\n",
    "from Recommenders.KNN.ItemKNNCustomSimilarityRecommender import ItemKNNCustomSimilarityRecommender\n",
    "from Evaluation.Evaluator import EvaluatorHoldout\n",
    "\n",
    "icm_weight = 0.5 # <- tunable hyperparameter\n",
    "\n",
    "# Train graph-based recommender\n",
    "# U -> I -> [U -> I] <-- normal RP3beta\n",
    "u_i_recommender = RP3betaRecommender(URM_train_val)\n",
    "u_i_recommender.fit(alpha=0.5, beta=0.3, implicit=True)\n",
    "\n",
    "# U -> I -> [A -> I] <-- tag-based RP3beta\n",
    "a_i_recommender = RP3betaRecommender(ICM_genres.T)\n",
    "a_i_recommender.fit(alpha=0.5, beta=0.3)\n",
    "\n",
    "custom_similarity = u_i_recommender.W_sparse + icm_weight * a_i_recommender.W_sparse # <- additionally, you could try normalizations\n",
    "\n",
    "# Hybrid similarity recommender\n",
    "recommender = ItemKNNCustomSimilarityRecommender(URM_train_val)\n",
    "recommender.fit(custom_similarity)\n",
    "\n",
    "evaluator_test = EvaluatorHoldout(URM_test, [10])\n",
    "\n",
    "result_df_hybrid, _ = evaluator_test.evaluateRecommender(recommender)\n",
    "result_df_hybrid"
   ]
  }
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