KNNRecommender.ipynb

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   "source": [
    "# Neighborhood-Based Collaborative Filtering"
   ]
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   "source": [
    "<img src=\"qr-code.png\" width=\"500\" height=\"500\"/>"
   ]
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    "Uno dei principi alla base degli algoritmi di raccomandazione è il **filtraggio collaborativo**, che sfrutta i comportamenti di valutazione storici per individuare somiglianze tra utenti e/o elementi e, quindi, arrivare a predizioni delle valutazioni. In questa sede, analizziamo un approccio semplice ma altamente intuitivo al filtraggio collaborativo, fondato sul concetto di **vicinato**.  \n",
    "\n",
    "Questo metodo non solo illustra chiaramente il principio del filtraggio collaborativo, ossia il collegamento tra utenti ed elementi attraverso la ricerca di similarità, ma offre anche un elevato livello di interpretabilità, come vedremo in questo tutorial.  "
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   "source": [
    "## 1. Setup"
   ]
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   "source": [
    "!pip install --quiet cornac==1.15.4\n",
    "!pip install pandas\n",
    "!pip install seaborn"
   ]
  },
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     "text": [
      "FM model is only supported on Linux.\n",
      "Windows executable can be found at http://www.libfm.org.\n",
      "System version: 3.8.2 (tags/v3.8.2:7b3ab59, Feb 25 2020, 23:03:10) [MSC v.1916 64 bit (AMD64)]\n",
      "Cornac version: 1.15.4\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import sys\n",
    "import textwrap\n",
    "from collections import defaultdict\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import cornac\n",
    "from cornac.utils import cache\n",
    "from cornac.datasets import movielens\n",
    "from cornac.eval_methods import RatioSplit\n",
    "from cornac.models import UserKNN, ItemKNN\n",
    "\n",
    "print(f\"System version: {sys.version}\")\n",
    "print(f\"Cornac version: {cornac.__version__}\")\n",
    "\n",
    "SEED = 42\n",
    "VERBOSE = False"
   ]
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   "source": [
    "## 2. Dati di esempio\n",
    "\n",
    "A scopo illustrativo, utilizziamo un semplice set di dati con 5 utenti e 6 oggetti."
   ]
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserID</th>\n",
       "      <th>ItemID</th>\n",
       "      <th>Rating</th>\n",
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       "      <th>0</th>\n",
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       "      <td>7</td>\n",
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       "      <th>1</th>\n",
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       "      <td>6</td>\n",
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       "   UserID  ItemID  Rating\n",
       "0       1       1       7\n",
       "1       1       2       6\n",
       "2       1       3       7\n",
       "3       1       4       4\n",
       "4       1       5       5"
      ]
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   "source": [
    "sample_df = pd.read_csv(\n",
    "  cache(\"https://static.preferred.ai/tutorials/recommender-systems/sample_data.csv\"), \n",
    "  sep=\",\", names=[\"UserID\", \"ItemID\", \"Rating\"]\n",
    ")\n",
    "sample_df.head()"
   ]
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   "source": [
    "### Matrice dei ratings\n",
    "\n",
    "Vediamo questo set di dati di esempio in forma di matrice.\n"
   ]
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       "      <th>Item 2</th>\n",
       "      <th>Item 3</th>\n",
       "      <th>Item 4</th>\n",
       "      <th>Item 5</th>\n",
       "      <th>Item 6</th>\n",
       "      <th>Mean Rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>User 1</th>\n",
       "      <td>7.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.5</td>\n",
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       "    <tr>\n",
       "      <th>User 2</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.8</td>\n",
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       "    <tr>\n",
       "      <th>User 3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>User 4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.5</td>\n",
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       "    <tr>\n",
       "      <th>User 5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
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       "        Item 1  Item 2  Item 3  Item 4  Item 5  Item 6  Mean Rating\n",
       "User 1     7.0     6.0     7.0     4.0     5.0     4.0          5.5\n",
       "User 2     6.0     7.0     NaN     4.0     3.0     4.0          4.8\n",
       "User 3     NaN     3.0     3.0     1.0     1.0     NaN          2.0\n",
       "User 4     1.0     2.0     2.0     3.0     3.0     4.0          2.5\n",
       "User 5     1.0     NaN     1.0     2.0     3.0     3.0          2.0"
      ]
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   "source": [
    "dataset = cornac.data.Dataset.from_uir(sample_df.itertuples(index=False))\n",
    "df = pd.DataFrame(dataset.matrix.A,\n",
    "                  index=[f\"User {u + 1}\" for u in np.arange(dataset.num_users)],\n",
    "                  columns=[f\"Item {i + 1}\" for i in np.arange(dataset.num_items)])\n",
    "df.replace(0, np.nan, inplace=True)\n",
    "df[\"Mean Rating\"] = df.mean(axis=1)\n",
    "df"
   ]
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   "source": [
    "### Matrice di valutazione centrata sulla media\n",
    "\n",
    "Uno dei problemi legati ai dati di valutazione è la loro natura soggettiva. In particolare, utenti diversi potrebbero utilizzare scale di valori differenti. Alcuni utenti tendono a essere più indulgenti, assegnando valutazioni più alte, mentre altri sono più severi e assegnano punteggi più bassi. Un approccio comunemente adottato per *normalizzare* queste valutazioni consiste nel calcolare la media delle valutazioni di ciascun utente e sottrarre tale media dalle singole valutazioni fornite dallo stesso utente."
   ]
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       "      <th>Item 6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <th>User 1</th>\n",
       "      <td>1.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-1.5</td>\n",
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       "    <tr>\n",
       "      <th>User 2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>2.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-1.8</td>\n",
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       "      <th>User 3</th>\n",
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       "      <td>-1.0</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>User 4</th>\n",
       "      <td>-1.5</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.5</td>\n",
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       "      <th>User 5</th>\n",
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       "        Item 1  Item 2  Item 3  Item 4  Item 5  Item 6\n",
       "User 1     1.5     0.5     1.5    -1.5    -0.5    -1.5\n",
       "User 2     1.2     2.2     NaN    -0.8    -1.8    -0.8\n",
       "User 3     NaN     1.0     1.0    -1.0    -1.0     NaN\n",
       "User 4    -1.5    -0.5    -0.5     0.5     0.5     1.5\n",
       "User 5    -1.0     NaN    -1.0     0.0     1.0     1.0"
      ]
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     "execution_count": 6,
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   "source": [
    "ratings = df[df.columns.difference([\"Mean Rating\"])].values\n",
    "means = df[\"Mean Rating\"].values[:, np.newaxis]\n",
    "df[df.columns.difference([\"Mean Rating\"])] = (ratings - means)\n",
    "df.drop(columns=\"Mean Rating\")"
   ]
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   "source": [
    "### 3. **Metodi Basati sull'Utente**\n",
    "\n",
    "Per ciascun utente, la valutazione media viene calcolata come segue:\n",
    "\n",
    "$$\n",
    "\\mu_u = \\frac{\\sum_{k \\in \\mathcal{I}_u} r_{uk}}{|\\mathcal{I}_u|} \\ \\ \\forall u \\in \\{1, \\dots, m\\}\n",
    "$$\n",
    "\n",
    "dove $ \\mathcal{I}_u $ è l'insieme degli elementi valutati dall'utente $ u $, e $ r_{uk} $ rappresenta la valutazione dell'utente $ u $ per l'elemento $ k $."
   ]
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   "source": [
    "### **Similarità tra Utenti**\n",
    "\n",
    "Esistono due approcci comuni per misurare la similarità tra due utenti $ \\mathrm{Sim}(u, v) $: **Similarità Coseno** e **Coefficiente di Correlazione di Pearson**."
   ]
  },
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   "source": [
    "#### **Similarità Coseno**\n",
    "Misura l'angolo tra due vettori di valutazioni:\n",
    "\n",
    "$$\n",
    "\\mathrm{Cosine}(u,v) = \\frac{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} r_{uk} \\cdot r_{vk}}{\\sqrt{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} r_{uk}^2} \\cdot \\sqrt{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} r_{vk}^2}}\n",
    "$$\n"
   ]
  },
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   "source": [
    "#### **Correlazione di Pearson**\n",
    "Misura la correlazione lineare tra le valutazioni degli utenti, centrando le valutazioni rispetto alla media:\n",
    "\n",
    "$$\n",
    "\\mathrm{Pearson}(u,v) = \\frac{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} (r_{uk} - \\mu_u) \\cdot (r_{vk} - \\mu_v)}{\\sqrt{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} (r_{uk} - \\mu_u)^2} \\cdot \\sqrt{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} (r_{vk} - \\mu_v)^2}}\n",
    "$$"
   ]
  },
  {
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   "source": [
    "### **Esempio di Calcolo tra Utente 1 e Utente 3**\n",
    "\n",
    "Dati i valori di valutazione della matrice, calcoliamo la similarità tra **Utente 1** e **Utente 3**:"
   ]
  },
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   "source": [
    "1. **Similarità Coseno**\n",
    "\n",
    "$$\n",
    "\\mathrm{Cosine}(1,3) = \\frac{6 \\cdot 3 + 7 \\cdot 3 + 4 \\cdot 1 + 5 \\cdot 1}{\\sqrt{6^2 + 7^2 + 4^2 + 5^2} \\cdot \\sqrt{3^2 + 3^2 + 1^2 + 1^2}}\n",
    "$$\n",
    "\n",
    "Calcoliamo passo per passo:\n",
    "\n",
    "- Numeratore: $ 6 \\cdot 3 + 7 \\cdot 3 + 4 \\cdot 1 + 5 \\cdot 1 = 18 + 21 + 4 + 5 = 48 $\n",
    "- Denominatore: $ \\sqrt{6^2 + 7^2 + 4^2 + 5^2} = \\sqrt{36 + 49 + 16 + 25} = \\sqrt{126} $  \n",
    "  $ \\sqrt{3^2 + 3^2 + 1^2 + 1^2} = \\sqrt{9 + 9 + 1 + 1} = \\sqrt{20} $\n",
    "\n",
    "$$\n",
    "\\mathrm{Cosine}(1,3) = \\frac{48}{\\sqrt{126} \\cdot \\sqrt{20}} \\approx 0.956\n",
    "$$\n"
   ]
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   "source": [
    "2. **Correlazione di Pearson**\n",
    "\n",
    "$$\n",
    "\\mathrm{Pearson}(1,3) = \\frac{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} (r_{uk} - \\mu_u) \\cdot (r_{vk} - \\mu_v)}{\\sqrt{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} (r_{uk} - \\mu_u)^2} \\cdot \\sqrt{\\sum_{k \\in \\mathcal{I}_u \\cap \\mathcal{I}_v} (r_{vk} - \\mu_v)^2}}\n",
    "$$\n",
    "\n",
    "Passo per passo:\n",
    "\n",
    "- Media di $ \\mathrm{User \\ 1} $: $ \\mu_1 = \\frac{6 + 7 + 4 + 5}{4} = 5.5 $\n",
    "- Media di $ \\mathrm{User \\ 3} $: $ \\mu_3 = \\frac{3 + 3 + 1 + 1}{4} = 2 $\n",
    "\n",
    "Calcolo delle differenze centrali:\n",
    "\n",
    "- $ r_{1k} - \\mu_1 $ (User 1): $ 6 - 5.5 = 0.5, \\ 7 - 5.5 = 1.5, \\ 4 - 5.5 = -1.5, \\ 5 - 5.5 = -0.5 $\n",
    "- $ r_{3k} - \\mu_3 $ (User 3): $ 3 - 2 = 1, \\ 3 - 2 = 1, \\ 1 - 2 = -1, \\ 1 - 2 = -1 $\n",
    "\n",
    "Prodotto delle differenze:\n",
    "\n",
    "- Numeratore: $ (0.5)(1) + (1.5)(1) + (-1.5)(-1) + (-0.5)(-1) = 0.5 + 1.5 + 1.5 + 0.5 = 4 $\n",
    "\n",
    "Denominatore:\n",
    "\n",
    "- Deviazione User 1: $ \\sqrt{0.5^2 + 1.5^2 + (-1.5)^2 + (-0.5)^2} = \\sqrt{0.25 + 2.25 + 2.25 + 0.25} = \\sqrt{5} $\n",
    "- Deviazione User 3: $ \\sqrt{1^2 + 1^2 + (-1)^2 + (-1)^2} = \\sqrt{1 + 1 + 1 + 1} = \\sqrt{4} $\n",
    "\n",
    "$$\n",
    "\\mathrm{Pearson}(1,3) = \\frac{4}{\\sqrt{5} \\cdot \\sqrt{4}} = \\frac{4}{\\sqrt{20}} \\approx 0.894\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### **Conclusione**\n",
    "I valori calcolati sono:\n",
    "\n",
    "- **Similarità del Coseno**: $ 0.956 $\n",
    "- **Correlazione di Pearson**: $ 0.894 $\n",
    "\n",
    "Questi risultati riflettono due diverse misure di similarità tra i vettori di valutazione dei due utenti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine(1,3) = 0.956\n",
      "Pearson(1,3) = 0.894\n"
     ]
    }
   ],
   "source": [
    "uknn_cosine = UserKNN(k=2, similarity=\"cosine\", verbose=VERBOSE).fit(dataset)\n",
    "print(f\"Cosine(1,3) = {uknn_cosine.sim_mat[0, 2]:.3f}\")\n",
    "\n",
    "uknn_pearson = UserKNN(k=2, similarity=\"pearson\", verbose=VERBOSE).fit(dataset)\n",
    "print(f\"Pearson(1,3) = {uknn_pearson.sim_mat[0, 2]:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "In questo contesto, utilizziamo la **media ponderata delle valutazioni centrate sulla media** per effettuare una previsione. La **funzione di previsione** basata sul metodo di *vicinato* è definita come segue:\n",
    "\n",
    "$$\n",
    "\\hat{r}_{uj} = \\mu_u + \\frac{\\sum_{v \\in P_u(j)} \\mathrm{Sim}(u,v) \\cdot (r_{vj} - \\mu_v)}{\\sum_{v \\in P_u(j)} |\\mathrm{Sim}(u,v)|}\n",
    "$$\n",
    "\n",
    "dove:  \n",
    "- $\\hat{r}_{uj}$ è la valutazione prevista dell'*Utente $u$* per l'*Oggetto $j$*;  \n",
    "- $\\mu_u$ è la media delle valutazioni date dall'Utente $u$;  \n",
    "- $P_u(j)$ rappresenta l'insieme degli utenti \"vicini\" a $u$ che hanno valutato l'oggetto $j$;  \n",
    "- $\\mathrm{Sim}(u,v)$ è la similarità tra l'Utente $u$ e l'Utente $v$;  \n",
    "- $r_{vj}$ è la valutazione data dall'Utente $v$ all'Oggetto $j$;  \n",
    "- $\\mu_v$ è la media delle valutazioni date dall'Utente $v$.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Esempio pratico  \n",
    "Consideriamo il caso di previsione delle valutazioni che l'*Utente 3* darà agli *Oggetti 1* e *6*. I dati si basano sui due vicini più prossimi: *Utente 1* e *Utente 2*.\n",
    "\n",
    "#### Calcolo per l'Oggetto 1  \n",
    "$$\n",
    "\\hat{r}_{31} = \\mu_3 + \\frac{\\mathrm{Sim}(3,1) \\cdot (r_{11} - \\mu_1) + \\mathrm{Sim}(3,2) \\cdot (r_{21} - \\mu_2)}{\\mathrm{Sim}(3,1) + \\mathrm{Sim}(3,2)}\n",
    "$$\n",
    "\n",
    "Sostituendo i valori numerici:  \n",
    "$$\n",
    "\\hat{r}_{31} = 2 + \\frac{1.5 \\cdot 0.894 + 1.2 \\cdot 0.939}{0.894 + 0.939} = 3.35\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "#### Calcolo per l'Oggetto 6  \n",
    "$$\n",
    "\\hat{r}_{36} = \\mu_3 + \\frac{\\mathrm{Sim}(3,1) \\cdot (r_{16} - \\mu_1) + \\mathrm{Sim}(3,2) \\cdot (r_{26} - \\mu_2)}{\\mathrm{Sim}(3,1) + \\mathrm{Sim}(3,2)}\n",
    "$$\n",
    "\n",
    "Sostituendo i valori numerici:  \n",
    "$$\n",
    "\\hat{r}_{36} = 2 + \\frac{-1.5 \\cdot 0.894 - 0.8 \\cdot 0.939}{0.894 + 0.939} = 0.86\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Verifica del calcolo  \n",
    "Le previsioni ottenute sono:  \n",
    "- Per l'**Oggetto 1**: $ \\hat{r}_{31} = 3.35 $  \n",
    "- Per l'**Oggetto 6**: $ \\hat{r}_{36} = 0.86 $\n",
    "\n",
    "Questi risultati confermano la correttezza del metodo di previsione applicato."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R(3,1) = 3.35\n",
      "R(3,6) = 0.86\n"
     ]
    }
   ],
   "source": [
    "print(f\"R(3,1) = {uknn_pearson.score(user_idx=2, item_idx=0):.2f}\")\n",
    "print(f\"R(3,6) = {uknn_pearson.score(user_idx=2, item_idx=5):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Proviamo con un Dataset Reale\n",
    "\n",
    "Ora applicheremo questi algoritmi al dataset [MovieLens](https://grouplens.org/datasets/movielens/). La nostra convenzione prevede l'utilizzo delle valutazioni centrate sulla media quando aggreghiamo le valutazioni dei vicini per produrre una previsione, correggendo poi in seguito per la media. Tuttavia, il calcolo della similarità può essere basato sia sulle valutazioni originali che su quelle centrate sulla media, come mostrato nelle varianti seguenti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data from http://files.grouplens.org/datasets/movielens/ml-100k/u.data\n",
      "will be cached into C:\\Users\\petru\\.cornac\\ml-100k/u.data\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cc8f2f6d8bef4114a0b2b3c38d65a5de",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "0.00B [00:00, ?B/s]"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File cached!\n",
      "\n",
      "TEST:\n",
      "...\n",
      "                   |   RMSE | Train (s) | Test (s)\n",
      "------------------ + ------ + --------- + --------\n",
      "UserKNN-Cosine     | 0.9099 |    0.0877 |   1.1660\n",
      "UserKNN-Cosine-MC  | 0.8947 |    0.1272 |   1.2687\n",
      "UserKNN-Pearson    | 0.8947 |    0.1009 |   1.3309\n",
      "UserKNN-Pearson-MC | 0.8947 |    0.0920 |   1.1329\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# UserKNN methods\n",
    "K = 50  # number of nearest neighbors\n",
    "uknn_cosine = UserKNN(\n",
    "  k=K, similarity=\"cosine\", name=\"UserKNN-Cosine\", verbose=VERBOSE\n",
    ")\n",
    "uknn_cosine_mc = UserKNN(\n",
    "  k=K, similarity=\"cosine\", mean_centered=True, name=\"UserKNN-Cosine-MC\", verbose=VERBOSE\n",
    ")\n",
    "uknn_pearson = UserKNN(\n",
    "  k=K, similarity=\"pearson\", name=\"UserKNN-Pearson\", verbose=VERBOSE\n",
    ")\n",
    "uknn_pearson_mc = UserKNN(\n",
    "  k=K, similarity=\"pearson\", mean_centered=True, name=\"UserKNN-Pearson-MC\", verbose=VERBOSE\n",
    ")\n",
    "\n",
    "feedback = movielens.load_feedback(variant=\"100K\")\n",
    "ratio_split = RatioSplit(feedback, test_size=0.1, seed=SEED, verbose=VERBOSE)\n",
    "cornac.Experiment(\n",
    "  eval_method=ratio_split,\n",
    "  models=[uknn_cosine, uknn_cosine_mc, uknn_pearson, uknn_pearson_mc],\n",
    "  metrics=[cornac.metrics.RMSE()],\n",
    ").run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Le similarità del coseno e *Pearson* possono essere applicate anche ai metodi *item-based*, con la differenza che i vettori di caratteristiche da considerare sono ora rappresentati dalle colonne anziché dalle righe, poiché stiamo misurando la similarità tra elementi.\n",
    "\n",
    "Quando la similarità del coseno è calcolata utilizzando una matrice di valutazioni *centrata sulla media*, otteniamo una variante chiamata **Adjusted Cosine**. La formula della similarità *Adjusted Cosine* tra due elementi (colonne) $ i $ e $ j $ è definita come:\n",
    "\n",
    "$$\n",
    "\\mathrm{AdjustedCosine}(i,j) = \\frac{\\sum_{u \\in \\mathcal{U}_i \\cap \\mathcal{U}_j} s_{ui} \\cdot s_{uj}}{\\sqrt{\\sum_{u \\in \\mathcal{U}_i \\cap \\mathcal{U}_j} s_{ui}^2} \\cdot \\sqrt{\\sum_{u \\in \\mathcal{U}_i \\cap \\mathcal{U}_j} s_{uj}^2}}\n",
    "$$\n",
    "\n",
    "dove $ s_{ui} $ rappresenta la valutazione *centrata sulla media* fornita dall'utente $ u $ per l'elemento $ i $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Esempio\n",
    "Consideriamo un esempio basato su un piccolo set di dati, dove vogliamo calcolare la similarità *Adjusted Cosine* tra **Elemento 1** ed **Elemento 3**. La formula applicata è la seguente:\n",
    "\n",
    "$$\n",
    "\\mathrm{AdjustedCosine}(1,3) = \\frac{1.5 \\cdot 1.5 + (-1.5) \\cdot (-0.5) + (-1) \\cdot (-1)}{\\sqrt{1.5^2 + (-1.5)^2 + (-1)^2} \\cdot \\sqrt{1.5^2 + (-0.5)^2 + (-1)^2}} = 0.912\n",
    "$$\n",
    "\n",
    "In questo caso:\n",
    "- $ 1.5 $, $ -1.5 $, e $ -1 $ rappresentano le valutazioni centrate sulla media per l'Elemento 1.\n",
    "- $ 1.5 $, $ -0.5 $, e $ -1 $ rappresentano le valutazioni centrate sulla media per l'Elemento 3.\n",
    "\n",
    "Il risultato finale è una similarità di **0.912**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdjustedCosine(1,3) = 0.912\n"
     ]
    }
   ],
   "source": [
    "iknn_adj = ItemKNN(k=2, similarity=\"cosine\", mean_centered=True, verbose=VERBOSE).fit(dataset)\n",
    "print(f\"AdjustedCosine(1,3) = {iknn_adj.sim_mat[0, 2]:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Per la previsione, utilizziamo la stessa forma della funzione di predizione adottata nei metodi *user-based*, ma aggreghiamo le valutazioni dell'utente sugli elementi vicini:\n",
    "\n",
    "$$\n",
    "\\hat{r}_{ut} = \\mu_u + \\frac{\\sum_{j \\in Q_t(u)} \\mathrm{Sim}(j,t) \\cdot (r_{uj} - \\mu_u)}{\\sum_{j \\in Q_t(u)} |\\mathrm{Sim}(j,t)|}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Esempio di calcolo\n",
    "Supponiamo di prevedere le valutazioni che *Utente 3* assegnerebbe a *Elemento 1* e *Elemento 6*.  \n",
    "Per *Elemento 1*, consideriamo i due vicini più prossimi (*Elemento 2* e *Elemento 3*), mentre per *Elemento 6*, consideriamo *Elemento 4* e *Elemento 5*.\n",
    "\n",
    "#### Calcolo per *Elemento 1*:\n",
    "$$\n",
    "\\hat{r}_{31} = 2 + \\frac{1 \\cdot 0.735 + 1 \\cdot 0.912}{0.735 + 0.912} = 3\n",
    "$$\n",
    "\n",
    "#### Calcolo per *Elemento 6*:\n",
    "$$\n",
    "\\hat{r}_{36} = 2 + \\frac{(-1) \\cdot 0.829 + (-1) \\cdot 0.730}{0.829 + 0.730} = 1\n",
    "$$\n",
    "\n",
    "In questa equazione, $ s_{ui} $ rappresenta la valutazione *media-centro* che l'utente $ u $ assegna all'elemento $ i $.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Esempio: Similitudine Coseno Corretto (Adjusted Cosine)\n",
    "Ad esempio, possiamo calcolare la *similarità coseno corretta* tra *Elemento 1* e *Elemento 3* usando il piccolo dataset campione riportato sopra:\n",
    "\n",
    "$$\n",
    "\\mathrm{AdjustedCosine}(1,3) = \\frac{1.5 \\cdot 1.5 + (-1.5) \\cdot (-0.5) + (-1) \\cdot (-1)}{\\sqrt{1.5^2 + (-1.5)^2 + (-1)^2} \\cdot \\sqrt{1.5^2 + (-0.5)^2 + (-1)^2}} = 0.912\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Spiegazione dei termini:\n",
    "- $\\hat{r}_{ut}$: previsione della valutazione dell'utente $ u $ sull'elemento $ t $.  \n",
    "- $\\mu_u$: valutazione media dell'utente $ u $.  \n",
    "- $Q_t(u)$: insieme degli elementi vicini (simili a $ t $) valutati dall'utente $ u $.  \n",
    "- $\\mathrm{Sim}(j,t)$: similarità tra l'elemento $ j $ e l'elemento $ t $.  \n",
    "- $r_{uj}$: valutazione data dall'utente $ u $ all'elemento $ j $.  \n",
    "\n",
    "L'approccio utilizza la *similarità pesata* tra elementi per prevedere le valutazioni degli utenti sugli elementi target."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R(3,1) = 3.0\n",
      "R(3,6) = 1.0\n"
     ]
    }
   ],
   "source": [
    "print(f\"R(3,1) = {iknn_adj.score(user_idx=2, item_idx=0):.1f}\")\n",
    "print(f\"R(3,6) = {iknn_adj.score(user_idx=2, item_idx=5):.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Proviamo con un Dataset Reale (ADAVER)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "TEST:\n",
      "...\n",
      "                       |   RMSE | Train (s) | Test (s)\n",
      "---------------------- + ------ + --------- + --------\n",
      "ItemKNN-Cosine         | 0.9689 |    0.2139 |   1.2651\n",
      "ItemKNN-Pearson        | 0.9624 |    0.2140 |   1.1942\n",
      "ItemKNN-Pearson-MC     | 0.9572 |    0.2233 |   1.2467\n",
      "ItemKNN-AdjustedCosine | 0.9098 |    0.2011 |   1.2989\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# ItemKNN methods\n",
    "K = 50  # number of nearest neighbors\n",
    "iknn_cosine = ItemKNN(\n",
    "  k=K, similarity=\"cosine\", name=\"ItemKNN-Cosine\", verbose=VERBOSE\n",
    ")\n",
    "iknn_pearson = ItemKNN(\n",
    "  k=K, similarity=\"pearson\", name=\"ItemKNN-Pearson\", verbose=VERBOSE\n",
    ")\n",
    "iknn_pearson_mc = ItemKNN(\n",
    "  k=K, similarity=\"pearson\", mean_centered=True, name=\"ItemKNN-Pearson-MC\", verbose=VERBOSE\n",
    ")\n",
    "iknn_adjusted = ItemKNN(\n",
    "  k=K, similarity=\"cosine\", mean_centered=True, name=\"ItemKNN-AdjustedCosine\", verbose=VERBOSE\n",
    ")\n",
    "\n",
    "feedback = movielens.load_feedback(variant=\"100K\")\n",
    "ratio_split = RatioSplit(feedback, test_size=0.1, seed=SEED, verbose=VERBOSE)\n",
    "cornac.Experiment(\n",
    "  eval_method=ratio_split, \n",
    "  models=[iknn_cosine, iknn_pearson, iknn_pearson_mc, iknn_adjusted],\n",
    "  metrics=[cornac.metrics.RMSE()],\n",
    ").run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 5. Ripesatura della Similarità  \n",
    "\n",
    "Dato che le nostre metriche di similarità sono il *Coseno* o la *Pearson*, i cui valori appartengono all'intervallo $[-1, 1]$, è possibile che i punteggi delle valutazioni varino su scale diverse a seconda della piattaforma. Una pratica comune per aumentare l'*importanza relativa* dei punteggi di similarità consiste nell'uso dell'*amplificazione esponenziale*. Ad esempio, un nuovo punteggio di similarità amplificato basato sulla correlazione *Pearson* può essere definito come:  \n",
    "\n",
    "$$\n",
    "\\mathrm{Sim}(u, v) = \\mathrm{Pearson}(u, v)^{\\mathrm{amplify}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Un ulteriore problema riguarda la distribuzione a coda lunga degli elementi. Alcuni item potrebbero essere molto popolari e, di conseguenza, risultare meno discriminativi tra utenti diversi. Questo fenomeno è ben noto anche nella letteratura sul *Information Retrieval* (IR). Per affrontarlo, possiamo adottare tecniche di *ri-pesatura* delle caratteristiche derivate dall'IR. Una di queste è il concetto di *Inverse Document Frequency (idf)*, che fa parte del modello [TF-IDF](https://en.wikipedia.org/wiki/Tf%E2%80%93idf). In questo caso, il peso di ciascun elemento $i$ può essere ricalcolato come:  \n",
    "\n",
    "$$\n",
    "w_i = \\log \\bigg( \\frac{N}{m_i} \\bigg),\n",
    "$$\n",
    "\n",
    "dove $N$ rappresenta il numero totale di utenti e $m_i$ è il numero di valutazioni assegnate all'elemento $i$.  \n",
    "\n",
    "Un'ulteriore evoluzione di questo approccio è il modello [Okapi BM25](https://en.wikipedia.org/wiki/Okapi_BM25), che rappresenta una versione migliorata del TF-IDF. Questo metodo è stato implementato all'interno della libreria *Cornac*.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "TEST:\n",
      "...\n",
      "               |   RMSE | Train (s) | Test (s)\n",
      "-------------- + ------ + --------- + --------\n",
      "UserKNN-Base   | 0.8947 |    0.1007 |   1.2046\n",
      "UserKNN-Amp0.5 | 0.8934 |    0.4712 |   1.1869\n",
      "UserKNN-Amp3.0 | 0.9135 |    0.4400 |   1.2035\n",
      "UserKNN-IDF    | 0.8956 |    0.1171 |   1.1159\n",
      "UserKNN-BM25   | 0.8955 |    0.1149 |   1.1462\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# UserKNN methods\n",
    "K = 50  # number of nearest neighbors\n",
    "uknn_base = UserKNN(\n",
    "  k=K, similarity=\"pearson\", name=\"UserKNN-Base\", verbose=VERBOSE\n",
    ")\n",
    "uknn_amp1 = UserKNN(\n",
    "  k=K, similarity=\"pearson\", amplify=0.5, name=\"UserKNN-Amp0.5\", verbose=VERBOSE\n",
    ")\n",
    "uknn_amp2 = UserKNN(\n",
    "  k=K, similarity=\"pearson\", amplify=3.0, name=\"UserKNN-Amp3.0\", verbose=VERBOSE\n",
    ")\n",
    "uknn_idf = UserKNN(\n",
    "  k=K, similarity=\"pearson\", weighting=\"idf\", name=\"UserKNN-IDF\", verbose=VERBOSE\n",
    ")\n",
    "uknn_bm25 = UserKNN(\n",
    "  k=K, similarity=\"pearson\", weighting=\"bm25\", name=\"UserKNN-BM25\", verbose=VERBOSE\n",
    ")\n",
    "\n",
    "feedback = movielens.load_feedback(variant=\"100K\")\n",
    "ratio_split = RatioSplit(feedback, test_size=0.1, seed=SEED, verbose=VERBOSE)\n",
    "cornac.Experiment(\n",
    "  eval_method=ratio_split,\n",
    "  models=[uknn_base, uknn_amp1, uknn_amp2, uknn_idf, uknn_bm25],\n",
    "  metrics=[cornac.metrics.RMSE()],\n",
    ").run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 6. Interpretazione delle Raccomandazioni"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Anziché trattare la previsione delle valutazioni come un'attività opaca e poco trasparente, è più utile comprendere meglio le ragioni dietro determinate raccomandazioni. Per interpretare i risultati delle raccomandazioni in modo più efficace, possiamo analizzare diverse fonti di informazioni, come i **metadati**, il contributo dei singoli \"vicini\" e l'interazione tra l'utente e gli elementi correlati.\n",
    "\n",
    "Il dataset **MovieLens 100K** fornisce alcuni tipi di [metadati](http://files.grouplens.org/datasets/movielens/ml-100k-README.txt). Possiamo utilizzare queste informazioni per approfondire le motivazioni delle raccomandazioni. Di seguito, esamineremo il **titolo** dei film e i loro **generi**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
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    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data from http://files.grouplens.org/datasets/movielens/ml-100k/u.user\n",
      "will be cached into C:\\Users\\petru\\.cornac\\u.user\n"
     ]
    },
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    {
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     "output_type": "stream",
     "text": [
      "File cached!\n",
      "Data from http://files.grouplens.org/datasets/movielens/ml-100k/u.item\n",
      "will be cached into C:\\Users\\petru\\.cornac\\u.item\n"
     ]
    },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File cached!\n"
     ]
    }
   ],
   "source": [
    "# Download some information of MovieLens 100K dataset\n",
    "user_df = pd.read_csv(\n",
    "  cache(\"http://files.grouplens.org/datasets/movielens/ml-100k/u.user\"), \n",
    "  sep=\"|\", names=[\"UserID\", \"Age\", \"Gender\", \"Occupation\", \"Zip Code\"]\n",
    ").set_index(\"UserID\")\n",
    "\n",
    "item_df = pd.read_csv(\n",
    "  cache(\"http://files.grouplens.org/datasets/movielens/ml-100k/u.item\"), \n",
    "  sep=\"|\", encoding=\"ISO-8859-1\",\n",
    "  names=[\"ItemID\", \"Title\", \"Release Date\", \"Video Release Date\", \"IMDb URL\", \n",
    "         \"unknown\", \"Action\", \"Adventure\", \"Animation\", \"Children's\", \"Comedy\", \n",
    "         \"Crime\", \"Documentary\", \"Drama\", \"Fantasy\", \"Film-Noir\", \"Horror\", \n",
    "         \"Musical\", \"Mystery\", \"Romance\", \"Sci-Fi\", \"Thriller\", \"War\", \"Western\"]\n",
    ").set_index(\"ItemID\").drop(columns=[\"Video Release Date\", \"IMDb URL\", \"unknown\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### UserKNN (Pearson)\n",
    "Per i metodi UserKNN, utilizziamo la variante *Pearson* come sistema di raccomandazione. Iniziamo selezionando un utente per esplorare il suo profilo e gli articoli con le valutazioni più alte nel dataset di addestramento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UserID = 1\n",
      "-------------------------\n",
      "Age                   24\n",
      "Gender                 M\n",
      "Occupation    technician\n",
      "Zip Code           85711\n",
      "Name: 1, dtype: object\n",
      "\n",
      "TOP 5 RATED ITEMS BY USER 1:\n"
     ]
    },
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       "                                     Title Release Date  Action  Adventure  \\\n",
       "ItemID                                                                       \n",
       "96       Terminator 2: Judgment Day (1991)  01-Jan-1991       1          0   \n",
       "48                      Hoop Dreams (1994)  01-Jan-1994       0          0   \n",
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       "\n",
       "        Animation  Children's  Comedy  Crime  Documentary  Drama  Fantasy  \\\n",
       "ItemID                                                                      \n",
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       "ItemID                                                                        \n",
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       "\n",
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     },
     "execution_count": 15,
     "metadata": {},
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    }
   ],
   "source": [
    "rating_mat = uknn_pearson.train_set.matrix\n",
    "user_id2idx = uknn_pearson.train_set.uid_map\n",
    "user_idx2id = list(uknn_pearson.train_set.user_ids)\n",
    "item_id2idx = uknn_pearson.train_set.iid_map\n",
    "item_idx2id = list(uknn_pearson.train_set.item_ids)\n",
    "\n",
    "TOPK = 5\n",
    "UID = 1\n",
    "UIDX = uknn_pearson.train_set.uid_map[str(UID)]\n",
    "\n",
    "print(f\"UserID = {UID}\")\n",
    "print(\"-\" * 25)\n",
    "print(user_df.loc[UID])\n",
    "\n",
    "rating_arr = rating_mat[UIDX].A.ravel()\n",
    "top_rated_items = np.argsort(rating_arr)[-TOPK:]\n",
    "print(f\"\\nTOP {TOPK} RATED ITEMS BY USER {UID}:\")\n",
    "item_df.loc[[int(item_idx2id[i]) for i in top_rated_items]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
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    "tags": []
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   "source": [
    "Ad esempio, tra i primi 5 film più apprezzati osservati per *Utente 1*, 2 di questi sono film drammatici.\n",
    "\n",
    "Le raccomandazioni per questo utente possono essere ottenute nel seguente modo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "TOP 5 RECOMMENDATIONS FOR USER 1:\n",
      "Scores: [6.11605904 5.48557688 5.32202542 5.30147822 5.09619216]\n"
     ]
    },
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       "      <th>1536</th>\n",
       "      <td>Aiqing wansui (1994)</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1500</th>\n",
       "      <td>Santa with Muscles (1996)</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1467</th>\n",
       "      <td>Saint of Fort Washington, The (1993)</td>\n",
       "      <td>01-Jan-1993</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                       Title Release Date  Action  Adventure  \\\n",
       "ItemID                                                                         \n",
       "1309            Very Natural Thing, A (1974)  01-Jan-1974       0          0   \n",
       "814            Great Day in Harlem, A (1994)  01-Jan-1994       0          0   \n",
       "1536                    Aiqing wansui (1994)  22-Jul-1996       0          0   \n",
       "1500               Santa with Muscles (1996)  08-Nov-1996       0          0   \n",
       "1467    Saint of Fort Washington, The (1993)  01-Jan-1993       0          0   \n",
       "\n",
       "        Animation  Children's  Comedy  Crime  Documentary  Drama  Fantasy  \\\n",
       "ItemID                                                                      \n",
       "1309            0           0       0      0            0      1        0   \n",
       "814             0           0       0      0            1      0        0   \n",
       "1536            0           0       0      0            0      1        0   \n",
       "1500            0           0       1      0            0      0        0   \n",
       "1467            0           0       0      0            0      1        0   \n",
       "\n",
       "        Film-Noir  Horror  Musical  Mystery  Romance  Sci-Fi  Thriller  War  \\\n",
       "ItemID                                                                        \n",
       "1309            0       0        0        0        0       0         0    0   \n",
       "814             0       0        0        0        0       0         0    0   \n",
       "1536            0       0        0        0        0       0         0    0   \n",
       "1500            0       0        0        0        0       0         0    0   \n",
       "1467            0       0        0        0        0       0         0    0   \n",
       "\n",
       "        Western  \n",
       "ItemID           \n",
       "1309          0  \n",
       "814           0  \n",
       "1536          0  \n",
       "1500          0  \n",
       "1467          0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recommendations, scores = uknn_pearson.rank(UIDX)\n",
    "print(f\"\\nTOP {TOPK} RECOMMENDATIONS FOR USER {UID}:\")\n",
    "print(\"Scores:\", scores[recommendations[:TOPK]])\n",
    "item_df.loc[[int(item_idx2id[i]) for i in recommendations[:TOPK]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "È interessante, e forse significativo, che delle cinque pellicole previste, tre siano film drammatici.\n",
    "\n",
    "Per comprendere meglio la natura di questa raccomandazione, vorremmo esaminare come i vicini più prossimi dell'utente contribuiscano alla previsione di ciascun film."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Recommendation</th>\n",
       "      <th>User NN</th>\n",
       "      <th>Similarity</th>\n",
       "      <th>Score by the NN</th>\n",
       "      <th>Contribution</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Very Natural Thing, A (1974)</td>\n",
       "      <td>703</td>\n",
       "      <td>-0.073508</td>\n",
       "      <td>-2.526316</td>\n",
       "      <td>2.526316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Great Day in Harlem, A (1994)</td>\n",
       "      <td>20</td>\n",
       "      <td>0.471303</td>\n",
       "      <td>1.895833</td>\n",
       "      <td>1.895833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Aiqing wansui (1994)</td>\n",
       "      <td>190</td>\n",
       "      <td>0.010587</td>\n",
       "      <td>1.732283</td>\n",
       "      <td>1.732283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Santa with Muscles (1996)</td>\n",
       "      <td>184</td>\n",
       "      <td>0.289477</td>\n",
       "      <td>1.711735</td>\n",
       "      <td>1.711735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Saint of Fort Washington, The (1993)</td>\n",
       "      <td>7</td>\n",
       "      <td>0.467937</td>\n",
       "      <td>1.640909</td>\n",
       "      <td>1.640909</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Recommendation  User NN  Similarity  Score by the NN  \\\n",
       "0          Very Natural Thing, A (1974)      703   -0.073508        -2.526316   \n",
       "1         Great Day in Harlem, A (1994)       20    0.471303         1.895833   \n",
       "2                  Aiqing wansui (1994)      190    0.010587         1.732283   \n",
       "3             Santa with Muscles (1996)      184    0.289477         1.711735   \n",
       "4  Saint of Fort Washington, The (1993)        7    0.467937         1.640909   \n",
       "\n",
       "   Contribution  \n",
       "0      2.526316  \n",
       "1      1.895833  \n",
       "2      1.732283  \n",
       "3      1.711735  \n",
       "4      1.640909  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = defaultdict(list)\n",
    "sim_arr = uknn_pearson.sim_mat[UIDX].A.ravel()\n",
    "for rec in recommendations[:TOPK]:\n",
    "  rated_users = np.array([u for u in range(len(sim_arr)) if rating_mat[u, rec] != 0])\n",
    "  nearest_neighbor = rated_users[np.argsort(sim_arr[rated_users])[-1:]].item()\n",
    "  sim = sim_arr[nearest_neighbor]\n",
    "  score = uknn_pearson.iu_mat[rec, nearest_neighbor]\n",
    "  df[\"Recommendation\"].append(item_df.loc[[int(item_idx2id[rec])]][\"Title\"].values[0])\n",
    "  df[\"User NN\"].append(nearest_neighbor)\n",
    "  df[\"Similarity\"].append(sim)\n",
    "  df[\"Score by the NN\"].append(score)\n",
    "  df[\"Contribution\"].append((score * sim) / np.abs(sim))\n",
    "pd.DataFrame.from_dict(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Curiosamente, per la prima raccomandazione di un film, il vicino più prossimo dell'utente è quello che ha una similarità negativa con l'utente stesso e che fornisce anche una valutazione negativa per l'oggetto. I due aspetti negativi danno però come risultato un contributo positivo!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### ItemKNN (AdjustedCosine)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Per i metodi ItemKNN, utilizziamo la variante *AdjustedCosine* come nostro sistema di raccomandazione. Scegliamo un utente e vediamo i suoi articoli con le valutazioni più alte tra i primi K."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UserID = 1\n",
      "-------------------------\n",
      "Age                   24\n",
      "Gender                 M\n",
      "Occupation    technician\n",
      "Zip Code           85711\n",
      "Name: 1, dtype: object\n",
      "\n",
      "TOP 5 RATED ITEMS BY USER 1:\n",
      "Ratings: [5. 5. 5. 5. 5.]\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Title</th>\n",
       "      <th>Release Date</th>\n",
       "      <th>Action</th>\n",
       "      <th>Adventure</th>\n",
       "      <th>Animation</th>\n",
       "      <th>Children's</th>\n",
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       "      <th>Documentary</th>\n",
       "      <th>Drama</th>\n",
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       "      <th>Horror</th>\n",
       "      <th>Musical</th>\n",
       "      <th>Mystery</th>\n",
       "      <th>Romance</th>\n",
       "      <th>Sci-Fi</th>\n",
       "      <th>Thriller</th>\n",
       "      <th>War</th>\n",
       "      <th>Western</th>\n",
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       "    <tr>\n",
       "      <th>ItemID</th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>Terminator 2: Judgment Day (1991)</td>\n",
       "      <td>01-Jan-1991</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>Hoop Dreams (1994)</td>\n",
       "      <td>01-Jan-1994</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>Godfather, The (1972)</td>\n",
       "      <td>01-Jan-1972</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>Swingers (1996)</td>\n",
       "      <td>18-Oct-1996</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>French Twist (Gazon maudit) (1995)</td>\n",
       "      <td>01-Jan-1995</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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      ],
      "text/plain": [
       "                                     Title Release Date  Action  Adventure  \\\n",
       "ItemID                                                                       \n",
       "96       Terminator 2: Judgment Day (1991)  01-Jan-1991       1          0   \n",
       "48                      Hoop Dreams (1994)  01-Jan-1994       0          0   \n",
       "127                  Godfather, The (1972)  01-Jan-1972       1          0   \n",
       "150                        Swingers (1996)  18-Oct-1996       0          0   \n",
       "16      French Twist (Gazon maudit) (1995)  01-Jan-1995       0          0   \n",
       "\n",
       "        Animation  Children's  Comedy  Crime  Documentary  Drama  Fantasy  \\\n",
       "ItemID                                                                      \n",
       "96              0           0       0      0            0      0        0   \n",
       "48              0           0       0      0            1      0        0   \n",
       "127             0           0       0      1            0      1        0   \n",
       "150             0           0       1      0            0      1        0   \n",
       "16              0           0       1      0            0      0        0   \n",
       "\n",
       "        Film-Noir  Horror  Musical  Mystery  Romance  Sci-Fi  Thriller  War  \\\n",
       "ItemID                                                                        \n",
       "96              0       0        0        0        0       1         1    0   \n",
       "48              0       0        0        0        0       0         0    0   \n",
       "127             0       0        0        0        0       0         0    0   \n",
       "150             0       0        0        0        0       0         0    0   \n",
       "16              0       0        0        0        1       0         0    0   \n",
       "\n",
       "        Western  \n",
       "ItemID           \n",
       "96            0  \n",
       "48            0  \n",
       "127           0  \n",
       "150           0  \n",
       "16            0  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rating_mat = iknn_adjusted.train_set.matrix\n",
    "user_id2idx = iknn_adjusted.train_set.uid_map\n",
    "user_idx2id = list(iknn_adjusted.train_set.user_ids)\n",
    "item_id2idx = iknn_adjusted.train_set.iid_map\n",
    "item_idx2id = list(iknn_adjusted.train_set.item_ids)\n",
    "\n",
    "TOPK = 5\n",
    "UID = 1\n",
    "UIDX = user_id2idx[str(UID)]\n",
    "\n",
    "print(f\"UserID = {UID}\")\n",
    "print(\"-\" * 25)\n",
    "print(user_df.loc[UID])\n",
    "\n",
    "rating_arr = rating_mat[UIDX].A.ravel()\n",
    "top_rated_items = np.argsort(rating_arr)[-TOPK:]\n",
    "print(f\"\\nTOP {TOPK} RATED ITEMS BY USER {UID}:\")\n",
    "print(\"Ratings:\", rating_arr[top_rated_items])\n",
    "item_df.loc[[int(item_idx2id[i]) for i in top_rated_items]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Quali sono le raccomandazioni fornite all'utente dal nostro sistema di raccomandazione?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "TOP 5 RECOMMENDATIONS FOR USER 1:\n",
      "Scores: [4.65533227 4.64790324 4.64234397 4.61749142 4.61334104]\n"
     ]
    },
    {
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       "      <th>War</th>\n",
       "      <th>Western</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ItemID</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>115</th>\n",
       "      <td>Haunted World of Edward D. Wood Jr., The (1995)</td>\n",
       "      <td>26-Apr-1996</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>Horseman on the Roof, The (Hussard sur le toit...</td>\n",
       "      <td>19-Apr-1996</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>Return of the Jedi (1983)</td>\n",
       "      <td>14-Mar-1997</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>Jean de Florette (1986)</td>\n",
       "      <td>01-Jan-1986</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>Nikita (La Femme Nikita) (1990)</td>\n",
       "      <td>01-Jan-1990</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    Title Release Date  \\\n",
       "ItemID                                                                   \n",
       "115       Haunted World of Edward D. Wood Jr., The (1995)  26-Apr-1996   \n",
       "113     Horseman on the Roof, The (Hussard sur le toit...  19-Apr-1996   \n",
       "181                             Return of the Jedi (1983)  14-Mar-1997   \n",
       "165                               Jean de Florette (1986)  01-Jan-1986   \n",
       "198                       Nikita (La Femme Nikita) (1990)  01-Jan-1990   \n",
       "\n",
       "        Action  Adventure  Animation  Children's  Comedy  Crime  Documentary  \\\n",
       "ItemID                                                                         \n",
       "115          0          0          0           0       0      0            1   \n",
       "113          0          0          0           0       0      0            0   \n",
       "181          1          1          0           0       0      0            0   \n",
       "165          0          0          0           0       0      0            0   \n",
       "198          0          0          0           0       0      0            0   \n",
       "\n",
       "        Drama  Fantasy  Film-Noir  Horror  Musical  Mystery  Romance  Sci-Fi  \\\n",
       "ItemID                                                                         \n",
       "115         0        0          0       0        0        0        0       0   \n",
       "113         1        0          0       0        0        0        0       0   \n",
       "181         0        0          0       0        0        0        1       1   \n",
       "165         1        0          0       0        0        0        0       0   \n",
       "198         0        0          0       0        0        0        0       0   \n",
       "\n",
       "        Thriller  War  Western  \n",
       "ItemID                          \n",
       "115            0    0        0  \n",
       "113            0    0        0  \n",
       "181            0    1        0  \n",
       "165            0    0        0  \n",
       "198            1    0        0  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recommendations, scores = iknn_adjusted.rank(UIDX)\n",
    "print(f\"\\nTOP {TOPK} RECOMMENDATIONS FOR USER {UID}:\")\n",
    "print(\"Scores:\", scores[recommendations[:TOPK]])\n",
    "item_df.loc[[int(item_idx2id[i]) for i in recommendations[:TOPK]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Vediamo come il vicino più prossimo di ciascun articolo consigliato contribuisce ai punteggi finali."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "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>Recommendation</th>\n",
       "      <th>Item NN</th>\n",
       "      <th>Similarity</th>\n",
       "      <th>Score of the NN</th>\n",
       "      <th>Contribution</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Haunted World of Edward D. Wood Jr., The (1995)</td>\n",
       "      <td>1565</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.410256</td>\n",
       "      <td>0.410256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Horseman on the Roof, The (Hussard sur le toit...</td>\n",
       "      <td>100</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.410256</td>\n",
       "      <td>1.410256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Return of the Jedi (1983)</td>\n",
       "      <td>305</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.410256</td>\n",
       "      <td>1.410256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Jean de Florette (1986)</td>\n",
       "      <td>1278</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.410256</td>\n",
       "      <td>0.410256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Nikita (La Femme Nikita) (1990)</td>\n",
       "      <td>364</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.410256</td>\n",
       "      <td>1.410256</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                      Recommendation  Item NN  Similarity  \\\n",
       "0    Haunted World of Edward D. Wood Jr., The (1995)     1565         1.0   \n",
       "1  Horseman on the Roof, The (Hussard sur le toit...      100         1.0   \n",
       "2                          Return of the Jedi (1983)      305         1.0   \n",
       "3                            Jean de Florette (1986)     1278         1.0   \n",
       "4                    Nikita (La Femme Nikita) (1990)      364         1.0   \n",
       "\n",
       "   Score of the NN  Contribution  \n",
       "0         0.410256      0.410256  \n",
       "1         1.410256      1.410256  \n",
       "2         1.410256      1.410256  \n",
       "3         0.410256      0.410256  \n",
       "4         1.410256      1.410256  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = defaultdict(list)\n",
    "score_arr = iknn_adjusted.ui_mat[UIDX].A.ravel()\n",
    "rated_items = np.nonzero(rating_mat[UIDX])[1]\n",
    "for rec in recommendations[:TOPK]:\n",
    "  sim_arr = iknn_adjusted.sim_mat[rec].A.ravel()\n",
    "  nearest_neighbor = rated_items[np.argsort(sim_arr[rated_items])[-1]]\n",
    "  sim = sim_arr[nearest_neighbor]\n",
    "  score = score_arr[nearest_neighbor]\n",
    "  df[\"Recommendation\"].append(item_df.loc[[int(item_idx2id[rec])]][\"Title\"].values[0])\n",
    "  df[\"Item NN\"].append(nearest_neighbor)\n",
    "  df[\"Similarity\"].append(sim)\n",
    "  df[\"Score of the NN\"].append(score)\n",
    "  df[\"Contribution\"].append((score * sim) / np.abs(sim))\n",
    "rec_df = pd.DataFrame.from_dict(df)\n",
    "rec_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Un altro modo per interpretare la raccomandazione è osservare quante voci vicine all'elemento consigliato sono state precedentemente consumate dall'utente. Se ce ne sono molte, è possibile che l'utente abbia una preferenza per film simili."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\petru\\AppData\\Local\\Temp\\ipykernel_30496\\1277681025.py:9: FutureWarning: \n",
      "\n",
      "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n",
      "\n",
      "  sns.barplot(x=\"Recommendation\", y=\"Number of rated NN\", data=rec_df, palette=\"ch:.25\", ax=ax);\n",
      "C:\\Users\\petru\\AppData\\Local\\Temp\\ipykernel_30496\\1277681025.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_xticklabels(textwrap.fill(x.get_text(), 25) for x in ax.get_xticklabels());\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rated_items = np.nonzero(rating_mat[UIDX])[1]\n",
    "n_nearest_neighbors = []\n",
    "for rec in recommendations[:TOPK]:\n",
    "  nearest_neighbors = np.argsort(iknn_adjusted.sim_mat[rec].A.ravel())[-K:]\n",
    "  n_nearest_neighbors.append(len(np.intersect1d(nearest_neighbors, rated_items)))\n",
    "rec_df[\"Number of rated NN\"] = n_nearest_neighbors\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sns.barplot(x=\"Recommendation\", y=\"Number of rated NN\", data=rec_df, palette=\"ch:.25\", ax=ax);\n",
    "ax.set_xticklabels(textwrap.fill(x.get_text(), 25) for x in ax.get_xticklabels());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "In questo caso, la raccomandazione principale è *Haunted World of Edward D. Wood Jr., The (1995)*, e 9 film tra i suoi 50 vicini più simili sono stati valutati (probabilmente guardati) dall'utente."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".env",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}