diff --git a/user_based.ipynb b/user_based.ipynb
index 28f2623ab91332f09cc146fbc0d19d0b70196d28..d75d83b3db17809d0ebb23375bddcec2364abea0 100644
--- a/user_based.ipynb
+++ b/user_based.ipynb
@@ -11,19 +11,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 10,
    "id": "00d1b249",
    "metadata": {},
    "outputs": [
     {
-     "ename": "ImportError",
-     "evalue": "cannot import name 'Constant' from 'constants' (/Library/Frameworks/Python.framework/Versions/3.12/lib/python3.12/site-packages/constants.py)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[1], line 14\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpandas\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpd\u001b[39;00m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;66;03m# -- add new imports here --\u001b[39;00m\n\u001b[1;32m     12\u001b[0m \n\u001b[1;32m     13\u001b[0m \u001b[38;5;66;03m# local imports\u001b[39;00m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mconstants\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Constant \u001b[38;5;28;01mas\u001b[39;00m C\n\u001b[1;32m     15\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mloaders\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m load_ratings,load_items \n\u001b[1;32m     16\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01msurprise\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m KNNWithMeans, accuracy, AlgoBase, PredictionImpossible\n",
-      "\u001b[0;31mImportError\u001b[0m: cannot import name 'Constant' from 'constants' (/Library/Frameworks/Python.framework/Versions/3.12/lib/python3.12/site-packages/constants.py)"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The autoreload extension is already loaded. To reload it, use:\n",
+      "  %reload_ext autoreload\n"
      ]
     }
    ],
@@ -59,7 +56,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "id": "aafd1712",
    "metadata": {},
    "outputs": [
@@ -69,59 +66,18 @@
      "text": [
       "Computing the msd similarity matrix...\n",
       "Done computing similarity matrix.\n",
-      "user: 11         item: 364        r_ui = 4.00   est = 3.42   {'was_impossible': True, 'reason': 'User and/or item is unknown.'}\n"
+      "user: 11         item: 364        r_ui = None   est = 2.49   {'actual_k': 2, 'was_impossible': False}\n"
      ]
     }
    ],
    "source": [
-    "\n",
     "# Create Surprise Dataset from the pandas DataFrame and Reader\n",
     "surprise_data = load_ratings(surprise_format=True)\n",
     "\n",
     "trainset = surprise_data.build_full_trainset()\n",
     "\n",
     "\n",
-    "testset = trainset.build_anti_testset()\n",
-    "\n",
-    "\n",
-    "sim_options = {\n",
-    "    'name': 'msd',  # Mean Squared Difference (Mean Square Error)\n",
-    "    'user_based': True,  # User-based collaborative filtering\n",
-    "    'min_support': 3  # Minimum number of common ratings required\n",
-    "}\n",
-    "\n",
-    "\n",
-    "# Build an algorithm, and train it.\n",
-    "algo = KNNWithMeans(sim_options=sim_options, k=3, min_k=2)\n",
-    "algo.fit(trainset)\n",
-    "algo.test(testset)\n",
-    "\n",
-    "\n",
-    "uid = str(11)  # raw user id (as in the ratings file). They are **strings**!\n",
-    "iid = str(364) \n",
-    "\n",
-    "pred = algo.predict(uid, iid, r_ui=4, verbose=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "cf3ccdc0",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# -- load data, build trainset and anti testset --\n",
-    "# it depends on the tiny dataset\n",
-    "surprise_data = load_ratings(surprise_format=True)\n",
-    "df_movies = load_items()\n",
-    "\n",
-    "# Assuming you have a pandas DataFrame named 'df' with columns ['user_id', 'item_id', 'rating']\n",
-    "\n",
-    "# Build train set with all available ratings\n",
-    "trainset = surprise_data.build_full_trainset()\n",
-    "\n",
-    "# Build anti-test set\n",
-    "testset = trainset.build_anti_testset()"
+    "testset = trainset.build_anti_testset()\n"
    ]
   },
   {
@@ -136,43 +92,34 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e6fb78b7",
+   "id": "ce078b43",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Computing the msd similarity matrix...\n",
-      "Done computing similarity matrix.\n",
-      "3.4190898791540785\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "# -- using surprise's user-based algorithm, explore the impact of different parameters and displays predictions --\n",
+    "#User-based prediction for the user 11 and the item 364\n",
     "\n",
-    "# Define the similarity options\n",
     "sim_options = {\n",
     "    'name': 'msd',  # Mean Squared Difference (Mean Square Error)\n",
     "    'user_based': True,  # User-based collaborative filtering\n",
     "    'min_support': 3  # Minimum number of common ratings required\n",
     "}\n",
     "\n",
-    "# Create an instance of KNNWithMeans with the specified options\n",
-    "knn_model = KNNWithMeans(k=3, min_k=2, sim_options=sim_options)\n",
     "\n",
-    "# Train the algorithm on the trainset\n",
-    "knn_model.fit(trainset).test(testset)\n",
+    "# Build an algorithm, and train it.\n",
+    "algo = KNNWithMeans(sim_options=sim_options, k=3, min_k=2)\n",
+    "algo.fit(trainset)\n",
+    "algo.test(testset)\n",
+    "\n",
+    "\n",
+    "uid = 11  # raw user id (as in the ratings file). They are **strings**!\n",
+    "iid = 364 \n",
     "\n",
-    "# Make an estimation for user 11 and item 364\n",
-    "prediction = knn_model.predict('11', '364')\n",
-    "print(prediction.est)"
+    "pred = algo.predict(uid, iid, verbose=True)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "ffe89c56",
    "metadata": {},
    "outputs": [
@@ -183,102 +130,102 @@
       "Computing the msd similarity matrix...\n",
       "Done computing similarity matrix.\n",
       "Predictions with min_k = 1:\n",
-      "User: 15, Item: 942, Rating: 3.7769516356699464\n",
-      "User: 15, Item: 2117, Rating: 2.9340004894942537\n",
-      "User: 15, Item: 2672, Rating: 2.371008709611413\n",
-      "User: 15, Item: 5054, Rating: 3.010328638497653\n",
-      "User: 15, Item: 6322, Rating: 1.711175832857413\n",
-      "User: 15, Item: 6323, Rating: 1.7645762379992287\n",
-      "User: 15, Item: 6757, Rating: 3.010328638497653\n",
-      "User: 15, Item: 7700, Rating: 3.561484741491386\n",
-      "User: 15, Item: 7981, Rating: 3.386000174210522\n",
-      "User: 15, Item: 8600, Rating: 3.320743223639117\n",
-      "User: 15, Item: 8620, Rating: 2.7538763809343654\n",
-      "User: 15, Item: 31952, Rating: 3.7409900837647396\n",
-      "User: 15, Item: 3, Rating: 2.222062601579949\n",
-      "User: 15, Item: 64, Rating: 0.9224387353614938\n",
-      "User: 15, Item: 206, Rating: 2.35668733389394\n",
-      "User: 15, Item: 249, Rating: 3.1290259851652826\n",
-      "User: 15, Item: 276, Rating: 2.1800017354806753\n",
-      "User: 15, Item: 369, Rating: 2.3082373858282694\n",
-      "User: 15, Item: 504, Rating: 2.2600496220227573\n",
-      "User: 15, Item: 515, Rating: 3.6575674086958188\n",
-      "User: 15, Item: 522, Rating: 2.4562020809509626\n",
-      "User: 15, Item: 580, Rating: 1.9073310817298395\n",
-      "User: 15, Item: 599, Rating: 2.780847470837928\n",
-      "User: 15, Item: 915, Rating: 2.761094249104645\n",
-      "User: 15, Item: 966, Rating: 3.0894953051643195\n",
-      "User: 15, Item: 1274, Rating: 2.9873500196382845\n",
-      "User: 15, Item: 1299, Rating: 3.0779327239728005\n",
-      "User: 15, Item: 1345, Rating: 2.2037629856623138\n",
-      "User: 15, Item: 1354, Rating: 2.001877412379849\n",
-      "User: 15, Item: 532, Rating: 2.7123071345260277\n",
+      "User: 11, Item: 1214, Rating: 3.6041666666666665\n",
+      "User: 11, Item: 364, Rating: 2.49203431372549\n",
+      "User: 11, Item: 4308, Rating: 1.6041666666666667\n",
+      "User: 11, Item: 527, Rating: 3.898897058823529\n",
+      "User: 13, Item: 1997, Rating: 2.8\n",
+      "User: 13, Item: 4993, Rating: 3.2375\n",
+      "User: 13, Item: 2700, Rating: 2.8\n",
+      "User: 13, Item: 1721, Rating: 1.2374999999999998\n",
+      "User: 13, Item: 527, Rating: 3.2375\n",
+      "User: 17, Item: 2028, Rating: 3.8125\n",
+      "User: 17, Item: 4993, Rating: 4.128289473684211\n",
+      "User: 17, Item: 1214, Rating: 3.6875\n",
+      "User: 17, Item: 4308, Rating: 1.6875\n",
+      "User: 19, Item: 1997, Rating: 3.5\n",
+      "User: 19, Item: 2028, Rating: 3.5\n",
+      "User: 19, Item: 4993, Rating: 3.5\n",
+      "User: 19, Item: 5952, Rating: 3.5\n",
+      "User: 19, Item: 2700, Rating: 3.5\n",
+      "User: 19, Item: 1721, Rating: 3.5\n",
+      "User: 19, Item: 1214, Rating: 3.5\n",
+      "User: 19, Item: 364, Rating: 3.5\n",
+      "User: 23, Item: 1997, Rating: 2.782649253731343\n",
+      "User: 23, Item: 2700, Rating: 2.349813432835821\n",
+      "User: 27, Item: 1997, Rating: 4.666666666666667\n",
+      "User: 27, Item: 2028, Rating: 5.0\n",
+      "User: 27, Item: 5952, Rating: 5.0\n",
+      "User: 27, Item: 2700, Rating: 4.666666666666667\n",
+      "User: 27, Item: 1721, Rating: 3.104166666666667\n",
+      "User: 27, Item: 364, Rating: 4.604166666666667\n",
+      "User: 27, Item: 4308, Rating: 3.104166666666667\n",
       "Computing the msd similarity matrix...\n",
       "Done computing similarity matrix.\n",
       "Predictions with min_k = 2:\n",
-      "User: 15, Item: 942, Rating: 3.7769516356699464\n",
-      "User: 15, Item: 2117, Rating: 2.9340004894942537\n",
-      "User: 15, Item: 2672, Rating: 2.371008709611413\n",
-      "User: 15, Item: 5054, Rating: 2.693661971830986\n",
-      "User: 15, Item: 6322, Rating: 1.711175832857413\n",
-      "User: 15, Item: 6323, Rating: 1.7645762379992287\n",
-      "User: 15, Item: 6757, Rating: 2.693661971830986\n",
-      "User: 15, Item: 7700, Rating: 3.561484741491386\n",
-      "User: 15, Item: 7981, Rating: 3.386000174210522\n",
-      "User: 15, Item: 8600, Rating: 3.320743223639117\n",
-      "User: 15, Item: 8620, Rating: 2.7538763809343654\n",
-      "User: 15, Item: 31952, Rating: 3.7409900837647396\n",
-      "User: 15, Item: 3, Rating: 2.222062601579949\n",
-      "User: 15, Item: 64, Rating: 0.9224387353614938\n",
-      "User: 15, Item: 206, Rating: 2.35668733389394\n",
-      "User: 15, Item: 249, Rating: 3.1290259851652826\n",
-      "User: 15, Item: 276, Rating: 2.1800017354806753\n",
-      "User: 15, Item: 369, Rating: 2.3082373858282694\n",
-      "User: 15, Item: 504, Rating: 2.2600496220227573\n",
-      "User: 15, Item: 515, Rating: 3.6575674086958188\n",
-      "User: 15, Item: 522, Rating: 2.4562020809509626\n",
-      "User: 15, Item: 580, Rating: 1.9073310817298395\n",
-      "User: 15, Item: 599, Rating: 2.780847470837928\n",
-      "User: 15, Item: 915, Rating: 2.761094249104645\n",
-      "User: 15, Item: 966, Rating: 2.693661971830986\n",
-      "User: 15, Item: 1274, Rating: 2.9873500196382845\n",
-      "User: 15, Item: 1299, Rating: 3.0779327239728005\n",
-      "User: 15, Item: 1345, Rating: 2.2037629856623138\n",
-      "User: 15, Item: 1354, Rating: 2.001877412379849\n",
-      "User: 15, Item: 532, Rating: 2.7123071345260277\n",
+      "User: 11, Item: 1214, Rating: 3.1666666666666665\n",
+      "User: 11, Item: 364, Rating: 2.49203431372549\n",
+      "User: 11, Item: 4308, Rating: 3.1666666666666665\n",
+      "User: 11, Item: 527, Rating: 3.898897058823529\n",
+      "User: 13, Item: 1997, Rating: 2.8\n",
+      "User: 13, Item: 4993, Rating: 2.8\n",
+      "User: 13, Item: 2700, Rating: 2.8\n",
+      "User: 13, Item: 1721, Rating: 2.8\n",
+      "User: 13, Item: 527, Rating: 2.8\n",
+      "User: 17, Item: 2028, Rating: 3.8125\n",
+      "User: 17, Item: 4993, Rating: 4.128289473684211\n",
+      "User: 17, Item: 1214, Rating: 3.25\n",
+      "User: 17, Item: 4308, Rating: 3.25\n",
+      "User: 19, Item: 1997, Rating: 3.5\n",
+      "User: 19, Item: 2028, Rating: 3.5\n",
+      "User: 19, Item: 4993, Rating: 3.5\n",
+      "User: 19, Item: 5952, Rating: 3.5\n",
+      "User: 19, Item: 2700, Rating: 3.5\n",
+      "User: 19, Item: 1721, Rating: 3.5\n",
+      "User: 19, Item: 1214, Rating: 3.5\n",
+      "User: 19, Item: 364, Rating: 3.5\n",
+      "User: 23, Item: 1997, Rating: 2.782649253731343\n",
+      "User: 23, Item: 2700, Rating: 2.349813432835821\n",
+      "User: 27, Item: 1997, Rating: 4.666666666666667\n",
+      "User: 27, Item: 2028, Rating: 4.666666666666667\n",
+      "User: 27, Item: 5952, Rating: 4.666666666666667\n",
+      "User: 27, Item: 2700, Rating: 4.666666666666667\n",
+      "User: 27, Item: 1721, Rating: 4.666666666666667\n",
+      "User: 27, Item: 364, Rating: 4.666666666666667\n",
+      "User: 27, Item: 4308, Rating: 4.666666666666667\n",
       "Computing the msd similarity matrix...\n",
       "Done computing similarity matrix.\n",
       "Predictions with min_k = 3:\n",
-      "User: 15, Item: 942, Rating: 3.7769516356699464\n",
-      "User: 15, Item: 2117, Rating: 2.9340004894942537\n",
-      "User: 15, Item: 2672, Rating: 2.371008709611413\n",
-      "User: 15, Item: 5054, Rating: 2.693661971830986\n",
-      "User: 15, Item: 6322, Rating: 2.693661971830986\n",
-      "User: 15, Item: 6323, Rating: 1.7645762379992287\n",
-      "User: 15, Item: 6757, Rating: 2.693661971830986\n",
-      "User: 15, Item: 7700, Rating: 2.693661971830986\n",
-      "User: 15, Item: 7981, Rating: 3.386000174210522\n",
-      "User: 15, Item: 8600, Rating: 2.693661971830986\n",
-      "User: 15, Item: 8620, Rating: 2.7538763809343654\n",
-      "User: 15, Item: 31952, Rating: 2.693661971830986\n",
-      "User: 15, Item: 3, Rating: 2.222062601579949\n",
-      "User: 15, Item: 64, Rating: 0.9224387353614938\n",
-      "User: 15, Item: 206, Rating: 2.35668733389394\n",
-      "User: 15, Item: 249, Rating: 3.1290259851652826\n",
-      "User: 15, Item: 276, Rating: 2.1800017354806753\n",
-      "User: 15, Item: 369, Rating: 2.3082373858282694\n",
-      "User: 15, Item: 504, Rating: 2.2600496220227573\n",
-      "User: 15, Item: 515, Rating: 3.6575674086958188\n",
-      "User: 15, Item: 522, Rating: 2.4562020809509626\n",
-      "User: 15, Item: 580, Rating: 1.9073310817298395\n",
-      "User: 15, Item: 599, Rating: 2.780847470837928\n",
-      "User: 15, Item: 915, Rating: 2.761094249104645\n",
-      "User: 15, Item: 966, Rating: 2.693661971830986\n",
-      "User: 15, Item: 1274, Rating: 2.9873500196382845\n",
-      "User: 15, Item: 1299, Rating: 3.0779327239728005\n",
-      "User: 15, Item: 1345, Rating: 2.2037629856623138\n",
-      "User: 15, Item: 1354, Rating: 2.001877412379849\n",
-      "User: 15, Item: 532, Rating: 2.7123071345260277\n"
+      "User: 11, Item: 1214, Rating: 3.1666666666666665\n",
+      "User: 11, Item: 364, Rating: 3.1666666666666665\n",
+      "User: 11, Item: 4308, Rating: 3.1666666666666665\n",
+      "User: 11, Item: 527, Rating: 3.1666666666666665\n",
+      "User: 13, Item: 1997, Rating: 2.8\n",
+      "User: 13, Item: 4993, Rating: 2.8\n",
+      "User: 13, Item: 2700, Rating: 2.8\n",
+      "User: 13, Item: 1721, Rating: 2.8\n",
+      "User: 13, Item: 527, Rating: 2.8\n",
+      "User: 17, Item: 2028, Rating: 3.25\n",
+      "User: 17, Item: 4993, Rating: 3.25\n",
+      "User: 17, Item: 1214, Rating: 3.25\n",
+      "User: 17, Item: 4308, Rating: 3.25\n",
+      "User: 19, Item: 1997, Rating: 3.5\n",
+      "User: 19, Item: 2028, Rating: 3.5\n",
+      "User: 19, Item: 4993, Rating: 3.5\n",
+      "User: 19, Item: 5952, Rating: 3.5\n",
+      "User: 19, Item: 2700, Rating: 3.5\n",
+      "User: 19, Item: 1721, Rating: 3.5\n",
+      "User: 19, Item: 1214, Rating: 3.5\n",
+      "User: 19, Item: 364, Rating: 3.5\n",
+      "User: 23, Item: 1997, Rating: 2.5625\n",
+      "User: 23, Item: 2700, Rating: 2.5625\n",
+      "User: 27, Item: 1997, Rating: 4.666666666666667\n",
+      "User: 27, Item: 2028, Rating: 4.666666666666667\n",
+      "User: 27, Item: 5952, Rating: 4.666666666666667\n",
+      "User: 27, Item: 2700, Rating: 4.666666666666667\n",
+      "User: 27, Item: 1721, Rating: 4.666666666666667\n",
+      "User: 27, Item: 364, Rating: 4.666666666666667\n",
+      "User: 27, Item: 4308, Rating: 4.666666666666667\n"
      ]
     }
    ],
@@ -333,7 +280,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "id": "cc806424",
    "metadata": {},
    "outputs": [
@@ -343,109 +290,108 @@
      "text": [
       "\n",
       "Prédictions avec min_support = 1:\n",
-      "User: 15, Item: 942, Actual_k: 3\n",
-      "User: 15, Item: 2117, Actual_k: 3\n",
-      "User: 15, Item: 2672, Actual_k: 3\n",
-      "User: 15, Item: 5054, Actual_k: 1\n",
-      "User: 15, Item: 6322, Actual_k: 2\n",
-      "User: 15, Item: 6323, Actual_k: 3\n",
-      "User: 15, Item: 6757, Actual_k: 1\n",
-      "User: 15, Item: 7700, Actual_k: 2\n",
-      "User: 15, Item: 7981, Actual_k: 3\n",
-      "User: 15, Item: 8600, Actual_k: 2\n",
-      "User: 15, Item: 8620, Actual_k: 3\n",
-      "User: 15, Item: 31952, Actual_k: 2\n",
-      "User: 15, Item: 3, Actual_k: 3\n",
-      "User: 15, Item: 64, Actual_k: 3\n",
-      "User: 15, Item: 206, Actual_k: 3\n",
-      "User: 15, Item: 249, Actual_k: 3\n",
-      "User: 15, Item: 276, Actual_k: 3\n",
-      "User: 15, Item: 369, Actual_k: 3\n",
-      "User: 15, Item: 504, Actual_k: 3\n",
-      "User: 15, Item: 515, Actual_k: 3\n",
-      "User: 15, Item: 522, Actual_k: 3\n",
-      "User: 15, Item: 580, Actual_k: 3\n",
-      "User: 15, Item: 599, Actual_k: 3\n",
-      "User: 15, Item: 915, Actual_k: 3\n",
-      "User: 15, Item: 966, Actual_k: 1\n",
-      "User: 15, Item: 1274, Actual_k: 3\n",
-      "User: 15, Item: 1299, Actual_k: 3\n",
-      "User: 15, Item: 1345, Actual_k: 3\n",
-      "User: 15, Item: 1354, Actual_k: 3\n",
-      "User: 15, Item: 532, Actual_k: 3\n",
+      "User: 11, Item: 1214, Actual_k: 1\n",
+      "User: 11, Item: 364, Actual_k: 2\n",
+      "User: 11, Item: 4308, Actual_k: 1\n",
+      "User: 11, Item: 527, Actual_k: 2\n",
+      "User: 13, Item: 1997, Actual_k: 0\n",
+      "User: 13, Item: 4993, Actual_k: 1\n",
+      "User: 13, Item: 2700, Actual_k: 0\n",
+      "User: 13, Item: 1721, Actual_k: 1\n",
+      "User: 13, Item: 527, Actual_k: 1\n",
+      "User: 17, Item: 2028, Actual_k: 2\n",
+      "User: 17, Item: 4993, Actual_k: 2\n",
+      "User: 17, Item: 1214, Actual_k: 1\n",
+      "User: 17, Item: 4308, Actual_k: 1\n",
+      "User: 19, Item: 1997, Actual_k: 0\n",
+      "User: 19, Item: 2028, Actual_k: 0\n",
+      "User: 19, Item: 4993, Actual_k: 0\n",
+      "User: 19, Item: 5952, Actual_k: 0\n",
+      "User: 19, Item: 2700, Actual_k: 0\n",
+      "User: 19, Item: 1721, Actual_k: 0\n",
+      "User: 19, Item: 1214, Actual_k: 0\n",
+      "User: 19, Item: 364, Actual_k: 0\n",
+      "User: 23, Item: 1997, Actual_k: 2\n",
+      "User: 23, Item: 2700, Actual_k: 2\n",
+      "User: 27, Item: 1997, Actual_k: 0\n",
+      "User: 27, Item: 2028, Actual_k: 1\n",
+      "User: 27, Item: 5952, Actual_k: 1\n",
+      "User: 27, Item: 2700, Actual_k: 0\n",
+      "User: 27, Item: 1721, Actual_k: 1\n",
+      "User: 27, Item: 364, Actual_k: 1\n",
+      "User: 27, Item: 4308, Actual_k: 1\n",
       "\n",
       "Prédictions avec min_support = 2:\n",
-      "User: 15, Item: 942, Actual_k: 3\n",
-      "User: 15, Item: 2117, Actual_k: 3\n",
-      "User: 15, Item: 2672, Actual_k: 3\n",
-      "User: 15, Item: 5054, Actual_k: 1\n",
-      "User: 15, Item: 6322, Actual_k: 2\n",
-      "User: 15, Item: 6323, Actual_k: 3\n",
-      "User: 15, Item: 6757, Actual_k: 1\n",
-      "User: 15, Item: 7700, Actual_k: 2\n",
-      "User: 15, Item: 7981, Actual_k: 3\n",
-      "User: 15, Item: 8600, Actual_k: 2\n",
-      "User: 15, Item: 8620, Actual_k: 3\n",
-      "User: 15, Item: 31952, Actual_k: 2\n",
-      "User: 15, Item: 3, Actual_k: 3\n",
-      "User: 15, Item: 64, Actual_k: 3\n",
-      "User: 15, Item: 206, Actual_k: 3\n",
-      "User: 15, Item: 249, Actual_k: 3\n",
-      "User: 15, Item: 276, Actual_k: 3\n",
-      "User: 15, Item: 369, Actual_k: 3\n",
-      "User: 15, Item: 504, Actual_k: 3\n",
-      "User: 15, Item: 515, Actual_k: 3\n",
-      "User: 15, Item: 522, Actual_k: 3\n",
-      "User: 15, Item: 580, Actual_k: 3\n",
-      "User: 15, Item: 599, Actual_k: 3\n",
-      "User: 15, Item: 915, Actual_k: 3\n",
-      "User: 15, Item: 966, Actual_k: 1\n",
-      "User: 15, Item: 1274, Actual_k: 3\n",
-      "User: 15, Item: 1299, Actual_k: 3\n",
-      "User: 15, Item: 1345, Actual_k: 3\n",
-      "User: 15, Item: 1354, Actual_k: 3\n",
-      "User: 15, Item: 532, Actual_k: 3\n",
+      "User: 11, Item: 1214, Actual_k: 1\n",
+      "User: 11, Item: 364, Actual_k: 2\n",
+      "User: 11, Item: 4308, Actual_k: 1\n",
+      "User: 11, Item: 527, Actual_k: 2\n",
+      "User: 13, Item: 1997, Actual_k: 0\n",
+      "User: 13, Item: 4993, Actual_k: 1\n",
+      "User: 13, Item: 2700, Actual_k: 0\n",
+      "User: 13, Item: 1721, Actual_k: 1\n",
+      "User: 13, Item: 527, Actual_k: 1\n",
+      "User: 17, Item: 2028, Actual_k: 2\n",
+      "User: 17, Item: 4993, Actual_k: 2\n",
+      "User: 17, Item: 1214, Actual_k: 1\n",
+      "User: 17, Item: 4308, Actual_k: 1\n",
+      "User: 19, Item: 1997, Actual_k: 0\n",
+      "User: 19, Item: 2028, Actual_k: 0\n",
+      "User: 19, Item: 4993, Actual_k: 0\n",
+      "User: 19, Item: 5952, Actual_k: 0\n",
+      "User: 19, Item: 2700, Actual_k: 0\n",
+      "User: 19, Item: 1721, Actual_k: 0\n",
+      "User: 19, Item: 1214, Actual_k: 0\n",
+      "User: 19, Item: 364, Actual_k: 0\n",
+      "User: 23, Item: 1997, Actual_k: 2\n",
+      "User: 23, Item: 2700, Actual_k: 2\n",
+      "User: 27, Item: 1997, Actual_k: 0\n",
+      "User: 27, Item: 2028, Actual_k: 1\n",
+      "User: 27, Item: 5952, Actual_k: 1\n",
+      "User: 27, Item: 2700, Actual_k: 0\n",
+      "User: 27, Item: 1721, Actual_k: 1\n",
+      "User: 27, Item: 364, Actual_k: 1\n",
+      "User: 27, Item: 4308, Actual_k: 1\n",
       "\n",
       "Prédictions avec min_support = 3:\n",
-      "User: 15, Item: 942, Actual_k: 3\n",
-      "User: 15, Item: 2117, Actual_k: 3\n",
-      "User: 15, Item: 2672, Actual_k: 3\n",
-      "User: 15, Item: 5054, Actual_k: 1\n",
-      "User: 15, Item: 6322, Actual_k: 2\n",
-      "User: 15, Item: 6323, Actual_k: 3\n",
-      "User: 15, Item: 6757, Actual_k: 1\n",
-      "User: 15, Item: 7700, Actual_k: 2\n",
-      "User: 15, Item: 7981, Actual_k: 3\n",
-      "User: 15, Item: 8600, Actual_k: 2\n",
-      "User: 15, Item: 8620, Actual_k: 3\n",
-      "User: 15, Item: 31952, Actual_k: 2\n",
-      "User: 15, Item: 3, Actual_k: 3\n",
-      "User: 15, Item: 64, Actual_k: 3\n",
-      "User: 15, Item: 206, Actual_k: 3\n",
-      "User: 15, Item: 249, Actual_k: 3\n",
-      "User: 15, Item: 276, Actual_k: 3\n",
-      "User: 15, Item: 369, Actual_k: 3\n",
-      "User: 15, Item: 504, Actual_k: 3\n",
-      "User: 15, Item: 515, Actual_k: 3\n",
-      "User: 15, Item: 522, Actual_k: 3\n",
-      "User: 15, Item: 580, Actual_k: 3\n",
-      "User: 15, Item: 599, Actual_k: 3\n",
-      "User: 15, Item: 915, Actual_k: 3\n",
-      "User: 15, Item: 966, Actual_k: 1\n",
-      "User: 15, Item: 1274, Actual_k: 3\n",
-      "User: 15, Item: 1299, Actual_k: 3\n",
-      "User: 15, Item: 1345, Actual_k: 3\n",
-      "User: 15, Item: 1354, Actual_k: 3\n",
-      "User: 15, Item: 532, Actual_k: 3\n",
+      "User: 11, Item: 1214, Actual_k: 1\n",
+      "User: 11, Item: 364, Actual_k: 2\n",
+      "User: 11, Item: 4308, Actual_k: 1\n",
+      "User: 11, Item: 527, Actual_k: 2\n",
+      "User: 13, Item: 1997, Actual_k: 0\n",
+      "User: 13, Item: 4993, Actual_k: 1\n",
+      "User: 13, Item: 2700, Actual_k: 0\n",
+      "User: 13, Item: 1721, Actual_k: 1\n",
+      "User: 13, Item: 527, Actual_k: 1\n",
+      "User: 17, Item: 2028, Actual_k: 2\n",
+      "User: 17, Item: 4993, Actual_k: 2\n",
+      "User: 17, Item: 1214, Actual_k: 1\n",
+      "User: 17, Item: 4308, Actual_k: 1\n",
+      "User: 19, Item: 1997, Actual_k: 0\n",
+      "User: 19, Item: 2028, Actual_k: 0\n",
+      "User: 19, Item: 4993, Actual_k: 0\n",
+      "User: 19, Item: 5952, Actual_k: 0\n",
+      "User: 19, Item: 2700, Actual_k: 0\n",
+      "User: 19, Item: 1721, Actual_k: 0\n",
+      "User: 19, Item: 1214, Actual_k: 0\n",
+      "User: 19, Item: 364, Actual_k: 0\n",
+      "User: 23, Item: 1997, Actual_k: 2\n",
+      "User: 23, Item: 2700, Actual_k: 2\n",
+      "User: 27, Item: 1997, Actual_k: 0\n",
+      "User: 27, Item: 2028, Actual_k: 1\n",
+      "User: 27, Item: 5952, Actual_k: 1\n",
+      "User: 27, Item: 2700, Actual_k: 0\n",
+      "User: 27, Item: 1721, Actual_k: 1\n",
+      "User: 27, Item: 364, Actual_k: 1\n",
+      "User: 27, Item: 4308, Actual_k: 1\n",
       "\n",
       "Matrice de similarité:\n",
-      "[[1.         0.39130435 0.35942029 ... 0.24358974 0.28513238 0.21451104]\n",
-      " [0.39130435 1.         0.32786885 ... 0.30967742 0.42424242 0.21621622]\n",
-      " [0.35942029 0.32786885 1.         ... 0.36666667 0.72727273 0.34375   ]\n",
-      " ...\n",
-      " [0.24358974 0.30967742 0.36666667 ... 1.         0.6779661  0.37569061]\n",
-      " [0.28513238 0.42424242 0.72727273 ... 0.6779661  1.         0.83333333]\n",
-      " [0.21451104 0.21621622 0.34375    ... 0.37569061 0.83333333 1.        ]]\n",
+      "[[1.         0.         0.24615385 0.         0.43243243 0.        ]\n",
+      " [0.         1.         0.         0.         0.17094017 0.        ]\n",
+      " [0.24615385 0.         1.         0.         0.53333333 0.        ]\n",
+      " [0.         0.         0.         1.         0.         0.        ]\n",
+      " [0.43243243 0.17094017 0.53333333 0.         1.         0.25      ]\n",
+      " [0.         0.         0.         0.         0.25       1.        ]]\n",
       "None\n"
      ]
     }
@@ -485,7 +431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "id": "d03ed9eb",
    "metadata": {},
    "outputs": [
@@ -493,13 +439,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[3.  1.5 4.  ... nan nan nan]\n",
-      " [nan nan nan ... nan nan nan]\n",
-      " [4.  3.  3.  ... nan nan nan]\n",
-      " ...\n",
-      " [4.5 nan nan ... nan nan nan]\n",
-      " [nan nan nan ... nan nan nan]\n",
-      " [2.  nan nan ... nan nan nan]]\n"
+      "[[1.5 4.  5.  4.5 3.  1.  nan nan nan nan]\n",
+      " [nan 2.  nan 2.  nan nan 1.  5.  4.  nan]\n",
+      " [5.  nan nan 4.5 3.  1.  nan 1.5 nan 4.5]\n",
+      " [nan nan nan nan nan nan nan nan 2.  5. ]\n",
+      " [nan 3.  3.  4.  nan 1.  3.  2.5 1.  3. ]\n",
+      " [nan nan 5.  nan nan nan 4.  nan nan 5. ]]\n"
      ]
     }
    ],
@@ -629,7 +574,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "id": "be53ae27",
    "metadata": {},
    "outputs": [
@@ -637,10 +582,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "UserBased MAE: 1.5398252671298895\n",
-      "UserBased RMSE: 1.5553141029705104\n",
-      "KNNWithMeans MAE: 0.5419110316300769\n",
-      "KNNWithMeans RMSE: 0.7019543155680094\n"
+      "UserBased MAE: 1.7175000000000002\n",
+      "UserBased RMSE: 1.7384170241918369\n",
+      "KNNWithMeans MAE: 0.661617428851614\n",
+      "KNNWithMeans RMSE: 0.8426896111887758\n"
      ]
     }
    ],
@@ -686,7 +631,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "id": "c20d8e19",
    "metadata": {},
    "outputs": [
@@ -698,10 +643,10 @@
       "Done computing similarity matrix.\n",
       "Computing the cosine similarity matrix...\n",
       "Done computing similarity matrix.\n",
-      "RMSE: 0.9799\n",
-      "RMSE: 0.9871\n",
-      "RMSE with MSD similarity: 0.9798533097556152\n",
-      "RMSE with Jaccard similarity: 0.9870653791755158\n"
+      "RMSE: 1.0812\n",
+      "RMSE: 1.0910\n",
+      "RMSE with MSD similarity: 1.0811758629789194\n",
+      "RMSE with Jaccard similarity: 1.0910225374454734\n"
      ]
     }
    ],