Es2_group11.ipynb

{"cells":[{"cell_type":"markdown","metadata":{"id":"QzPVjkgO6PVb"},"source":["# Data Analysis Exercise 2\n","Group 11:\n","*   Antonello Avella\n","*   Eugenio Carpentieri\n","*   Valerio Costantino\n","*   Claudio De Pisapia\n"]},{"cell_type":"code","execution_count":1,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":25110,"status":"ok","timestamp":1676293870824,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"aXNh8CYQQ57T","outputId":"8a6fff07-8eaa-42e1-d4f6-39a424f0fda1"},"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/gdrive/\n"]}],"source":["from google.colab import drive\n","\n","drive.mount('/content/gdrive/')"]},{"cell_type":"code","execution_count":3,"metadata":{"id":"YEll6AGfE_Zb","executionInfo":{"status":"ok","timestamp":1676293888209,"user_tz":-60,"elapsed":2,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"}}},"outputs":[],"source":["import seaborn as sns; sns.set()\n","import pandas as pd\n","import numpy as np\n","import matplotlib.pyplot as plt\n","import scipy.io\n","\n","from sklearn.decomposition import PCA\n","from sklearn.preprocessing import StandardScaler\n","\n","# set a seed for random generator\n","#np.random.seed(5)"]},{"cell_type":"markdown","metadata":{"id":"rzWaJHYRScw8"},"source":["## Dataset loading "]},{"cell_type":"code","execution_count":95,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":241,"status":"ok","timestamp":1676295141137,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"jItWsnJXRgZs","outputId":"19f5a859-db79-44ee-fabf-f3e96feffafd"},"outputs":[{"output_type":"stream","name":"stdout","text":["Train data shape:  (24000, 21)\n","Test data shape:  (80, 21)\n"]}],"source":["data_train = scipy.io.loadmat('/content/gdrive/MyDrive/2023/Data Analysis/finalProject_DA/Gruppo11-Prova/train_8feb23.mat')['train']\n","data_test = scipy.io.loadmat('/content/gdrive/MyDrive/2023/Data Analysis/finalProject_DA/Gruppo11-Prova/test_8feb23.mat')['test']\n","\n","\n","print('Train data shape: ', data_train.shape)\n","print('Test data shape: ', data_test.shape)\n","\n","\n","#np.random.shuffle(data_train)\n","\n","X_train = data_train[:,:-1]\n","Y_train = data_train[:,-1]\n","\n","data_test = data_test[data_test[:, -1].argsort()]  # sort by time\n","\n","X_test = data_test[:,:-1]\n","Time_test = data_test[:,-1]\n"]},{"cell_type":"code","source":["Time_test"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"K1owl8TKVCmr","executionInfo":{"status":"ok","timestamp":1675851064799,"user_tz":-60,"elapsed":3,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"}},"outputId":"02cc1fa6-27c9-451a-a1d8-7c0ee19af00a"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([  300.,   600.,   900.,  1200.,  1500.,  1800.,  2100.,  2400.,\n","        2700.,  3000.,  3300.,  3600.,  3900.,  4200.,  4500.,  4800.,\n","        5100.,  5400.,  5700.,  6000.,  6300.,  6600.,  6900.,  7200.,\n","        7500.,  7800.,  8100.,  8400.,  8700.,  9000.,  9300.,  9600.,\n","        9900., 10200., 10500., 10800., 11100., 11400., 11700., 12000.,\n","       12300., 12600., 12900., 13200., 13500., 13800., 14100., 14400.,\n","       14700., 15000., 15300., 15600., 15900., 16200., 16500., 16800.,\n","       17100., 17400., 17700., 18000., 18300., 18600., 18900., 19200.,\n","       19500., 19800., 20100., 20400., 20700., 21000., 21300., 21600.,\n","       21900., 22200., 22500., 22800., 23100., 23400., 23700., 24000.])"]},"metadata":{},"execution_count":7}]},{"cell_type":"markdown","metadata":{"id":"zWZe9fjPS7bj"},"source":["# Scatter and Correlation matrix"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000,"output_embedded_package_id":"1UpZZJX36_0H5OfdmFyB-CdySMjxoJrYg"},"executionInfo":{"elapsed":288420,"status":"ok","timestamp":1675851514697,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"ScxI2fnvFLps","outputId":"d0056dae-dd94-4254-b711-5e62ca41f532"},"outputs":[{"output_type":"display_data","data":{"text/plain":"Output hidden; open in https://colab.research.google.com to view."},"metadata":{}}],"source":["# ORIGINAL DATA VISUALIZATION\n","# Visualizing data in a 2- or 3-dimensional plot gives loads of information\n","# about data distribution and correlations, however it is not suitable for high\n","# dimensional data, as in our application. \n","# For example, we can explore data by observing the relationship existing \n","# between couples of features. From this activity we can detect that some of the\n","# features are heavily correlated. However, we cannot understand the \"big picture\"\n","\n","df = pd.DataFrame(X_train)\n","\n","sns.pairplot(df, palette='viridis')"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":293},"executionInfo":{"elapsed":1212,"status":"ok","timestamp":1675851541117,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"lMCS_iAOFnZY","outputId":"8d6a7b96-932b-409e-fbd9-ce90ceb03105"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["<matplotlib.axes._subplots.AxesSubplot at 0x7f77d5f6a820>"]},"metadata":{},"execution_count":18},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 2 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["sns.heatmap(df.corr())"]},{"cell_type":"markdown","metadata":{"id":"GMpT__W_ZwLz"},"source":["# PCA Sklearn"]},{"cell_type":"code","execution_count":71,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":675},"executionInfo":{"elapsed":1672,"status":"ok","timestamp":1676294965475,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"NqxxTnkJHosX","outputId":"e4e7ee7f-c381-4678-82cf-7fbf3e39ec4b"},"outputs":[{"output_type":"stream","name":"stdout","text":["Variance with scaled data\n","    Eigenvalues  Explained variance\n","0      2.482751            0.124132\n","1      1.939623            0.096977\n","2      1.866575            0.093325\n","3      1.508626            0.075428\n","4      1.454699            0.072732\n","5      1.337340            0.066864\n","6      1.270851            0.063540\n","7      1.120305            0.056013\n","8      1.100607            0.055028\n","9      0.969279            0.048462\n","10     0.887861            0.044391\n","11     0.786476            0.039322\n","12     0.664406            0.033219\n","13     0.584611            0.029229\n","14     0.542516            0.027125\n","15     0.451303            0.022564\n","16     0.392624            0.019630\n","17     0.335457            0.016772\n","18     0.295678            0.014783\n","19     0.009245            0.000462\n"]},{"output_type":"execute_result","data":{"text/plain":["<matplotlib.axes._subplots.AxesSubplot at 0x7f83e8f69e20>"]},"metadata":{},"execution_count":71},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 2 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["# Scaling\n","scaler = StandardScaler()\n","X_scale = scaler.fit_transform(X_train)\n","\n","# PCA computation\n","pca_scale = PCA()\n","pca_scale.fit(X_scale)\n","X_pca_scale = pca_scale.transform(X_scale)\n","\n","# Principal directions and the variance\n","print('Variance with scaled data')\n","pc_dirs = pca_scale.components_\n","pc_var = pca_scale.explained_variance_\n","var_pca_scale = pd.DataFrame(np.stack((pca_scale.explained_variance_, pca_scale.explained_variance_ratio_), axis=1), columns=['Eigenvalues', 'Explained variance'])\n","print(var_pca_scale)\n","\n","# Correlation matrix after PCA\n","dft = pd.DataFrame(X_pca_scale)\n","sns.heatmap(dft.corr())"]},{"cell_type":"markdown","metadata":{"id":"FrQx_KT_abzJ"},"source":["## Plotting Cumulative and Explained variance"]},{"cell_type":"code","execution_count":72,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":655},"executionInfo":{"elapsed":1286,"status":"ok","timestamp":1676294968850,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"-e6YyS-tJTuY","outputId":"ad7c2296-8122-400b-f061-6277880b689b"},"outputs":[{"output_type":"stream","name":"stdout","text":["    Proportion of variance explained  cumulative\n","1                           0.124132    0.124132\n","2                           0.096977    0.221109\n","3                           0.093325    0.314434\n","4                           0.075428    0.389862\n","5                           0.072732    0.462594\n","6                           0.066864    0.529459\n","7                           0.063540    0.592999\n","8                           0.056013    0.649011\n","9                           0.055028    0.704039\n","10                          0.048462    0.752501\n","11                          0.044391    0.796893\n","12                          0.039322    0.836215\n","13                          0.033219    0.869434\n","14                          0.029229    0.898663\n","15                          0.027125    0.925788\n","16                          0.022564    0.948352\n","17                          0.019630    0.967982\n","18                          0.016772    0.984754\n","19                          0.014783    0.999538\n","20                          0.000462    1.000000\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 2 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["idx = np.arange(20) + 1\n","df_explained_variance_scale = pd.DataFrame([pca_scale.explained_variance_ratio_, np.cumsum(pca_scale.explained_variance_ratio_)], \n","                                     index=['Proportion of variance explained', 'cumulative'], \n","                                     columns=idx).T\n","\n","print(df_explained_variance_scale)\n","\n","\n","fig, ax1 = plt.subplots()\n","ax1.set_xlabel('Principal component', fontsize=14)\n","ax1.set_ylabel('Proportion of variance explained', fontsize=14)\n","ax2 = sns.barplot(x=idx, y='Proportion of variance explained', data=df_explained_variance_scale, palette='rocket_r')\n","ax2 = ax1.twinx()\n","ax2.grid(False)\n","ax2.set_ylabel('Cumulative variance explained', fontsize=14)\n","ax2 = sns.lineplot(x=idx-1, y='cumulative', data=df_explained_variance_scale, color='k')"]},{"cell_type":"markdown","metadata":{"id":"GKXwx4RObSnL"},"source":["## Dimensionality reduction"]},{"cell_type":"code","execution_count":73,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":354,"status":"ok","timestamp":1676294972062,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"4HeeVC-NYUB2","outputId":"c72302de-6433-45ef-da5e-5e0f33eb2eb8"},"outputs":[{"output_type":"stream","name":"stdout","text":["Train Set\n","\toriginal shape:    (24000, 20)\n","\ttransformed shape: (24000, 17)\n","\n","Test Set\n","\toriginal shape:    (80, 20)\n","\ttransformed shape: (80, 17)\n"]}],"source":["# the plot shows that 17 principal components allow to preserve more than\n","# 95% of the total data set variance! So, we re-apply PCA setting the \n","# number of components to 17\n","m = 17\n","pca2 = PCA(n_components=m)\n","pca2.fit(X_scale)\n","X_train_pca = pca2.transform(X_train)\n","X_test_pca = pca2.transform(X_test)\n","\n","print(\"Train Set\")\n","print(\"\\toriginal shape:   \", X_train.shape)\n","print(\"\\ttransformed shape:\", X_train_pca.shape)\n","\n","print(\"\\nTest Set\")\n","print(\"\\toriginal shape:   \", X_test.shape)\n","print(\"\\ttransformed shape:\", X_test_pca.shape)"]},{"cell_type":"markdown","metadata":{"id":"0Tr1rbx6d-vV"},"source":["# SkLearn Logistic Regression (not used)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"mfUPm8A-d-V5"},"outputs":[],"source":["from sklearn.linear_model import SGDClassifier\n","\n","# use only to obtain quickly the solution \n","def my_lr_classification(XX_train, XX_test, YY_train):\n","    lr = SGDClassifier('log') \n","    lr.fit(XX_train, YY_train)\n","    YY_estimated = lr.predict(XX_test) \n","\n","    return YY_estimated;"]},{"cell_type":"markdown","metadata":{"id":"Qc4xjOGzCbmP"},"source":["# Logistic Regression model"]},{"cell_type":"code","execution_count":133,"metadata":{"id":"Ogn9HqPMhsol","executionInfo":{"status":"ok","timestamp":1676295628827,"user_tz":-60,"elapsed":242,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"}}},"outputs":[],"source":["def sigmoid(z):\n","    sig = 1 / (1 + np.exp(-z))\n","    return sig\n","\n","def loss(x, y, beta):\n","  return np.log(1 / sigmoid(np.dot(x.T, beta).sum() * y))\n","\n","def predict(x, beta):\n","    sum = np.dot(x.T, beta).sum()\n","    if sum > 0:\n","        return 1\n","    return -1\n","\n","def calc_loss_and_acc(x, y, beta):\n","    temp_loss=[]\n","    temp_acc=[]\n","    for x_i, y_i in zip(x, y):\n","        temp_loss = np.append(temp_loss, loss(x_i, y_i, beta))\n","        temp_acc = np.append(temp_acc, predict(x_i, beta)==y_i)\n","    return np.mean(temp_loss), np.mean(temp_acc)\n","\n","def sgd(x_train, y_train, lr=0.1, epochs=1,):\n","    beta_total = np.random.normal(size = x_train.shape[1])\n","\n","    temp_loss, temp_acc = calc_loss_and_acc(x_train, y_train, beta_total)\n","    epochs_train_loss = [temp_loss]\n","    epochs_train_acc = [temp_acc]\n","\n","    for i in range(epochs):\n","        beta_approx = []\n","        for x_i, y_i in zip(x_train, y_train):\n","            grad = -(x_i.T * y_i) / (np.exp(np.dot(x_i.T, beta_total) * y_i) + 1)\n","            beta_total -= lr * grad\n","            beta_approx.append(beta_total)\n","        \n","        temp_loss, temp_acc = calc_loss_and_acc(x_train, y_train, beta_total)\n","        epochs_train_loss.append(temp_loss)\n","        epochs_train_acc.append(temp_acc)\n","\n","        print(\"Epoch \", i+1, \" ->  Train loss: \", np.round(epochs_train_loss[-1], 3), \"  Train acc: \", np.round(epochs_train_acc[-1], 4))\n","   \n","    return beta_approx, epochs_train_loss, epochs_train_acc"]},{"cell_type":"markdown","metadata":{"id":"tDmjYlbjCrdG"},"source":["### Training phase"]},{"cell_type":"code","execution_count":132,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":19351,"status":"ok","timestamp":1676295622442,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"uleEI7cW031Q","outputId":"482eeddf-0925-41d9-f340-5b4c96d42ed3"},"outputs":[{"output_type":"stream","name":"stdout","text":["[  7.69968463   8.42526179 -10.05247494 -14.37479599  -4.33431028\n","   8.27474299   3.45303557  -3.40038114  -9.35775095 -17.13856305\n"," -19.32011494  13.93798009 -22.12418782  -1.03679208  -9.23041586\n","  -4.88400963  -7.55902095  23.97747117  -4.74738658   1.72596027]\n","[-12.06932205 -11.60885741  14.16523163  19.74106689   5.83955729\n"," -10.59190526  -6.54808852   5.95844143  14.4019408   26.71318024\n","  28.41568496 -22.56671116  31.30838859  -0.61659962  12.57166226\n","   6.03177908  13.23087794 -35.0119716    6.55461929  -4.20657085]\n","[-12.35724123 -10.09117283  12.71493662  17.07660806   4.90678193\n","  -8.17274919  -7.97957443   6.8062883   14.44627631  27.18008925\n","  26.99461285 -23.91239452  28.26852707  -3.14921388  10.74080162\n","   4.35169662  15.09878373 -32.95736468   5.71478506  -5.99292909]\n","[  8.13338401   7.35629519  -9.08067404 -12.48776268  -3.65636179\n","   6.44281644   4.74438952  -4.19888494  -9.62747964 -17.95741212\n"," -18.60307705  15.41745267 -20.11343666   1.07043565  -7.91768655\n","  -3.59032804  -9.31989654  22.84252857  -4.15797168   3.27329879]\n","[-12.41461435 -11.6543946   14.28492734  19.80515214   5.83542179\n"," -10.46826698  -6.93907177   6.24160069  14.76618344  27.4502175\n","  28.89345315 -23.34124849  31.59939125  -1.03632268  12.59106574\n","   5.91307359  13.85728349 -35.55215644   6.58305877  -4.59615469]\n","[  8.17773725   7.40938091  -9.1431169  -12.57852156  -3.68404896\n","   6.49726056   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1.85119736  15.18797031]\n","[-12.22878449 -14.70876432  14.01820412 -20.59079279  -7.11620518\n","   6.7654458  -22.42597152   8.68103841   5.10029433  -6.51495172\n","  32.8424694   -1.32551171  -7.01376687 -12.6760798   20.85686764\n","  24.33138319   6.565907     3.34745236   4.95012939  17.67737151]\n","[ 14.54288034  13.25617874  -8.31619124  21.65529228  10.10971426\n","  -7.77543807  21.30452925  -5.84250099  -4.31941338  10.89913779\n"," -33.03586781   1.91646172   3.90021829  13.06953989 -16.42521183\n"," -20.72372224  -8.39844762  -9.32762237  -2.89070714 -17.88757621]\n","[ 14.03889992  13.31103433  -9.04225543  21.24863242   9.55943323\n","  -7.53879097  21.21755666  -6.1840558   -4.38169197  10.13885939\n"," -32.62202389   1.80875689   4.30416673  12.86005773 -16.87314255\n"," -21.00247596  -8.03576928  -8.35528625  -3.15426186 -17.64826713]\n"]},{"output_type":"stream","name":"stderr","text":["<ipython-input-131-c21e2fde4dcb>:2: RuntimeWarning: overflow encountered in exp\n","  sig = 1 / (1 + np.exp(-z))\n","<ipython-input-131-c21e2fde4dcb>:6: RuntimeWarning: divide by zero encountered in double_scalars\n","  return np.log(1 / sigmoid(np.dot(x.T, beta).sum() * y))\n"]},{"output_type":"stream","name":"stdout","text":["Epoch  1  ->  Train loss:  inf   Train acc:  0.9617\n"]}],"source":["num_epochs = 1\n","lr = 1\n","\n","beta, epochs_train_loss, epochs_train_acc = sgd(X_train, Y_train, lr, num_epochs)"]},{"cell_type":"code","source":["beta[1]"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"8vaAeXJu_Wpp","executionInfo":{"status":"ok","timestamp":1676295545715,"user_tz":-60,"elapsed":5,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"}},"outputId":"d3992ed7-df97-4e9c-f386-32540b7c6102"},"execution_count":128,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([108.45835536, 114.00235418,  -4.55651689,  19.43680157,\n","       -19.3482868 ,  32.08390285,  -5.64429653, -13.84933336,\n","       -21.87443641, -15.61751178,   6.44069172, -10.29308006,\n","        10.61232474,   0.81575205, -14.8894035 ,  14.53170642,\n","       -17.27756405,  25.32032588,   1.85186847,  12.62488607])"]},"metadata":{},"execution_count":128}]},{"cell_type":"code","source":["beta_plot = []\n","for i in beta:\n","  beta_plot.append(i[0])"],"metadata":{"id":"f9EwVBeJ6YoR","executionInfo":{"status":"ok","timestamp":1676295548550,"user_tz":-60,"elapsed":239,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"}}},"execution_count":129,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"oEMxQuY9Cv7X"},"source":["## Plotting Loss and Accuracy"]},{"cell_type":"code","execution_count":130,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":869},"executionInfo":{"elapsed":1292,"status":"ok","timestamp":1676295552008,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"s7-LbpWsLxck","outputId":"73e87b5d-b0c4-475d-ed87-781d397652aa"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":["<Figure 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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":["<Figure 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\n"},"metadata":{}}],"source":["# Loss plot\n","plt.title(\"Train vs Val loss\")\n","plt.plot(np.arange(0,num_epochs+1), epochs_train_loss, color=\"red\")\n","plt.legend([\"Train\"])\n","plt.xlabel(\"Epochs\")\n","plt.ylabel(\"Loss\")\n","plt.ylim(top=0.5, bottom=0)\n","plt.show()\n","\n","# Accuracy plot\n","plt.title(\"Train vs Val accuracy\")\n","plt.plot(np.arange(0,num_epochs+1), epochs_train_acc, color=\"red\")\n","plt.legend([\"Train\"])\n","plt.xlabel(\"Epochs\")\n","plt.ylabel(\"Accuracy\")\n","plt.ylim(top=1, bottom=0.9)\n","plt.show()\n","\n","# beta plot\n","plt.title(\"Beta\")\n","plt.plot(range(0,len(beta_plot)), beta_plot, color=\"red\")\n","plt.legend([\"Train\"])\n","plt.xlabel(\"Epochs\")\n","plt.ylabel(\"Accuracy\")\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"RSuyPjSvLqRF"},"source":["# Predict on Test Set"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":223,"status":"ok","timestamp":1675876679952,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"8ddWSoPbsLsr","outputId":"3642fa07-09ee-4eec-d512-fcb074adba31"},"outputs":[{"output_type":"stream","name":"stdout","text":["[-1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1]\n"]}],"source":["y_pred=[]\n","\n","for x, i in  zip(X_test_pca, Time_test):\n","    y_pred.append(predict(x, beta[int(i-1)]))\n","\n","print(y_pred)"]},{"cell_type":"markdown","metadata":{"id":"E0461othhcos"},"source":["## String decode"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":1,"status":"ok","timestamp":1675876681232,"user":{"displayName":"ANTONELLO AVELLA","userId":"15688316060644635007"},"user_tz":-60},"id":"Dhw68TZ7eF1e","outputId":"3bcef0bb-a8e1-4b08-a909-64765ab5f50c"},"outputs":[{"output_type":"stream","name":"stdout","text":["String converted: WntrComing\n"]}],"source":["#y_pred = my_lr_classification(X_train_pca, X_test_pca, Y_train)\n","\n","bits = \"\"\n","for bit in y_pred:\n","  if(bit == -1):\n","    bits += \"0\"\n","  else:\n","    bits += \"1\"\n","\n","def BinaryToDecimal(binary):\n","    binary1 = binary\n","    decimal, i, n = 0, 0, 0\n","    while(binary != 0):\n","        dec = binary % 10\n","        decimal = decimal + dec * pow(2, i)\n","        binary = binary//10\n","        i += 1\n","    return (decimal) \n","\n","str_data=\"\"  \n","\n","for i in range(0, len(bits), 8):\n","    temp_data = int(bits[i : i + 8])\n","    decimal_data = BinaryToDecimal(temp_data)\n","    str_data = str_data + chr(decimal_data)\n","  \n","# printing the result\n","print(\"String converted:\", str_data)\n"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0}