decision_boundary_logisitc_regression.ipynb

{
 "cells":[
  {
   "cell_type":"markdown",
   "source":[
    "**In this notebook we will plot the decision boundary for a logistic regression model**"
   ],
   "attachments":{
    
   },
   "metadata":{
    "datalore":{
     "node_id":"TEyvS3HKI5yRi52eNwuwQk",
     "type":"MD",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's import the required libraries\n",
    "\n",
    "import numpy as np\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import matplotlib.pyplot as plt"
   ],
   "execution_count":11,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"iHICVlymtxqUOnlgXExsLv",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's define the sigmoid function\n",
    "\n",
    "def sigmoid_fn(z):\n",
    "\n",
    "    g = 1\/(1+np.exp(-z))\n",
    "\n",
    "    return g"
   ],
   "execution_count":49,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"ZeQkjRnz9D9TWdgas5PPXN",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's define the sigmoid function prediction based on a threshold value\n",
    "\n",
    "def sigmoid_fn_pred(z):\n",
    "\n",
    "    g = 1\/(1+np.exp(-z))\n",
    "\n",
    "    threshold = 0.5  # You can adjust this threshold\n",
    "    binary_prediction = (g >= threshold).astype(int)\n",
    "    return binary_prediction"
   ],
   "execution_count":50,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"ZhpISo2VoGxARr0E6n3zw8",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's define our training data set\n",
    "# Sample training data (input features X_train and corresponding labels y_train)\n",
    "x_train = np.array([\n",
    "    [3.2, 1.5],\n",
    "    [2.5, 2.8],\n",
    "    [1.9, 3.1],\n",
    "    [3.6, 4.0],\n",
    "    [2.8, 1.0],\n",
    "    [2.0, 2.7]\n",
    "])\n",
    "\n",
    "y_train = np.array([0, 1, 1, 0, 1, 0])  # Binary labels: 0 (class 0) and 1 (class 1)\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(x_train)\n",
    "\n",
    "sgd = SGDRegressor(max_iter=10000, alpha=0.0001)\n",
    "\n",
    "sgd.fit(X_train, y_train)\n",
    "\n",
    "x_test = np.array([   [3.2, 1.5],\n",
    "    [2.5, 2.8],\n",
    "    [1.9, 3.1],\n",
    "    [3.6, 4.0],\n",
    "    [2.8, 1.0],\n",
    "    [2.0, 2.7]])\n",
    "\n",
    "# Scale the test data using the same scaler\n",
    "x_test = scaler.fit_transform(x_test)\n",
    "\n",
    "y_pred = sgd.predict(x_test)\n",
    "\n",
    "print(f\"Weight used is: {sgd.coef_}\")\n",
    "print(f\"Bias used is: {sgd.intercept_}\")\n",
    "print(f\"Predicted value is: {y_pred}\")\n",
    "\n",
    "y = np.dot(x_test, sgd.coef_.T) + sgd.intercept_\n",
    "\n",
    "print(f\"Predicted value is: {y}\")"
   ],
   "execution_count":51,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Weight used is: [-0.12770139 -0.06134126]\n",
      "Bias used is: [0.29144914]\n",
      "Predicted value is: [0.24224032 0.30893755 0.41610456 0.00501299 0.35666568 0.41973374]\n",
      "Predicted value is: [0.24224032 0.30893755 0.41610456 0.00501299 0.35666568 0.41973374]\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"V5v0EKMnPQfk4wrWiejO79",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's use sigmoid function to predict value of y\n",
    "\n",
    "\n",
    "y_sig = sigmoid_fn(y)\n",
    "\n",
    "print(f\"Predicted value is: {y_sig}\")"
   ],
   "execution_count":52,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Predicted value is: [0.56026567 0.57662591 0.60255073 0.50125324 0.58823305 0.60341953]\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"bMtDjrULfnuOwabuWnKirw",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's plot distributed values of test y input to sigmoid function\n",
    "\n",
    "y_samp = np.arange(-10,11)\n",
    "\n",
    "sig_fn_res = sigmoid_fn(y_samp)\n",
    "\n",
    "# Decision boundary line\n",
    "decision_boundary = 0\n",
    "\n",
    "plt.plot(y_samp, sig_fn_res, marker=\"\", color=\"b\")\n",
    "# Add the vertical decision boundary line\n",
    "plt.axvline(x=decision_boundary, linestyle=\"--\", color=\"k\", label=\"Decision Boundary\")\n",
    "# Fill the regions left and right of the decision boundary\n",
    "# Fill the entire left side of the decision boundary as red and right side as green\n",
    "plt.fill_between(y_samp, 1, where=(y_samp <= decision_boundary), color='red', alpha=0.3, label=\"Left Side\")\n",
    "plt.fill_between(y_samp, 1, where=(y_samp >= decision_boundary), color='green', alpha=0.3, label=\"Right Side\")\n",
    "\n",
    "plt.title(\"Sigmoid function\")\n",
    "plt.ylabel('sigmoid(z)')\n",
    "plt.xlabel('z')"
   ],
   "execution_count":53,
   "outputs":[
    {
     "data":{
      "text\/plain":[
       "Text(0.5, 0, 'z')"
      ]
     },
     "metadata":{
      
     },
     "output_type":"display_data"
    },
    {
     "data":{
      "image\/png":[
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\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"M4q1Tzlxry9cn2h4rA2hqu",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    
   ],
   "execution_count":null,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"Vq1K4P6TU2GWxEi9TLTQ3Z",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  }
 ],
 "metadata":{
  "kernelspec":{
   "display_name":"Python",
   "language":"python",
   "name":"python"
  },
  "datalore":{
   "computation_mode":"JUPYTER",
   "package_manager":"pip",
   "base_environment":"default",
   "packages":[
    
   ],
   "report_row_ids":[
    
   ],
   "version":3
  }
 },
 "nbformat":4,
 "nbformat_minor":4
}