Clarification for 0.5 value in the formula of Regression model

Jupyter_Notebooks/Chapter_01_Supervised_Learning/02-Linear Classification/02-Linear_Classification.ipynb

@@ -130,6 +130,39 @@
         "# Plot the decision boundary: w1 * x1 + w2 * x2 + b = 0.5\n",
         "x_vals = np.linspace(-4, 6, 100)\n",
         "decision_boundary = (-w1 * x_vals - w0 + 0.5) / w2\n",
+        "# Note: This example uses a regression formulation to illustrate a classification problem.\n",
+        "# Regression is intended for continuous outputs, while classification is for discrete labels.\n",
+        "# In this illustrative case, we assume (wrongly, but intentionally for educational purposes) that:\n",
+        "# - We have two features (x1, x2).\n",
+        "# - The actual labels are 0 and 1.\n",
+        "# - The regression model will try to generate outputs as close as possible to 0 and 1 for the corresponding inputs.\n",
+        "#\n",
+        "# In other words, we're trying to fit a plane such that when applied to (x1, x2), \n",
+        "# the output is close to either 0 or 1 depending on the class.\n",
+        "# The regression model fits a plane of the form: \n",
+        "#       y = w1 * x1 + w2 * x2 + w0\n",
+        "# After fitting, we obtain w0, w1, and w2. That gives us the plane equation.\n",
+        "#\n",
+        "# Since the predicted outputs are expected to cluster around 0 and 1, we can introduce a simple threshold of 0.5 \n",
+        "# (i.e., the midpoint between 0 and 1) to separate the classes:\n",
+        "#       If predicted y > 0.5 → Class A; else → Class B.\n",
+        "#\n",
+        "# To visualize this boundary, we solve:\n",
+        "#       0.5 = w1 * x1 + w2 * x2 + w0\n",
+        "# which can be rearranged for x2 as:\n",
+        "#       x2 = -(w1 * x1 + w0 - 0.5) / w2\n",
+        "# This gives us the decision boundary line to plot.\n",
+        "#\n",
+        "# 🔬 Remark: Technically, this model is behaving like a *discriminant function*, \n",
+        "# since it assigns a score to any input vector and applies a threshold to classify.\n",
+        "# In fact, the fitted linear function:\n",
+        "#       g(x1, x2) = w1 * x1 + w2 * x2 + w0\n",
+        "# is formally a linear discriminant function.\n",
+        "# However, since it was trained using squared error rather than a classification loss, \n",
+        "# its decision boundary may not be optimal for classification purposes.\n",
+        "#\n",
+        "# ⚠️ This is purely an illustrative use of regression for classification, \n",
+        "# and should NOT be considered an appropriate substitute for proper classification algorithms.\n",
         "\n",
         "plt.figure(figsize=(8, 6))\n",
         "plt.scatter(class_A[:, 0], class_A[:, 1], label='Class A', color='blue')\n",