Update pages/15_SVM.py

pages/15_SVM.py

@@ -81,7 +81,7 @@ with st.expander("📐 Mathematical Formulation"):
     st.latex(r"y_i (w^T x_i + b) \geq 1 - \xi_i")
 
     st.markdown(r"### Slack Variable \( \xi_i \) Interpretation:")
-    st.write("""
+    st.write(r"""
     - \( \xi_i = 0 \): Correct and outside the margin  
     - \( 0 < \xi_i \leq 1 \): Inside the margin, but correctly classified  
     - \( \xi_i > 1 \): Misclassified
@@ -105,13 +105,16 @@ with st.expander("✅ Pros & Cons of SVM"):
 # Dual Form & Kernel Trick
 with st.expander("🔄 Dual Form & Kernel Trick"):
     st.markdown(r"""
+    When data is not linearly separable in its original space, we use the **kernel trick** to transform it.
+
     ### Common Kernels:
     - **Linear Kernel**: \( K(x, x') = x^T x' \)  
     - **Polynomial Kernel**: \( K(x, x') = (x^T x' + c)^d \)  
     - **RBF (Gaussian)**: \( K(x, x') = \exp(-\gamma \|x - x'\|^2) \)  
     - **Sigmoid Kernel**: Mimics activation of neural networks
-    """)
 
+    ✅ The kernel trick allows working in higher dimensions **without explicitly transforming** the data.
+    """)
 
 # Hyperparameters
 with st.expander("⚙️ Hyperparameter Tuning"):
@@ -130,4 +133,3 @@ with st.expander("⚙️ Hyperparameter Tuning"):
 # Outro
 st.markdown("---")
 st.success("SVMs are powerful and flexible. Mastering margins, kernels, and regularization is key to using them effectively!")
-