Update pages/14_SVM.py

pages/14_SVM.py

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+import streamlit as st
+
+st.set_page_config(page_title="Support Vector Machines", page_icon="🧭", layout="wide")
+
+st.sidebar.title("🔍 Support Vector Machines")
+st.sidebar.markdown("Learn how SVM works for classification and regression tasks.")
+st.sidebar.markdown("---")
+
+section = st.radio(
+    "📚 Select a section to explore:",
+    [
+        "📘 What is SVM?",
+        "🧠 Types of SVM",
+        "🛠️ Working of SVC",
+        "📏 Hard Margin vs Soft Margin",
+        "📐 Mathematical Formulation",
+        "✅ Pros & Cons of SVM",
+        "🔄 Dual Form & Kernel Trick",
+        "⚙️ Hyperparameter Tuning"
+    ]
+)
+
+st.markdown("<h1 style='text-align: center;'>🤖 Support Vector Machines (SVM)</h1>", unsafe_allow_html=True)
+
+if section == "📘 What is SVM?":
+    st.write("""
+    Support Vector Machines (SVM) is a **supervised learning algorithm** used for both **classification** and **regression** problems.  
+    In practice, it's most often used for **classification** tasks.
+    
+    🧠 SVM finds the **optimal decision boundary (hyperplane)** that maximizes the **margin** between classes.
+    """)
+
+elif section == "🧠 Types of SVM":
+    st.write("""
+    1. **Support Vector Classifier (SVC)**: Used for classification  
+    2. **Support Vector Regression (SVR)**: Used for predicting continuous values
+    """)
+
+elif section == "🛠️ Working of SVC":
+    st.write("""
+    Steps:
+    1. Start with a random separating hyperplane.
+    2. Identify **support vectors** (closest points from each class).
+    3. Adjust the hyperplane to **maximize the margin** between the support vectors.
+    
+    🔑 Goal: Maximize the distance between the hyperplane and the nearest data points.
+    """)
+
+elif section == "📏 Hard Margin vs Soft Margin":
+    st.write("""
+    - **Hard Margin**:
+        - Assumes **perfectly separable** data.
+        - No misclassifications allowed.
+    - **Soft Margin**:
+        - Allows **some misclassification**.
+        - More flexible, better for real-world noisy data.
+    """)
+
+elif section == "📐 Mathematical Formulation":
+    st.markdown("### Hard Margin Condition:")
+    st.latex(r"y_i (w^T x_i + b) \geq 1")
+
+    st.markdown("### Soft Margin Condition:")
+    st.latex(r"y_i (w^T x_i + b) \geq 1 - \xi_i")
+
+    st.markdown("### Slack Variable \( \xi_i \) Interpretation:")
+    st.write("""
+    - \( \xi_i = 0 \): Correct and outside the margin  
+    - \( 0 < \xi_i \leq 1 \): Inside the margin, but correctly classified  
+    - \( \xi_i > 1 \): Misclassified
+    """)
+
+elif section == "✅ Pros & Cons of SVM":
+    st.markdown("### Advantages:")
+    st.write("""
+    - Works well in **high-dimensional** spaces  
+    - Effective with both linear and **non-linear** data (using kernels)  
+    - Resistant to **overfitting**
+    """)
+
+    st.markdown("### Disadvantages:")
+    st.write("""
+    - Computationally **slow** for large datasets  
+    - Requires tuning of hyperparameters (`C`, `gamma`)
+    """)
+
+elif section == "🔄 Dual Form & Kernel Trick":
+    st.markdown("""
+    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.
+    """)
+
+elif section == "⚙️ Hyperparameter Tuning":
+    st.write("""
+    - **C (Regularization)**:
+        - Controls the trade-off between maximizing margin and minimizing misclassification.
+        - High C → strict on misclassification (may overfit)  
+        - Low C → allows more slack (better generalization)
+        
+    - **Gamma** (only for RBF/Polynomial Kernels):
+        - Defines how far the influence of a single data point reaches.  
+        - High Gamma → close points matter more → can overfit  
+        - Low Gamma → wider influence → can underfit
+    """)
+
+st.markdown("---")
+st.success("SVMs are powerful and flexible. Mastering margins, kernels, and regularization is key to using them effectively!")