Update pages/6SVM-Algorthim.py

pages/6SVM-Algorthim.py

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+import streamlit as st
+
+# Page configuration
+st.set_page_config(page_title="Support Vector Machines (SVM)", page_icon="🤖", layout="wide")
+
+# Custom CSS styling for the app
+st.markdown("""
+    <style>
+        .stApp {
+            background-color: #E8F0FE; /* A light, modern background */
+        }
+        h1, h2, h3 {
+            color: #002244;
+        }
+        .custom-font, p {
+            font-family: 'Arial', sans-serif;
+            font-size: 18px;
+            color: #000000;
+            line-height: 1.6;
+        }
+    </style>
+    """, unsafe_allow_html=True)
+
+# Page title
+st.markdown("<h1 style='color: #002244;'>Support Vector Machines (SVM) in Machine Learning</h1>", unsafe_allow_html=True)
+
+def main():
+    # Introduction to SVM
+    st.write("""
+    Support Vector Machines (SVM) is a powerful **supervised learning algorithm** employed for both **classification** and **regression** tasks.
+    Although it can perform regression (SVR), SVM is predominantly applied for classification in many real-world scenarios.
+    
+    At its core, SVM is a **parametric** and **linear model**, designed to determine the optimal decision boundary (hyperplane) that separates classes by maximizing the margin between them.
+    """)
+    st.image("svm.png", width=700)
+    
+    # Types of SVM
+    st.subheader("Types of SVM")
+    st.write("""
+    - **Support Vector Classifier (SVC)**: Used mainly for classification tasks.
+    - **Support Vector Regression (SVR)**: Applied for regression challenges.
+    """)
+    
+    # SVC Explanation
+    st.subheader("Working of Support Vector Classifier (SVC)")
+    st.write("""
+    The SVC algorithm works by:
+    1. Randomly initializing the hyperplane (decision boundary).
+    2. Identifying support vectors—data points closest to the decision boundary.
+    3. Calculating the **margin**, which is the distance between these support vectors.
+    4. Optimizing the hyperplane position such that the margin is maximized while minimizing misclassifications.
+    """)
+    
+    # Hard Margin vs Soft Margin Explanation
+    st.subheader("Hard Margin vs Soft Margin")
+    st.write("""
+    - **Hard Margin SVC**: Assumes that data is perfectly separable with no errors allowed.
+    - **Soft Margin SVC**: Permits some misclassifications to enhance model generalization on unseen data.
+    """)
+    st.image("soft vs hard.png", width=700)
+    
+    # Mathematical Formulation of SVM
+    st.subheader("Mathematical Formulation")
+    
+    st.write("**Hard Margin Constraint:** The model enforces that for all data points,")
+    st.latex(r"y_i (w^T x_i + b) \geq 1")
+    
+    st.write("**Soft Margin Constraint:** With slack variable \( \xi_i \) to allow misclassification,")
+    st.latex(r"y_i (w^T x_i + b) \geq 1 - \xi_i")
+    
+    st.write("**Interpretation of the Slack Variable \( \xi_i \):**")
+    st.latex(r"""
+        \begin{cases}
+        \xi_i = 0 & \text{Correct classification, point lies outside the margin} \\
+        0 < \xi_i \leq 1 & \text{Correct classification, but the point lies within the margin} \\
+        \xi_i > 1 & \text{Misclassification occurs}
+        \end{cases}
+    """)
+    
+    # Advantages and Disadvantages of SVM
+    st.subheader("Advantages & Disadvantages")
+    st.write("""
+    **Advantages:**
+    - Effective in high-dimensional spaces.
+    - Versatile as it works with both linearly separable and non-linearly separable datasets (using kernel methods).
+    - Robust against overfitting, especially in scenarios with many features.
+    
+    **Disadvantages:**
+    - Can be computationally intensive for large datasets.
+    - Requires careful hyperparameter tuning (e.g., regularization parameter **C** and kernel parameters like **gamma**).
+    """)
+    
+    # Dual Form and Kernel Trick Explanation
+    st.subheader("Dual Form and Kernel Trick")
+    st.write("""
+    When the data is not linearly separable, SVM employs the **Kernel Trick** to map data into a higher-dimensional space where a linear separation becomes possible.
+    
+    **Common Kernel Functions:**
+    - **Linear Kernel:** For data that is already linearly separable.
+    - **Polynomial Kernel:** For transforming data into a polynomial feature space.
+    - **Radial Basis Function (RBF) Kernel:** Captures complex relationships with non-linear boundaries.
+    - **Sigmoid Kernel:** Behaves similarly to activation functions in neural networks.
+    """)
+    st.image("dualform.png", width=700)
+    
+    # Hyperparameter Tuning
+    st.header("Hyperparameter Tuning in SVM")
+    st.write("""
+    **C Parameter (Regularization):**
+    - **High C:** Less tolerance for misclassification resulting in a smaller margin (risk of overfitting).
+    - **Low C:** Higher tolerance for misclassification, which can lead to a larger margin (better generalization).
+    
+    **Gamma (for RBF Kernel):**
+    - **High Gamma:** Each training point has more influence, potentially leading to overfitting.
+    - **Low Gamma:** Each training point has less influence, which might result in underfitting.
+    """)
+
+if __name__ == "__main__":
+    main()