import streamlit as st

st.set_page_config(page_title="Support Vector Machine", page_icon="🧠", layout="wide")

# Title
st.markdown("<h1 style='color:#4CAF50;'>🧠 Support Vector Machine (SVM)</h1>", unsafe_allow_html=True)

# Introduction
st.markdown("### 📚 What is SVM?")
st.markdown("""
Support Vector Machine (SVM) is a powerful **supervised learning algorithm** used for both **classification** and **regression**, though it is mostly used for classification tasks.

The core idea is to find the **optimal hyperplane** that best separates the data points of different classes by maximizing the **margin** between them.
""")

# Use Cases
st.markdown("### 🎯 Where is SVM Used?")
st.markdown("""
- Face Recognition  
- Handwriting Recognition  
- Bioinformatics (e.g., gene classification)  
- Email Spam Detection  
- Image Classification
""")

# How It Works
st.markdown("### ⚙️ How Does SVM Work?")

with st.expander("🔹 Step 1: Find a Hyperplane"):
    st.markdown("""
    A **hyperplane** is a decision boundary that separates the data points of different classes.
    SVM tries to find the hyperplane that **maximizes the margin** between classes.
    """)

with st.expander("🔹 Step 2: Identify Support Vectors"):
    st.markdown("""
    **Support vectors** are the data points that lie closest to the hyperplane.  
    These points are critical in defining the position and orientation of the hyperplane.
    """)

with st.expander("🔹 Step 3: Handle Non-Linearly Separable Data"):
    st.markdown("""
    When the data is not linearly separable, SVM uses the **kernel trick** to project it into a higher-dimensional space where it becomes separable.
    """)

# Kernel Functions
st.markdown("### 🧪 Kernels in SVM")

with st.expander("📌 Common Kernel Functions"):
    st.markdown("""
    - **Linear Kernel**: For linearly separable data  
    - **Polynomial Kernel**: For curved decision boundaries  
    - **RBF (Radial Basis Function)**: Most popular, handles complex data  
    - **Sigmoid Kernel**: Similar to neural networks  
    """)

# Mathematical Intuition
st.markdown("### 🧠 Mathematical Formulation")

with st.expander("📌 Decision Function"):
    st.latex(r"f(x) = w \cdot x + b")

with st.expander("📌 Classification Rule"):
    st.markdown("""
    - If \\( f(x) > 0 \\): Predict **Class 1**  
    - If \\( f(x) < 0 \\): Predict **Class 0**  
    """)

with st.expander("📌 Optimization Objective"):
    st.latex(r"\text{Maximize Margin} = \frac{2}{\|w\|}")
    st.markdown("We want to maximize the margin between support vectors and the hyperplane.")

with st.expander("📌 Soft Margin & C Parameter"):
    st.latex(r" \min \frac{1}{2} \|w\|^2 + C \sum \xi_i ")
    st.markdown("""
    - The **C parameter** balances margin maximization vs classification error.
    - A **small C** allows for a wider margin but more errors.
    - A **large C** aims for perfect classification but might overfit.
    """)

# Evaluation Metrics
st.markdown("### 📏 Evaluation Metrics")

st.markdown("#### ✅ Accuracy")
st.latex(r"Accuracy = \frac{TP + TN}{TP + TN + FP + FN}")
st.markdown("The percentage of correct predictions.")

st.markdown("#### 🎯 Precision")
st.latex(r"Precision = \frac{TP}{TP + FP}")
st.markdown("Out of all predicted positives, how many are actually positive?")

st.markdown("#### 📣 Recall (Sensitivity)")
st.latex(r"Recall = \frac{TP}{TP + FN}")
st.markdown("Out of all actual positives, how many did we correctly predict?")

st.markdown("#### ⚖️ F1 Score")
st.latex(r"F1 = 2 \cdot \frac{Precision \cdot Recall}{Precision + Recall}")
st.markdown("Balances precision and recall — especially useful in imbalanced datasets.")

st.markdown("#### 📈 ROC-AUC")
st.markdown("""
- Plots True Positive Rate (TPR) vs False Positive Rate (FPR).  
- **AUC (Area Under Curve)** closer to 1 indicates a better model.
""")

# Pros and Cons
st.markdown("### ✅ Advantages of SVM")
st.markdown("""
- Effective in high-dimensional spaces  
- Works well even when features > samples  
- Memory efficient (uses support vectors)  
- Handles non-linearity with kernels  
""")

st.markdown("### ❌ Limitations of SVM")
st.markdown("""
- Not ideal for large datasets (computationally expensive)  
- Requires careful parameter tuning (C, kernel)  
- Hard to interpret compared to decision trees  
""")

# Summary
st.markdown("### 🔚 Summary")
st.markdown("""
Support Vector Machine is a **robust**, **flexible**, and **accurate** classification algorithm.  
Great for:
- Text data
- Image recognition
- Biomedical data

Make sure to:
- Scale your features  
- Use kernel wisely  
- Tune the **C** and **gamma** parameters

✅ Powerful for **both linear and non-linear** decision boundaries!
""")