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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()
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