Indhu27/MachineLearning_Algorithms

1import streamlit as st2 3st.set_page_config(page_title="svm", page_icon="🤖", layout="wide")4st.markdown("""5    <style>6        .stApp {7            background-color: #4A90E2;8        }9        h1, h2, h3 {10            color: #003366; /* Adjust this if needed to match your background */11        }12        .custom-font, p {13            font-family: 'Arial', sans-serif;14            font-size: 18px;15            color: white; /* Making all inside text white */16            line-height: 1.6;17        }18    </style>19    """, unsafe_allow_html=True)20 21 22# Title of the Streamlit Application23st.markdown("<h1 style='color: #003366;'>Support Vector Machines (SVM) in Machine Learning</h1>",unsafe_allow_html=True)24 25 26def main():27    28    st.write("""29    Support Vector Machines (SVM) is a **supervised learning algorithm** used for both **classification** and **regression** problems. 30    However, it is mostly used for classification tasks in real-world applications.31    32    SVM is a **parametric model** and is also known as a **linear model** in its basic form. It works by finding the optimal decision 33    boundary that maximizes the margin between different classes.34    """)35    st.image("svm.png",width=700)36    37    st.subheader("Types of SVM")38    st.write("""39    1. **Support Vector Classifier (SVC)** - Used for classification problems.40    2. **Support Vector Regression (SVR)** - Used for regression problems.41    """)42    43    st.markdown("</h2 style='color:'#003366;'>SVC: Support Vector Classifier</h2>",unsafe_allow_html=True)44    st.subheader("Working of SVC")45    st.write("""46    1. Randomly initialize weights and draw a line (hyperplane) to separate classes.47    2. Draw parallel lines (support vectors) at equal distances until one of the lines touches a data point.48    3. The **margin** is calculated as the distance between these support vectors.49    4. The objective is to **maximize this margin** while minimizing misclassification.50    """)51    52    st.markdown("</h2 style='color:'#003366;'>Hard Margin vs. Soft Margin SVC</h2>",unsafe_allow_html=True)53    st.write("""54    - **Hard Margin SVC**: Assumes data is **perfectly linearly separable** and does not allow misclassification.55    - **Soft Margin SVC**: Allows **some misclassification** to improve generalization on new data.56    """)57    st.image("soft vs hard.png",width=700)58    59    st.subheader("Mathematical Formulation")60    st.write("""61    - **Hard Margin Condition**: Ensures all points are correctly classified and lie outside the margin.62    """)63    st.latex(r" y_i (w^T x_i + b) \geq 1")64 65    st.write("""66    - **Soft Margin Condition**: Introduces a slack variable to allow misclassification.67    """)68    st.latex(r"y_i (w^T x_i + b) \geq 1 - \xi_i")69 70    st.write("""71    ### Interpretation of Slack Variable \( \xi \)72    - \( \xi_i = 0 \) : Correct classification, point lies outside the margin.73    - \( 0 < \xi_i \leq 1 \) : Correct classification, but the point is inside the margin.74    - \( \xi_i > 1 \) : Misclassification occurs.75    """)76 77    78    st.subheader("Advantages & Disadvantages")79    st.write("""80    **Advantages:**81    - Effective in high-dimensional spaces.82    - Works well with both linearly and non-linearly separable data (using kernels).83    - Robust against overfitting in high-dimensional datasets.84    85    **Disadvantages:**86    - Computationally expensive for large datasets.87    - Requires careful tuning of hyperparameters (C, kernel type).88    """)89    90    st.markdown("</h2 style='color:'#003366;'>Dual form of SVM</h2>",unsafe_allow_html=True)91    st.write("""92    When data is **not linearly separable**, we use the **Kernel Trick** to transform the data into a higher-dimensional space where 93    it becomes separable.94    95    **Types of Kernels:**96    - **Linear Kernel**: Used when data is already linearly separable.97    - **Polynomial Kernel**: Maps data into a polynomial feature space.98    - **Radial Basis Function (RBF) Kernel**: Captures complex relationships.99    - **Sigmoid Kernel**: Mimics the behavior of a neural network.100    """)101    st.image("dualform.png",width=700)102    103    st.header("Hyperparameter Tuning in SVM")104    st.write("""105    - **C Parameter**: Controls trade-off between maximizing margin and minimizing classification error.106      - **High C**: Less misclassification, smaller margin (risk of overfitting).107      - **Low C**: More misclassification, larger margin (better generalization).108    - **Gamma (for RBF kernel)**: Determines the influence of individual training points.109      - **High Gamma**: Each point has more influence (risk of overfitting).110      - **Low Gamma**: Each point has less influence (risk of underfitting).111    """)112 113 114if __name__ == "__main__":115    main()116