🔍 Introduction

In real-life scenarios like medical diagnosis, classifying patients as healthy or diseased often involves complex relationships between multiple biological indicators. These relationships are non-linear, which means a straight line (linear model) simply isn’t good enough. To tackle this, I designed a Logistic Regression model with Polynomial Features that can handle such non-linear decision boundaries with high accuracy.

In this blog post, I’ll walk you through:

• What I built and why

• How I created synthetic but realistic data

• The algorithms and techniques I used

• The results, visualization, and GitHub repository

🔗 GitHub Repository:
👉 Logistic Regression with Polynomial Features

🏥 Real-World Analogy: A Medical Diagnosis System

Imagine a simple system that predicts whether a patient is sick or healthy based on two lab test results (e.g., X1 = blood sugar, X2 = blood pressure). If the symptoms follow a circular or ring-shaped pattern (which is common when data clusters form), we need something more powerful than a straight-line model.

That’s where Polynomial Logistic Regression comes in.

📘 Techniques and Algorithms Used

Here are all the techniques and components that make up this project:

🔹 1. Data Generation (Synthetic Medical Data)

• Two features per sample (X1 and X2)

• 100 total samples:

  • Class 0 (Healthy) → Clustered near the center (inner circle)

  • Class 1 (Diseased) → Spread in an outer ring

🔹 2. Logistic Regression Model

• Binary Classification using the Sigmoid function:

  $$\sigma(z) = \frac{1}{1 + e^{-z}}$$

🔹 3. Polynomial Feature Mapping

• Instead of using raw features [x1, x2], we map them to:

  $$[1, x1, x2, x1^2, x1 \cdot x2, x2^2]$$

• This allows the model to learn curved (non-linear) decision boundaries.

🔹 4. Cost Function

• Standard logistic loss:

  $$J(w, b) = -\frac{1}{m} \sum_{i=1}^{m} [y_i \log(f_wb) + (1 - y_i) \log(1 - f_wb)]$$

🔹 5. Gradient Descent Optimization

• I implemented gradient descent manually to minimize the cost:

  • Compute gradients: ∂J/∂w and ∂J/∂b

  • Update weights iteratively using learning rate α = 0.01

  • Total iterations: 10,000

🔹 6. Accuracy Evaluation

• The model achieved ~95% to 100% training accuracy, depending on the random seed.

🔹 7. Visualization

• Scatter plot of the original dataset

• Decision boundary plotted using a contour plot

• Clearly shows the model has learned a curved boundary that separates both classes effectively

🧪 Results

• ✅ Training Accuracy: ~95%–100%

• 🟦 Class 1 (Diseased): Blue circles

• 🟥 Class 0 (Healthy): Red crosses

• 📈 Decision Boundary: Curved yellow line

• 🔍 Boundary learned only because of polynomial features; without them, the model would fail

📁 Project Structure

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logistic-regression-polynomial/
 ┣ logistic_diagnosis.py     # Main model code
 ┣ README.md                 # GitHub readme

💻 How to Run the Code

1. Clone the repository:

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git clone https://github.com/your-username/logistic-regression-polynomial
cd logistic-regression-polynomial

2. Install required libraries:

bash
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pip install numpy matplotlib

3. Run the model:

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python logistic_diagnosis.py

You’ll see both the original dataset and the decision boundary plotted.

💬 Conclusion

This project demonstrates how basic algorithms, when combined with feature engineering (like polynomial expansion), can solve non-linear classification problems — just like a real-world medical diagnosis system might require. Everything was implemented from scratch, without relying on any machine learning libraries like Scikit-learn or TensorFlow.

💡 What’s Next?

• Add L2 regularization to prevent overfitting

• Try degree 3 or 4 polynomials

• Build a web interface (Flask/Streamlit) to test predictions

• Test on real-world healthcare datasets

📍 Introduction

Have you ever wondered how businesses can predict their profits based on the population of a city? Using Supervised Learning, specifically Linear Regression, we can build a simple yet powerful model that learns from past data and makes predictions for future inputs. 🚀

In this blog, I’ll walk you through a project where a Linear Regression model was trained on a dataset of city populations and their corresponding profits. The goal? To predict future profits for a business by simply inputting the population of a new city.

📂 Dataset

The dataset consists of 100 samples, each containing:

• Population (in 10,000s)

• Profit (in $10,000s)

Here’s a glimpse of the data:

This data follows a linear trend with some noise — perfect for a supervised learning task.

🔧 Model Training

Using Python, NumPy, and a bit of linear algebra, I trained a Linear Regression model with the following steps:

1. Data Loading: The CSV file is loaded using pandas.

2. Model Initialization: Parameters w (weight) and b (bias) are initialized.

3. Cost Function: The Mean Squared Error (MSE) is calculated to evaluate predictions.

4. Gradient Descent: The parameters are updated iteratively to minimize the cost.

5. Prediction: Once trained, the model predicts profits based on new population values.

💻 Try It Yourself

You can view the full source code, dataset, training logic, and prediction demo here:

👉 🔗 GitHub Repository: Machine Learning Profit-Population Model

Feel free to clone the repo, run the notebook, and experiment with your own population values.

📈 Sample Prediction

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population = 7.5  # in 10,000s
predicted_profit = w * population + b
print(f"Predicted profit: ${predicted_profit * 10000:.2f}")

When entering a population of 75,000, the model might predict a profit of around $125,000, depending on the final trained weights.

📚 Conclusion

This project is a classic example of Supervised Learning — training a model on labeled data to predict outcomes. It demonstrates how a simple linear model can help businesses make data-driven decisions.

If you're a beginner in machine learning or data science, this is a perfect project to understand the fundamentals of:

• Data preprocessing

• Gradient descent

• Cost function optimization

• Real-world applications of ML

💬 Got questions or want to collaborate? Drop a comment on GitHub or connect with me on LinkedIn!

Happy Learning! 🤖💡

Introduction

Have you ever dreamed of creating a website that not only looks great but also functions as a real service? That’s exactly what I did with Travellix, my own travel booking platform. With the help of AI and my web development skills, I’ve created a website where users can explore travel packages, book trips, write reviews, and manage their bookings—all in one place.

This blog post shares how I built it, the features I added, the challenges I faced, and how it works behind the scenes.

🌐 Features of Travellix

Travellix is designed to be simple yet powerful. Here’s what it offers:

✅ Dynamic Travel Packages – Pulled directly from the database so every update is reflected instantly on the website.
✅ Secure Booking System – Users can fill out a booking form to confirm their trips.
✅ Review System – Visitors can leave reviews, which are displayed on the website in real-time.
✅ User Authentication – Includes Login, Sign Up, and Logout features for a personalized experience.
✅ Responsive Multi-Page Website – Fully functional pages: Home, Booking, Contact Us, Reviews, Login, and Sign Up.

🛠️ Tech Stack Used

• Frontend: HTML5, CSS3, JavaScript

• Backend: PHP

• Database: MySQL

• Tools: VS Code, XAMPP, phpMyAdmin

🔗 How the Website Works (Backend Overview)

The website dynamically fetches travel packages from the MySQL database. Whenever a new package is added in the database, it instantly appears on the homepage.

🔧 Example Code to Fetch Packages:

php
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<?php
include 'connection.php';
$query = "SELECT * FROM packages";
$result = mysqli_query($conn, $query);
while($row = mysqli_fetch_assoc($result)){
    echo "<div class='package'>";
    echo "<h2>".$row['destination']."</h2>";
    echo "<p>".$row['description']."</p>";
    echo "<p>Price: ".$row['price']."</p>";
    echo "</div>";
}
?>

📝 Review Submission Feature:

Users can submit their travel experiences, and these reviews are stored in the database. On the same Reviews page, all submitted reviews are displayed dynamically.

🔒 Authentication Feature:

The Sign Up and Login pages are designed to securely handle user information. Only logged-in users can make bookings or submit reviews.

📑 Booking Form Functionality:

• Users select a destination, enter their details (name, date, contact info), and submit the form.

• Data is stored in the bookings table in the database.

🔗 Sample Booking Form Code Snippet:

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<form action="booking.php" method="POST">
  <input type="text" name="name" placeholder="Your Name" required>
  <input type="email" name="email" placeholder="Email" required>
  <select name="destination">
    <option value="Maldives">Maldives</option>
    <option value="Dubai">Dubai</option>
    <!-- Add more destinations -->
  </select>
  <input type="date" name="travel_date" required>
  <button type="submit">Book Now</button>
</form>

⚙️ Database Structure:

The website is powered by a MySQL database that contains several key tables:

• packages – Stores destination info, description, and price.

• users – Stores user login details.

• reviews – Stores customer reviews.

• bookings – Stores booking details.

❗ Challenges I Faced:

• Setting up the connection between PHP and MySQL.

• Handling form validations and data security.

• Making the website responsive across devices.

• Designing a clean UI/UX that’s easy for users to navigate.

🌟 What I Learned:

Building Travellix improved my skills in:

• Frontend and backend integration.

• Database handling.

• Managing user sessions and authentication.

• Real-world project deployment structure.

🚀 Conclusion

Travellix isn’t just a project—it's a reflection of my growth as a developer. It shows how a simple idea, with dedication and the right tools, can turn into a fully functional product.

If you’re interested in seeing it in action, visit the website and explore the travel packages. You can even try booking a package or leaving a review to test how it works!

👉 Comment below your thoughts or suggestions. If you want the full code or step-by-step tutorial, let me know in the comments or contact me directly!