ML for Robotic Fabrication: Predicting the Hypotenuse

Overview

This project applies machine learning to Pythagoras’ theorem to predict the hypotenuse of a right-angle triangle given the lengths of its legs.

Dataset Description

• Features:
  • leg1: Length of the first leg (randomly generated between 1 and 100).
  • leg2: Length of the second leg (randomly generated between 1 and 100).
• Target:
  • hypotenuse: Computed using the formula ( \sqrt{leg1^2 + leg2^2} ).
• Generation: 1,000 samples are generated with random values to simulate right-angle triangles.

Model Details

• Model Used: Linear Regression
• Input Features: leg1 and leg2
• Target Variable: hypotenuse
• Rationale: Although the true relationship is non-linear, Linear Regression provides a simple baseline model for this regression task.

Evaluation Results

After splitting the dataset (80% training, 20% testing), the model was trained and evaluated. Below are the evaluation metrics:

• Mean Squared Error (MSE): [insert printed value]
• R² Score: [insert printed value]

Graphs:

1. Actual vs. Predicted Hypotenuse:
   A scatter plot showing the correlation between actual hypotenuse values and the model's predictions, with a red dashed line indicating the ideal prediction.

2. Residuals Histogram:
   A histogram of the residuals (difference between actual and predicted hypotenuse values) to inspect the error distribution.

Observations

• The model captures the trend of the hypotenuse well, but due to the inherent non-linearity of the square root function, the linear regression model has limitations.
• The error distribution (residuals) suggests that while most predictions are close to the actual values, there are systematic deviations that may be improved with non-linear models or feature engineering (e.g., including squared features).
• Future work could involve testing polynomial regression or more complex models such as neural networks to capture the non-linear behavior more accurately.

How to Run

1. Clone the repository.
2. Ensure that you have Python installed along with the required packages (numpy, pandas, scikit-learn, matplotlib).
3. Navigate to the src folder and run the pythagoras_ml.ipynb notebook in Jupyter Notebook.

Feel free to reach out if you have any questions or need further clarifications.