This repository documents an academic project focusing on the classification of pulsar candidates from astronomical survey data. The goal is to differentiate true pulsars from spurious signals (Radio Frequency Interference/Noise).

The objective is to accurately perform binary classification on highly imbalanced astronomical data. The methodology includes:

1. Z-Normalization: All eight input features are standardized to handle differing scales, means, and variances.
2. Comparative Modeling: A wide range of statistical and machine learning classifiers were implemented and rigorously tested.
3. Cost-Sensitive Evaluation: The models are evaluated primarily using the Minimum Detection Cost Function (minDCF) across various effective prior probabilities (π), recognizing the high cost associated with missing a true, rare pulsar (a false negative).

The project uses the HTRU2 dataset, which contains statistical features derived from pulsar candidates collected during the High Time Resolution Universe Survey.

The dataset is highly imbalanced, with 16,259 spurious examples (RFI/noise) and 1,639 real pulsar examples.

The following models were developed and analyzed for their performance, particularly focusing on their efficacy in low-prior conditions (π=0.1):

1. Multi-Variate Gaussian (MVG) Classifiers: Tested various covariance types, including the robust Tied Full Covariance model.
2. Linear Logistic Regression (LR): Implemented with different regularization strengths (λ) to control model complexity and overfitting.
3. Support Vector Machines (SVM): Utilized a Linear Kernel with balancing techniques and hyperparameter tuning (C) to handle the skewed dataset.
4. Gaussian Mixture Models (GMM): Explored models with complex structures (e.g., Full Covariance with 8 components) to capture non-linear class boundaries.

The analysis successfully identified the most effective classifiers for minimizing the detection cost in a rare-event search scenario.

• Overall Best Performance: Linear SVM with C=0 (balanced) and GMM Full Covariance (8 components) consistently achieved the lowest Minimum Detection Cost across all tested prior probabilities, demonstrating superior robustness and accuracy for this challenging, imbalanced dataset.

• Language: Python 3.x
• Core Libraries: numpy, pandas, matplotlib

A complete explanation of the mathematical models, parameter choices, experimental procedures, and conclusions is available in the project's presentation:
pulsar.pdf

This is a completed academic project; however, feedback on the methodology or analysis is welcome.
Project by Gabriele Cassetta