Gene Expression Analysis: PCA and Sparse PCA and Classification

Overview

This project applies dimensionality reduction (PCA) and classification techniques to a gene expression dataset from the ALL/AML (Acute Lymphoblastic Leukemia / Acute Myeloid Leukemia) dataset. The goal was to identify key genes and reduce the high-dimensional data (7,129 genes expressions).

Dataset

• Training samples: 38 patients (27 ALL, 11 AML)
• Gene features: 7,129 expression values per sample

Methods

1. Principal Component Analysis (PCA)

A PCA was applied to identify principal components.

• PCA (38 components): ~95% of variance explained by first 30 components
• First 5 components: ~52% explained variance
• First 3 components: ~39% explained variance

Finding: Most variation is concentrated in early principal components.

2. Sparse PCA

L1 regularization to enforce feature selection:

• 3 components: 42.1% sparsity, 30.0% explained variance
• 5 components: 50.2% sparsity, 36.9% explained variance
• 10 components: 60.5% sparsity, 47.9% explained variance

Finding: Sparsity increases with more components. Trade off between interpretability and explained variance.

3. Sparse Logistic Regression

L1-regularized logistic regression to identify a small set of genes for classification:

• Selected genes: 3 features (out of 7,129)
• Training accuracy: 71.1% accuracy on a 5-Fold Cross-Validation
• ROC-AUC: Computed both on training and CV folds
• Convergence: Achieved at 2,546 iterations (max: 10,000)

Files Included

• sparse_pca.ipynb: Complete PCA and Sparse PCA analysis with all visualizations and improvements
• sparse_logreg.ipynb: L1-regularized logistic regression with cross-validation, evaluation metrics, and ROC curves