High-Dimensional Breast Cancer Diagnostics from Scratch

An end-to-end framework implementing supervised learning classifiers, orthogonal dimension reductions (PCA via SVD), and multi-solver optimization architectures completely from scratch using vectorized NumPy mathematics.

🚀 Key Performance Benchmarks

Model Identifier	Accuracy	F1-Score	Type
LogReg_gd_fixed	98.23%	97.62%	Scratch Model
LogReg_PCA10	98.23%	97.62%	Scratch + PCA
SVM_rbf	98.23%	97.56%	scikit-learn Baseline
LinReg_normal	94.69%	92.50%	Closed-Form Scratch

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📊 Empirical Analysis & Visualization Grid

Model Artifact	Diagnostic Insights
	Clinical Risk Optimization: Retains an optimal recall profile by limiting critical diagnostic false negatives to exactly 1 missed instance out of 113 test samples.
	Multicollinearity Mapping: Visualizes the extreme structural dependency ($r \geq 0.95$) between cell metrics which challenges unregularized matrix inversions.
	Orthogonal Class Separation: Demonstrates distinct geometric class clustering along the first Principal Component (PC1) via SVD dimension reduction.
	Optimization Dynamics: Contrasts second-order curvature-aware Newton-Raphson solvers (immediate convergence) against iterative first-order routines.

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🛠️ Installation & Reproduction

1. Clone the repository:

   git clone [https://github.com/YOUR_USERNAME/week1-rls-breast-cancer.git](https://github.com/YOUR_USERNAME/week1-rls-breast-cancer.git)
   cd week1-rls-breast-cancer