This repository contains a comprehensive academic benchmark of Unsupervised Machine Learning algorithms. The primary objective is to analyze, project, and cluster high-dimensional data, rigorously comparing the mathematical behavior, inductive biases, and geometric limitations of various models against known (but completely hidden during inference) ground-truth topologies.
The benchmark is conducted on two distinct vector spaces to test algorithm robustness across different spatial topologies:
- Real Dataset: 333 patterns, 5 continuous physical variables. Highly linear topology with dense, well-separated convex clusters.
- Synthetic Dataset: 360 patterns, 4 continuous variables. Characterized by complex, non-linear manifolds.
Note on Pre-processing: Both datasets undergo rigorous Z-score standardization (
$z = \frac{x - \\mu}{\\sigma}$ ) to ensure distance-based metrics (like Euclidean distance) and variance maximization algorithms operate without magnitude bias.
- Role: Linear dimensionality reduction and variance analysis.
- Findings: Successfully captured ~85% of variance in the Real dataset within 2 components, yielding highly separable clusters. However, it suffered a catastrophic information loss (~55% variance retained) on the Synthetic dataset, empirically proving the presence of non-linear structures.
- Role: Non-linear manifold learning and local topology preservation.
- Findings: A grid search over the
perplexityhyperparameter successfully "unrolled" the complex geometries of the Synthetic dataset (revealing concentric rings and sine waves) that PCA had collapsed, proving its superiority for non-linear data visualization.
- Role: Centroid-based, isotropic clustering.
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Evaluation: Extrinsic validation using the Adjusted Rand Index (ARI) across a search space of
$K \in [2, 8]$ . - Findings: K-Means achieved strong results on the convex Real dataset (ARI ~0.64). However, due to its inductive bias assuming spherical clusters, it failed entirely on the Synthetic dataset (ARI < 0.3), arbitrarily fracturing continuous non-linear manifolds.
- Planned: UPGMA and Complete Linkage dendrogram construction using Euclidean distance matrices.
- Planned: Neural network-based non-linear projections and topological mapping via U-matrices.
This project is developed to run consistently inside an isolated Docker container environment to guarantee eproducibility.
python >= 3.11.6numpypandasscikit-learnmatplotlibseaborn