Dimensionality reduction: PCA vs Isomap

What this project does

This small project compares a linear projection (Principal Component Analysis, PCA) with a nonlinear embedding (Isomap) on a documented teaching dataset. It evaluates what each method preserves by inspecting (1) reconstruction error where that is defined (PCA), (2) neighbourhood preservation (k-nearest neighbour overlap), and (3) downstream predictive quality when a simple classifier is trained on the reduced 2D representations. The goal is pedagogical: to show differences between linear and nonlinear dimensionality reduction and to measure how those differences affect simple tasks.

Data

I use the built-in scikit-learn wine dataset (load_wine). It has 13 numeric chemical measurements for three wine classes. The dataset is small and documented; no external downloads are needed. Features are standardised before applying dimensionality reduction.

How to build it

1. Prepare the data — load sklearn.datasets.load_wine and standardise features with sklearn.preprocessing.StandardScaler. Use a stratified train/test split with a fixed seed.
2. Build the experiment — fit PCA (2 components) and Isomap (2 components, n_neighbors=5) on the training set with fixed parameters and seeds where applicable.
3. Evaluate the result — for PCA compute reconstruction mean squared error on the test set (using inverse_transform); for both methods compute k-nearest-neighbour overlap (neighbourhood preservation) between high-dimensional and low-dimensional spaces; train a simple LogisticRegression classifier on original features and separately on each 2D embedding and evaluate held-out accuracy.
4. Define a reviewable output — return a small JSON-like dictionary with the numeric metrics and short text explaining what each metric means; this is printed when the module is run.

How to run

Run the module as a script: python project.py. It prints a JSON object with the metrics.

How to test

This repository includes pytest tests. Run: pytest -q. Tests check keys, sensible metric ranges, a conservative metric floor on PCA 2D accuracy, and determinism of the main metric when run with the same seed.

Results

Measured by running python project.py (seed 42) on 2026-10-23; the tests in test_project.py assert the floor.

Metric	Value
pca_recon_mse	0.4541
knn_overlap_pca	0.1649
knn_overlap_isomap	0.2116
acc_original	0.9815
acc_pca2d	0.9444
acc_isomap2d	0.8889

Also returned (see python project.py output): explanations (object).

Limitations

The wine dataset is small and low-dimensional (13 features); reducing to 2D is aggressive and loses information. Isomap is a manifold method that preserves local geodesic structure; PCA preserves global linear variance. The downstream classifier is a simple LogisticRegression — it is only an illustrative probe of utility, not a comprehensive benchmark. Neighbourhood overlap is a simple proxy for local structure preservation and has its own limitations.

Next steps

Extend to larger or higher-dimensional datasets (for example digits or custom data), try other nonlinear embeddings (e.g. t-SNE, UMAP), evaluate different classifiers, or measure other preservation criteria (trustworthiness, continuity, mutual information).

---

Full case study, build steps and evaluation checks: Dimensionality reduction techniques on networkershome.com

Built by Networkers Home · Learn the skills in the AI Engineer Course · Part of 100 AI projects with code