Flatten, Then Find Density

DBSCAN struggles in 13 dimensions, where everything is far from everything. Squash the wine data with PCA first and try again.

Task: write density_groups(n_components, eps, min_samples).

• Load load_wine(return_X_y=True, as_frame=True) and scale the 13 columns with StandardScaler().fit_transform(X).
• Reduce them with PCA(n_components=n_components).fit_transform(...).
• Fit DBSCAN(eps=eps, min_samples=min_samples) on the reduced data.
• Return a dict:
  • "sizes": the number of wines in each cluster, sorted from largest to smallest, with noise left out
  • "noise": how many wines were labelled -1
  • "match": adjusted_rand_score(y, labels) with the labels exactly as DBSCAN gave them, as a plain float rounded to 3 decimal places

If every wine is noise, "sizes" is an empty list.