Editing Unsupervised Clustering (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Unsupervised learning discovers '''inherent structure''' in data. The key challenge: without labels, how do we know if the discovered structure is meaningful? This is the fundamental evaluation problem of unsupervised learning.

'''K-means''' is the simplest and most widely used clustering algorithm. Initialize K cluster centers (randomly or with K-means++). Assign each point to the nearest center. Recompute centers as the mean of assigned points. Repeat until convergence. Pros: simple, fast. Cons: assumes spherical clusters of equal size, requires K to be specified, sensitive to initialization.

'''DBSCAN''' doesn't require K, can find clusters of arbitrary shape, and identifies outliers as noise points not belonging to any cluster. Works by: a "core" point has ≥ MinPts neighbors within radius ε; reachable points form a cluster; unreachable points are noise. Critical for applications where cluster number and shape are unknown.

'''Dimensionality reduction''' is essential before clustering in high-dimensional spaces (the curse of dimensionality makes all points equidistant). PCA gives a linear compression preserving maximum variance. t-SNE/UMAP give non-linear compressions suited for visualization. Autoencoders give deep non-linear compressions suited for representation learning.

'''The curse of dimensionality''': In high-dimensional spaces, data becomes increasingly sparse and the notion of "nearest neighbor" breaks down — all points become equidistant. K-means fails above ~20 dimensions without dimensionality reduction. This motivates learning compact representations before clustering.
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