Unsupervised Learning

Learning patterns or structure in data without labeled outcomes.

Grouping observations so that points within a group are more similar to each other than to those in other groups.

An algorithm that partitions data into \(k\) clusters by assigning observations to the nearest centroid.

• Clusters are roughly spherical
• Clusters are of similar size
• Distance is measured using Euclidean distance

• \(k\): number of clusters
• Initialization method: starting centroid locations
• Max iterations / tolerance: convergence control
• Elbow method: choose \(k\) where additional clusters give diminishing reductions in within-cluster variance

A density-based clustering algorithm that groups points based on local point density and labels low-density points as noise.

• Clusters are defined by regions of high density
• A distance metric meaningfully defines neighborhoods
• Density is reasonably consistent within clusters

• \(\varepsilon\) (epsilon): neighborhood radius
• minPts: minimum number of points required to form a dense region

DBSCAN forms clusters by expanding from dense core points.

• Choose a distance metric (Euclidean by default).
• For each point, count neighbors within distance \(\varepsilon\).
• Label points as:
  • Core points: at least minPts neighbors
  • Border points: reachable from a core point
  • Noise points: not reachable from any core point
• Connect density-reachable core points to form clusters.

A linear technique that finds orthogonal directions (eigenvectors) of the data’s covariance matrix and projects the original data onto those directions to reduce dimensionality.

• Relationships are approximately linear
• Variance captures meaningful structure
• Features are on comparable scales (or standardized)

• Number of components retained
• Covariance vs correlation matrix
• Explained variance threshold