Implement DBSCAN (Density-Based Spatial Clustering)

[noahgift]

Problem Statement

DBSCAN is a powerful density-based clustering algorithm that can find arbitrarily-shaped clusters and identify outliers. Currently missing from aprender.

Advantages over K-Means:

• No need to specify number of clusters
• Finds arbitrarily-shaped clusters
• Identifies outliers as noise points
• Robust to different cluster densities

Proposed Solution

Implement DBSCAN following sklearn API with EXTREME TDD methodology.

Algorithm

Core Concepts:

• eps: Maximum distance between two samples to be neighbors
• min_samples: Minimum points to form a dense region
• Core point: Has ≥ min_samples within eps distance
• Border point: Within eps of core point, but not core itself
• Noise point: Neither core nor border

Steps:

1. For each unvisited point p:
   • Find all points within eps distance (neighbors)
   • If neighbors < min_samples: mark as noise
   • Else: create new cluster, expand from p
2. Expand cluster: recursively add reachable core points

Implementation

Trait: UnsupervisedEstimator

API Design:

pub struct DBSCAN {
    eps: f32,
    min_samples: usize,
    labels: Option<Vec<i32>>,  // -1 for noise, 0+ for cluster ID
}

impl UnsupervisedEstimator for DBSCAN {
    type Labels = Vec<i32>;
    fn fit(&mut self, x: &Matrix<f32>) -> Result<(), &'static str>;
    fn predict(&self, x: &Matrix<f32>) -> Vec<i32>;
}

Success Criteria

• ✅ DBSCAN struct with UnsupervisedEstimator trait
• ✅ eps and min_samples parameters
• ✅ Noise detection (label = -1)
• ✅ 12+ tests passing
• ✅ Zero clippy warnings
• ✅ Example: examples/dbscan_clustering.rs

Estimated Effort

Timeline: 2-3 days
Complexity: Medium-High (spatial indexing for performance)

[noahgift]

✅ DBSCAN implementation complete with:

• Core algorithm with region query and cluster expansion
• 12 comprehensive tests (all 560 tests passing)
• Full example demonstrating parameter effects and K-Means comparison
• Complete case study book chapter documenting EXTREME TDD process
• Zero clippy warnings, all quality gates passing

Commits: 01cbefe, 10c5aa7