Problem Statement

LOF (Local Outlier Factor) detects anomalies based on local density deviation. Unlike global methods, it finds outliers in varying density regions. Currently missing from aprender.

Advantages:

• Detects local outliers (not just global)
• Works with varying density clusters
• No global threshold needed
• Intuitive score interpretation

Use Cases:

• Fraud detection in transactions
• Network intrusion detection
• Sensor anomaly detection
• Quality control with varying densities

Proposed Solution

Implement LOF following sklearn API with EXTREME TDD.

Algorithm

Core Idea: Compare local density to neighbors' densities

Steps:

1. For each point p:
   • Find k-nearest neighbors
   • Compute reachability distance
   • Compute local reachability density (LRD)
2. Compute LOF score:
   • LOF(p) = avg(LRD(neighbor)) / LRD(p)
   • LOF ≈ 1: similar density to neighbors (normal)
   • LOF >> 1: lower density than neighbors (outlier)

Implementation

API Design:

pub struct LocalOutlierFactor {
    n_neighbors: usize,
    contamination: f32,  // Expected proportion of outliers
    lof_scores: Option<Vec<f32>>,
}

impl LocalOutlierFactor {
    pub fn fit(&mut self, x: &Matrix<f32>) -> Result<(), &'static str>;
    pub fn predict(&self, x: &Matrix<f32>) -> Vec<i32>;  // 1=normal, -1=anomaly
    pub fn score_samples(&self, x: &Matrix<f32>) -> Vec<f32>;  // LOF scores
    pub fn negative_outlier_factor(&self) -> &[f32];  // Opposite of LOF
}

Success Criteria

• ✅ LOF with k-NN and reachability distance
• ✅ fit/predict/score_samples methods
• ✅ contamination parameter for threshold
• ✅ 12+ tests (including varying density clusters)
• ✅ Zero clippy warnings
• ✅ Example: examples/lof_anomaly.rs

Estimated Effort

Timeline: 3-4 days
Complexity: Medium (k-NN search, density calculation)