Problem Statement

Spectral Clustering uses graph theory and eigenvalue decomposition to find clusters in non-convex shapes. Currently missing from aprender.

Advantages over K-Means:

• Handles non-convex clusters
• Based on graph connectivity
• Works with similarity matrices
• Captures manifold structure

Use Cases:

• Image segmentation
• Community detection in networks
• Clustering on graphs
• Non-linear cluster shapes

Proposed Solution

Implement Spectral Clustering following sklearn API with EXTREME TDD.

Algorithm

Steps:

1. Construct similarity graph (k-NN or ε-neighborhood)
2. Build affinity matrix W (Gaussian similarity)
3. Compute graph Laplacian: L = D - W
4. Eigendecomposition: find k smallest eigenvectors
5. Cluster in eigenspace using K-Means

Implementation

Trait: UnsupervisedEstimator

API Design:

pub struct SpectralClustering {
    n_clusters: usize,
    affinity: Affinity,  // RBF, KNN, Precomputed
    gamma: f32,          // Kernel coefficient for RBF
    labels: Option<Vec<usize>>,
}

pub enum Affinity {
    RBF,           // Gaussian kernel
    KNN,           // k-nearest neighbors
    Precomputed,   // User-provided affinity matrix
}

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

Success Criteria

• ✅ SpectralClustering with graph Laplacian
• ✅ Multiple affinity types (RBF, KNN)
• ✅ Eigenvalue solver integration
• ✅ 12+ tests (including non-convex shapes)
• ✅ Zero clippy warnings
• ✅ Example: examples/spectral_clustering.rs

Estimated Effort

Timeline: 4-5 days
Complexity: High (eigendecomposition, graph construction)