# ============================================================================
# T12 — Clustering algorithm comparison on synthetic geometric datasets
# ----------------------------------------------------------------------------
# Unlike paper_replication's P01-P07, the "synthesis" here frames a research
# QUESTION rather than a known paper's method. The model must design the
# experiment (conditions, metrics, datasets) — we only commit to what a
# competent study of this topic would include and what the rubric expects.
# ============================================================================

id: ML12
title: "Comparing clustering algorithms on synthetic non-convex and anisotropic shapes"
arxiv_id: null
venue: "ARC-Bench 2026"
paper_asset: null

# The "synthesis" plays the role of the upstream briefing: research question,
# background, why the question matters, what "a reasonable experiment" looks
# like. It deliberately does NOT pre-specify a single method to reproduce.
synthesis: |
  Clustering algorithms encode very different geometric assumptions. K-means
  prefers spherical, equal-variance groups; agglomerative clustering can adapt
  to hierarchical structure depending on linkage; DBSCAN finds dense regions
  and can recover non-convex shapes while labeling outliers as noise; spectral
  clustering can separate manifolds when graph affinity is appropriate.
  Because these assumptions interact strongly with data geometry, a single
  benchmark score often hides systematic failure modes.

  Synthetic datasets are ideal for a fast but meaningful comparison because we
  can generate known structures with ground-truth labels: intertwined moons,
  concentric circles, and anisotropic Gaussian blobs. These patterns expose
  strengths and weaknesses that are difficult to isolate in real-world data.
  With labeled synthetic data, external clustering metrics like adjusted rand
  index (ARI) and normalized mutual information (NMI) directly quantify
  partition recovery quality.

  A credible CPU-scale study should compare several algorithms under a shared
  protocol: standardized inputs, fixed train-size generation per seed, and
  explicit handling of methods that output noise labels. It should include at
  least one centroid baseline (k-means) and one density method (DBSCAN), then
  test whether non-linear methods systematically outperform centroid methods on
  non-convex shapes while avoiding large regressions on anisotropic blobs.

  The practical goal is not to crown one universally best algorithm, but to
  establish data-shape-dependent guidance. If shape complexity changes which
  method wins, practitioners should choose clustering tools by geometric prior
  rather than habit.

  *How strongly does dataset geometry (non-convex vs anisotropic) determine which clustering algorithm achieves the best ground-truth agreement under a fixed CPU-budget protocol?*

hypotheses:
  - id: H1
    statement: "On the two non-convex datasets (moons and circles), at least one of {DBSCAN, SpectralClustering} achieves mean ARI that is at least 0.15 higher than k-means, averaged over ≥5 seeds."
    measurable: true
  - id: H2
    statement: "On the anisotropic-blobs dataset, agglomerative clustering (ward linkage) achieves ARI greater than or equal to k-means in the seed-averaged result (difference >= 0.00)."
    measurable: true
  - id: H3
    statement: "No single algorithm ranks first in ARI on all evaluated datasets; i.e., the best-ARI method differs on at least one dataset from the global winner."
    measurable: true

experiment_design:
  research_question: "How strongly does dataset geometry (non-convex vs anisotropic) determine which clustering algorithm achieves the best agreement with ground-truth labels under a fixed CPU-budget protocol?"
  conditions:
    - name: "kmeans_k2_or_k3"
      description: "KMeans baseline with n_clusters set to dataset ground-truth class count; n_init>=10."
    - name: "agglomerative_ward"
      description: "AgglomerativeClustering with ward linkage and n_clusters equal to ground-truth class count."
    - name: "dbscan_tuned_eps"
      description: "DBSCAN with eps selected from a small grid per dataset (e.g., 0.1 to 0.5) and fixed min_samples (e.g., 5)."
    - name: "spectral_rbf"
      description: "SpectralClustering with RBF affinity and n_clusters equal to ground-truth class count."
  baselines:
    - "kmeans_k2_or_k3 as centroid-based baseline"
    - "agglomerative_ward as hierarchical baseline"
  metrics:
    - name: "adjusted_rand_score"
      direction: "maximize"
      description: "Adjusted Rand Index against ground-truth labels, averaged over seeds."
    - name: "normalized_mutual_info"
      direction: "maximize"
      description: "Normalized Mutual Information against ground-truth labels."
    - name: "silhouette_score"
      direction: "maximize"
      description: "Internal cohesion/separation score computed from predicted labels (excluding noise-only failures)."
  datasets:
    - name: "moons"
      source: "sklearn.datasets.make_moons (n_samples~800, noise~0.08)"
    - name: "circles"
      source: "sklearn.datasets.make_circles (n_samples~800, noise~0.06, factor~0.5)"
    - name: "anisotropic_blobs"
      source: "sklearn.datasets.make_blobs followed by linear transformation to create anisotropy"
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 420

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML12.json"