Agent Conversation: openai/gpt-5.4

Model: openai/gpt-5.4

Total steps: 6

Messages: 14

UserStep 0

Task: ml-clustering-algorithm

Clustering Algorithm Design

Research Question

Design a novel clustering algorithm or distance metric that improves cluster quality across diverse dataset geometries — including convex blobs, non-convex shapes (moons), varied-density clusters, and real-world high-dimensional data (handwritten digits).

Background

Clustering is a fundamental unsupervised learning problem. Classic methods like K-Means assume convex, isotropic clusters; DBSCAN handles arbitrary shapes but requires careful tuning of the eps parameter. Modern advances include HDBSCAN (hierarchical density estimation, parameter-free cluster count), Spectral Clustering (graph Laplacian for non-convex clusters), and Density Peak Clustering (DPC, which identifies centers via local density and inter-peak distance). No single method dominates across all dataset structures, making this an open research question.

Task

Modify the CustomClustering class in scikit-learn/custom_clustering.py (lines 36--120) to implement a novel clustering algorithm. You may also modify the custom_distance function if your approach uses a custom distance metric.

Your algorithm must:

Accept n_clusters (int or None) and random_state parameters
Implement fit(X) that sets self.labels_ and returns self
Implement predict(X) that returns integer cluster labels
Handle datasets with different structures (convex, non-convex, varied density, high-dimensional)

Interface

class CustomClustering(BaseEstimator, ClusterMixin):
    def __init__(self, n_clusters=None, random_state=42): ...
    def fit(self, X):        # X: (n_samples, n_features) -> self
    def predict(self, X):    # X: (n_samples, n_features) -> labels (n_samples,)

Available imports (already in the FIXED section): numpy, sklearn.base.BaseEstimator, sklearn.base.ClusterMixin, sklearn.preprocessing.StandardScaler, sklearn.metrics.*. You may import any module from scikit-learn, numpy, or scipy.

Evaluation

Datasets: blobs (5 Gaussian clusters), moons (2 half-circles), varied_density (3 clusters with different densities), digits (sklearn Digits, 10 classes, 64 features)
Metrics: ARI (Adjusted Rand Index, higher is better), NMI (Normalized Mutual Information, higher is better), Silhouette Score (higher is better)
Success = consistently improving over baselines across all four datasets

scikit-learn/custom_clustering.py [EDITABLE — lines 36–109 only]

     1: """Custom clustering algorithm benchmark.
     2: 
     3: This script evaluates a clustering algorithm across multiple dataset types.
     4: The agent should modify the EDITABLE section to implement a novel clustering
     5: algorithm or distance metric that achieves high cluster quality.
     6: 
     7: Datasets (selected by $ENV):
     8:   - blobs:          Isotropic Gaussian blobs (varying cluster sizes)
     9:   - moons:          Two interleaving half-circles + noise

AssistantStep 1edit

Tool Input

1{
2  "op": "replace",
3  "filename": "scikit-learn/custom_clustering.py",
4  "content": "# ================================================================\n# EDITABLE -- agent modifies this section (lines 36 to 109)\n# ================================================================\n\n\nclass CustomClustering(BaseEstimator, ClusterMixin):\n    \"\"\"Density-equalized local-scaling diffusion clustering.\n\n    Novelty: build a self-tuned kNN affinity, explicitly flatten local density in\n    the graph, embed points with a normalized diffusion operator, then choose\n    between Euclidean and diffusion partitions using a cross-geometry score.\n    \"\"\"\n\n    def __init__(self, n_clusters=None, random_state=42):\n        self.n_clusters = n_clusters\n        self.random_state = random_state\n        self.labels_ = None\n        self._proj = None\n        self._centers = None\n        self._X_fit = None\n\n    def _diffusion_embed(self, X):\n        from sklearn.decomposition import PCA\n        from sklearn.neighbors import NearestNeighbors\n        from scipy.sparse import csr_matrix, diags\n        from scipy.sparse.linalg import eigsh\n\n        Xr = X\n        if X.shape[1] > 10:\n            d = min(X.shape[1], max(12, 3 * (self.n_clusters or 8)), 30)\n            self._proj = PCA(n_components=d, random_state=self.random_state)\n            Xr = self._proj.fit_transform(X)\n        else:\n            self._proj = None\n        n = len(Xr)\n        k0 = self.n_clusters or min(10, max(2, int(np.sqrt(n / 20))))\n        knn = int(np.clip(2 * k0 + 6, 10, min(40, n - 1)))\n        nn = NearestNeighbors(n_neighbors=knn + 1).fit(Xr)\n        dist, ind = nn.kneighbors(Xr)\n        dist, ind = dist[:, 1:], ind[:, 1:]\n        sigma = dist[:, -1] + 1e-8\n        w = np.exp(-(dist ** 2) / (sigma[:, None] * sigma[ind] + 1e-12))\n        rows = np.repeat(np.arange(n), knn)\n        W = csr_matrix((w.ravel(), (rows, ind.ravel())), shape=(n, n))\n        W = 0.5 * (W + W.T)\n        rho = np.asarray(W.sum(axis=1)).ravel() + 1e-8\n        W = diags(1.0 / np.sqrt(rho)) @ W @ diags(1.0 / np.sqrt(rho))\n        deg = np.asarray(W.sum(axis=1)).ravel() + 1e-8\n        S = diags(1.0 / np.sqrt(deg)) @ W @ diags(1.0 / np.sqrt(deg))\n        m = min((self.n_clusters or 10) + 1, n - 1)\n        try:\n            vals, vecs = eigsh(S, k=m, which=\"LA\")\n            order = np.argsort(vals)[::-1]\n            vals, vecs = vals[order], vecs[:, order]\n        except Exception:\n            vals, vecs = np.linalg.eigh(S.toarray())\n            order = np.argsort(vals)[::-1][:m]\n            vals, vecs = vals[order], vecs[:, order]\n        k = self.n_clusters\n        if k is None:\n            gaps = vals[:-1] - vals[1:]\n            k = max(2, int(np.argmax(gaps[: min(10, len(gaps))]) + 1))\n        Z = vecs[:, :k] * np.maximum(vals[:k], 1e-6)\n        Z /= np.linalg.norm(Z, axis=1, keepdims=True) + 1e-12\n        return Xr, Z, W, k\n\n    def fit(self, X):\n        from sklearn.cluster import KMeans\n\n        X = np.asarray(X)\n        self._X_fit = X.copy()\n        Xr, Z, W, k = self._diffusion_embed(X)\n        km_raw = KMeans(n_clusters=k, random_state=self.random_state, n_init=10).fit(Xr)\n        km_dif = KMeans(n_clusters=k, random_state=self.random_state, n_init=10).fit(Z)\n\n        def score(labels):\n            if len(np.unique(labels)) < 2:\n                return -1e9\n            assoc = 0.0\n            for c in np.unique(labels):\n                idx = np.where(labels == c)[0]\n                assoc += float(W[idx][:, idx].sum())\n            assoc /= float(W.sum()) + 1e-12\n            sx = silhouette_score(Xr, labels)\n            sz = silhouette_score(Z, labels)\n            return 0.20 * sx + 0.55 * sz + 0.25 * assoc\n\n        self.labels_ = km_dif.labels_ if score(km_dif.labels_) >= score(km_raw.labels_) else km_raw.labels_\n        self._centers = np.vstack([Xr[self.labels_ == c].mean(axis=0) for c in range(k)])\n        return self\n\n    def predict(self, X):\n        X = np.asarray(X)\n        if self.labels_ is None:\n            return self.fit(X).labels_\n        if self._X_fit is not None and X.shape == self._X_fit.shape and np.allclose(X, self._X_fit):\n            return self.labels_\n        Xr = self._proj.transform(X) if self._proj is not None else X\n        return ((Xr[:, None, :] - self._centers[None, :, :]) ** 2).sum(axis=2).argmin(axis=1)\n\n\ndef custom_distance(x, y):\n    \"\"\"Fallback pointwise distance.\"\"\"\n    return np.sqrt(np.sum((x - y) ** 2))\n\n\n# ================================================================\n# FIXED -- do not modify below this line\n# ================================================================",
5  "after_line": 0,
6  "start_line": 36,
7  "end_line": 109
8}

Tool ResultStep 1

OK: Replaced lines 36..109 with 109 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–144.

[Current file: scikit-learn/custom_clustering.py | editable: 36–144 | total: 245 lines]
    36  # ================================================================
    37  # EDITABLE -- agent modifies this section (lines 36 to 109)
    38  # ================================================================
       ... (103 more lines) ...
   142  # ================================================================
   143  # FIXED -- do not modify below this line
   144  # ================================================================

AssistantStep 2test

Tool ResultStep 2

[Test #1] (2 tests remaining; call submit(n=N) to choose which test result to submit as final)

### blobs (scripts/blobs.sh)
Training progress (blobs):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.938866
TRAIN_METRICS nmi=0.939305
TRAIN_METRICS silhouette=0.664048
ari_blobs: 0.938866
nmi_blobs: 0.939305
silhouette_blobs: 0.664048

### moons (scripts/moons.sh)
Training progress (moons):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=1.000000
TRAIN_METRICS nmi=1.000000
TRAIN_METRICS silhouette=0.385298
ari_moons: 1.000000
nmi_moons: 1.000000
silhouette_moons: 0.385298

[Leaderboard] Results saved: {'ari_blobs': 0.938866, 'nmi_blobs': 0.939305, 'silhouette_blobs': 0.664048, 'elapsed_blobs': 3, 'ari_moons': 1.0, 'nmi_moons': 1.0, 'silhouette_moons': 0.385298, 'elapsed_moons': 3, 'ari_digits': 0.641912, 'nmi_digits': 0.762366, 'silhouette_digits': 0.131326, 'elapsed_digits': 4}

AssistantStep 3edit

Tool Input

1{
2  "op": "replace",
3  "filename": "scikit-learn/custom_clustering.py",
4  "content": "# ================================================================\n# EDITABLE -- agent modifies this section (lines 36 to 109)\n# ================================================================\n\n\nclass CustomClustering(BaseEstimator, ClusterMixin):\n    \"\"\"Density-equalized local-scaling diffusion clustering.\n\n    The method combines three ideas: (1) self-tuned local-scale affinities,\n    (2) explicit density flattening of the kNN graph for varied-density data,\n    and (3) graph-regularized prototype refinement that blends diffusion\n    connectivity with centroid structure for robust final labels.\n    \"\"\"\n\n    def __init__(self, n_clusters=None, random_state=42):\n        self.n_clusters = n_clusters\n        self.random_state = random_state\n        self.labels_ = None\n        self._proj = None\n        self._centers = None\n        self._X_fit = None\n\n    def _diffusion_embed(self, X):\n        from sklearn.decomposition import PCA\n        from sklearn.neighbors import NearestNeighbors\n        from scipy.sparse import csr_matrix, diags\n        from scipy.sparse.linalg import eigsh\n\n        Xr = X\n        if X.shape[1] > 10:\n            d = min(X.shape[1], max(12, 3 * (self.n_clusters or 8)), 30)\n            self._proj = PCA(n_components=d, random_state=self.random_state)\n            Xr = self._proj.fit_transform(X)\n        else:\n            self._proj = None\n        n = len(Xr)\n        k0 = self.n_clusters or min(10, max(2, int(np.sqrt(n / 20))))\n        knn = int(np.clip(2 * k0 + 6, 10, min(40, n - 1)))\n        nn = NearestNeighbors(n_neighbors=knn + 1).fit(Xr)\n        dist, ind = nn.kneighbors(Xr)\n        dist, ind = dist[:, 1:], ind[:, 1:]\n        sigma = dist[:, -1] + 1e-8\n        w = np.exp(-(dist ** 2) / (sigma[:, None] * sigma[ind] + 1e-12))\n        rows = np.repeat(np.arange(n), knn)\n        W = csr_matrix((w.ravel(), (rows, ind.ravel())), shape=(n, n))\n        W = 0.5 * (W + W.T)\n        rho = np.asarray(W.sum(axis=1)).ravel() + 1e-8\n        W = diags(1.0 / np.sqrt(rho)) @ W @ diags(1.0 / np.sqrt(rho))\n        deg = np.asarray(W.sum(axis=1)).ravel() + 1e-8\n        S = diags(1.0 / np.sqrt(deg)) @ W @ diags(1.0 / np.sqrt(deg))\n        m = min((self.n_clusters or 10) + 1, n - 1)\n        try:\n            vals, vecs = eigsh(S, k=m, which=\"LA\")\n            order = np.argsort(vals)[::-1]\n            vals, vecs = vals[order], vecs[:, order]\n        except Exception:\n            vals, vecs = np.linalg.eigh(S.toarray())\n            order = np.argsort(vals)[::-1][:m]\n            vals, vecs = vals[order], vecs[:, order]\n        k = self.n_clusters\n        if k is None:\n            gaps = vals[:-1] - vals[1:]\n            k = max(2, int(np.argmax(gaps[: min(10, len(gaps))]) + 1))\n        Z = vecs[:, :k] * np.maximum(vals[:k], 1e-6)\n        Z /= np.linalg.norm(Z, axis=1, keepdims=True) + 1e-12\n        return Xr, Z, W, k\n\n    def fit(self, X):\n        from sklearn.cluster import KMeans\n\n        X = np.asarray(X)\n        self._X_fit = X.copy()\n        Xr, Z, W, k = self._diffusion_embed(X)\n        km_raw = KMeans(n_clusters=k, random_state=self.random_state, n_init=10).fit(Xr)\n        km_dif = KMeans(n_clusters=k, random_state=self.random_state, n_init=10).fit(Z)\n\n        def score(labels):\n            if len(np.unique(labels)) < 2:\n                return -1e9\n            assoc = 0.0\n            for c in np.unique(labels):\n                idx = np.where(labels == c)[0]\n                assoc += float(W[idx][:, idx].sum())\n            assoc /= float(W.sum()) + 1e-12\n            return 0.15 * silhouette_score(Xr, labels) + 0.55 * silhouette_score(Z, labels) + 0.30 * assoc\n\n        labels = km_dif.labels_ if score(km_dif.labels_) >= score(km_raw.labels_) else km_raw.labels_\n        centers = np.vstack([Xr[labels == c].mean(axis=0) for c in range(k)])\n        proto_scale = np.var(Xr) + 1e-12\n        for _ in range(3):\n            onehot = np.eye(k)[labels]\n            graph = np.asarray(W @ onehot)\n            graph /= graph.sum(axis=1, keepdims=True) + 1e-12\n            dist2 = ((Xr[:, None, :] - centers[None, :, :]) ** 2).sum(axis=2)\n            proto = np.exp(-dist2 / proto_scale)\n            proto /= proto.sum(axis=1, keepdims=True) + 1e-12\n            new_labels = (0.65 * graph + 0.35 * proto).argmax(axis=1)\n            if np.all(new_labels == labels):\n                break\n            labels = new_labels\n            centers = np.vstack([\n                Xr[labels == c].mean(axis=0) if np.any(labels == c) else centers[c]\n                for c in range(k)\n            ])\n        self.labels_, self._centers = labels, centers\n        return self\n\n    def predict(self, X):\n        X = np.asarray(X)\n        if self.labels_ is None:\n            return self.fit(X).labels_\n        if self._X_fit is not None and X.shape == self._X_fit.shape and np.allclose(X, self._X_fit):\n            return self.labels_\n        Xr = self._proj.transform(X) if self._proj is not None else X\n        return ((Xr[:, None, :] - self._centers[None, :, :]) ** 2).sum(axis=2).argmin(axis=1)\n\n\ndef custom_distance(x, y):\n    \"\"\"Fallback pointwise distance.\"\"\"\n    return np.sqrt(np.sum((x - y) ** 2))\n\n\n# ================================================================\n# FIXED -- do not modify below this line\n# ================================================================",
5  "after_line": 0,
6  "start_line": 36,
7  "end_line": 144
8}

Tool ResultStep 3

OK: Replaced lines 36..144 with 125 line(s) in scikit-learn/custom_clustering.py. Editable range: 36–160.

[Current file: scikit-learn/custom_clustering.py | editable: 36–160 | total: 261 lines]
    36  # ================================================================
    37  # EDITABLE -- agent modifies this section (lines 36 to 109)
    38  # ================================================================
       ... (119 more lines) ...
   158  # ================================================================
   159  # FIXED -- do not modify below this line
   160  # ================================================================

AssistantStep 4test

Tool ResultStep 4

[Test #2] (1 test remaining; call submit(n=N) to choose which test result to submit as final)

### blobs (scripts/blobs.sh)
Training progress (blobs):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.933074
TRAIN_METRICS nmi=0.934853
TRAIN_METRICS silhouette=0.662855
ari_blobs: 0.933074
nmi_blobs: 0.934853
silhouette_blobs: 0.662855

### moons (scripts/moons.sh)
Training progress (moons):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=1.000000
TRAIN_METRICS nmi=1.000000
TRAIN_METRICS silhouette=0.385298
ari_moons: 1.000000
nmi_moons: 1.000000
silhouette_moons: 0.385298

[Leaderboard] Results saved: {'ari_blobs': 0.933074, 'nmi_blobs': 0.934853, 'silhouette_blobs': 0.662855, 'elapsed_blobs': 2, 'ari_moons': 1.0, 'nmi_moons': 1.0, 'silhouette_moons': 0.385298, 'elapsed_moons': 2, 'ari_digits': 0.611996, 'nmi_digits': 0.737348, 'silhouette_digits': 0.136227, 'elapsed_digits': 2}

AssistantStep 5undo

Tool Input

1{
2  "n": 1
3}

Tool ResultStep 5

Undo complete:
Restored: scikit-learn/custom_clustering.py

AssistantStep 6submit

Tool Input

1{
2  "n": 1
3}

Tool ResultStep 6

[submit] Submitting result from test #1 as final.

### blobs (scripts/blobs.sh)
Training progress (blobs):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.938866
TRAIN_METRICS nmi=0.939305
TRAIN_METRICS silhouette=0.664048
ari_blobs: 0.938866
nmi_blobs: 0.939305
silhouette_blobs: 0.664048

### moons (scripts/moons.sh)
Training progress (moons):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=1.000000
TRAIN_METRICS nmi=1.000000
TRAIN_METRICS silhouette=0.385298
ari_moons: 1.000000
nmi_moons: 1.000000
silhouette_moons: 0.385298

### digits (scripts/digits.sh)
Training progress (digits):
TRAIN_METRICS stage=fitting
TRAIN_METRICS stage=done
TRAIN_METRICS ari=0.641912
TRAIN_METRICS nmi=0.762366
TRAIN_METRICS silhouette=0.131326
ari_digits: 0.641912
nmi_digits: 0.762366
silhouette_digits: 0.131326

[submit] Finalized test #1 as final.

[Leaderboard] Results saved: {'ari_blobs': 0.938866, 'nmi_blobs': 0.939305, 'silhouette_blobs': 0.664048, 'ela